Oddly, the distance that seems to work well for long lever matches root 12 which matches the moment of inertia of a spinning rod *spinning from its end*. So it's as if we're matching the moment of inertia of just one side of the rod. That doesn't sit right with me though. Hmmm. The sponsor is Odoo: click here to try it for free www.odoo.com/r/aykZ
Doesn't the pivot point matter here? Doesn't it have to be able to handle the mass being pushed, regardless of the mass? It doesn't seem like the variable here is the mass or the force being applied by your finger. It's how the pivot point is anchored and how much mass it can take being applied to it, Doesn't it have to be able to take the forces applied to it in order to move the ball? Doesn't the lever have to deal with these forces on the point of contact with the pivot point? P.S - I'm a stupid person, so I apologize if none of that makes sense.
I'd like to point out that your lever isn't really pivoting around its center, but rather rolling on the thing you attached it to. I don't know how important that is, but it might partly account for the difference between the theory and practice. Also, wouldn't a horizontal lever on a vertical axle, with side by side lines of balls, be easier to fine tune? At least it wouldn't be affected by gravity.
'root 12 which matches the moment of inertia of a spinning rod *spinning from its end*.' is wrong, its (ML*2)/3, its (ML*2)/12 for a rod spinning about its centre. just wanted to let u know🤗
Possibly one of THE MOST important reason to do Science(TM) to things is to test things against our intuition. "Of course it works this way, it's obvious, it just makes intuitive sense!" is an extremely limiting and often wrong way to understand the world.
@@crawley6957 It's like that one student in every class student: "What if we do [thing] this way?" teacher: "Intuitively it doesn't work" student: "yeah but what happens if we do it anyways?"
and the other word isn't unintuitive or anti-intuitive or something you would think with a standard Latin prefix for no or the opposite. counter intuitive... it must be important that they really needed the word counter. because that's not what you would expect... lol
It beautifully shows me that had I signed up for 2 paid years of Brilliant, I would have been no further ahead in physics _intuition_ than when I started.
In high school like 22 years ago this dude, Peter F....... said exactly the same thing in a classroom discussion involving dynamics... The classic pendulum schwang, and then weather patterns and predictions, in a math class of all things! But we were all kinda taken aback when he said those words... "Why are we observing, and recording a static image of a dynamic system?" And our teacher made the point of being able to record a data point, but then acknowledging the need for changing the approach of teaching and studying dynamic everythings in her classrooms! When Mrs. Garrison told us to "just take a few minutes..." We knew some shit was changing her gray matter!
@@TheTechnopider lol yeah. the option for me to take dynamics (as an EE) was so nice for understanding when static forces are enough or i need to go a step further.
This topic comes up a lot in tennis rackets. There's a measurement called "swing weight" (unit is kg/m^2). It represents how hard it is to accelerate (swing) a racket rather than how hard to hold it still horizontally. Two rackets can have the same weight and balance point but different swing weights. The one with smaller mass near the tip will be harder to accelerate than the one with larger mass near the handle despite "mass x distance" being the same.
Wouldn't the one with smaller mass at the tip be the same one that had larger mass at the handle? What is the mass distribution that makes them different? I would think a larger mass at the tip would be harder to move (like how it's easier to balance something with the heavy part on top and the light part below because inertia makes the top part react more slowly to changes and you can readjust with the more responsive light bottom mass.
it’s also super important in any fencing/sword fighting sport, especially the ones using historical swords (i.e. not olympic fencing). The balance of the sword has a tremendous impact on how the sword handles, how fast it moves, how stable it is, how present in the bind it is, how much weight/power the strikes have. the balance is far more important than overall weight, and i’ve held 2 kg swords (quite heavy by sword standards) that feel lighter than 1.3 kg swords, simply because the poiof balance was closer to the hands.
That reminds me of this modern classic: Steve Smith identifying his bats blindfolded based on his impressive sense of the bat's inertia and weight. ua-cam.com/video/RaOCuDdBn90/v-deo.html
This video reminds me of the famous quote: “Aristotle said a bunch of stuff that was wrong. Galileo and Newton fixed things up. Then Einstein broke everything again. Now, we’ve basically got it all worked out, except for small stuff, big stuff, hot stuff, cold stuff, fast stuff, heavy stuff, dark stuff, turbulence, and the concept of time”.
Aristotle said some stuff that was spot on, too. He was pretty much wrong about all the science stuff, but some of his ideas about rhetoric and politics still hold true today.
@13donstalos This is not a criticism on Aristotle. Also, the quote does not say all of his stuff was wrong - only a bunch of them. Also-also, the quote is not meant to be taken seriously. :)
sounds like nonsense to me. just a bunch of words for a sake of words. for some sleeping minds "may sound cool" - the only purpose of this givberish. may also be used to impress girls of illegal age.
You may want to look up the term "reflected inertia". It explains why the inertia does not scale linearly with mechanical advantage, but quadratically. And actually, it can be generalized to reflected impedance, as all mechanical impedance scales quadratically with mechanical advantage. So this includes stiffness and damping. This is very important in gearboxes for instance. Also, the same principle has been used in theater equipment that makes you fly over the podium, to counteract gravity without adding much inertia.
@@dominicparker6124 I can imagine, lots of technical terms in there. I'd like to look at reflected inertia like this: In straight motions, inertia is also called mass. So let's talk about mass. Then, as we learn from Newton, mass defines the relation between force and acceleration (F=ma). So the mass you experience (the reflected mass) is all about how much acceleration you get, given a certain force you apply. Now the funny thing is that the force and acceleration go through the lever in different directions. Here is what I mean with that: Suppose you have a lever such that the actual mass is moving twice as fast as your hand. This means that the force on that mass is half of the force you apply. So the acceleration of that mass is half of F/m =0.5F/m. Next, this acceleration goes through the lever in the opposite direction. Accelerations are twice as low on the side of your hand. This means that the acceleration of your hand is half of 0.5F/m = 0.25F/m =F/(4m). The term 4m is what is called the reflected mass, or reflected inertia. Although the lever ratio is 1:2, the mass ratio is 1:4. With the same reasoning, quadratic relations can be found for stiffness (springs) and damping (viscous friction). I hope this clarifies the terms a bit.
So, as a civil engineering student (25 years ago), I took a lot of semesters of statics and dynamics and so on in uni. Apparently I remembered enough of them to scoff at your "black box" step and mutter "surely the inertia moments of the two systems is different so they behave differently in a dynamic system", but other than that I almost followed your logic as well. I think the intuition fail when discussing levers (and pulleys and inclined planes...) is that the way we're taught about them (at around 10-12 years old in most countries, I believe) is always in a static setup, and the intuition that's drilled into our brains is about their behaviour at equilibrium so we're always reaching for that intuition before thinking about conservation of energy. Not sure what a good framing would be to help shift the viewer intuition that dynamic problems behave differently than static ones. In uni I've been taught the virtual work principle to analyze dynamical equilibrium, not sure what a good explanation would look like. Unrelated, at some point you touch about how we perceive forces in a somewhat indirect way: I'd point out that 1kg feels WAY heavier if you hold it at an arms length so the brain is doing some sort of proxy measurement there to estimate the force (my engineer's brain would reach for the virtual work concept again, but maybe it's wrong).
greater difficulty moving the lever PROVED the half kg mass DID HAVE MORE KINETIC ENERGY, because the difficulty was in reversing the direction NOT in the initial movement. seriously, how can't people see the whole conclusion of this video is BACK TO FRONT ?
i'm pretty happy that i was suspicious of that black box step as well, even though I have never formally studied dynamics
9 днів тому+17
Yes, I was already skeptical at 4:20 when our host proclaimed that you couldn't tell the two systems apart. Exactly because kinetic energy grows quadratically with speed and impulse grows linearly, and the parts of the system in the box conserve both impulse and energy. (The fulcrum is outside the box.)
>Unrelated, at some point you touch about how we perceive forces in a somewhat indirect way: I'd point out that 1kg feels WAY heavier if you hold it at an arms length so the brain is doing some sort of proxy measurement there to estimate the force (my engineer's brain would reach for the virtual work concept again, but maybe it's wrong). >proxy measurement there to estimate the force intuitive thinking moment: your brain knows exactly how much force there is because that's what you sense, you then translate THAT into the weight of the object. "if X strain on muscle then Y weight" but X is dynamic and Y isn't, so we have to rely on heuristics to guess the weight, which is only as accurate as the amount of data points we have.
I program physics games and it was the same step I stopped at, "surely inertia plays a factor here, I mean think of a fly wheel and the distribution of mass"
Enjoyed how you showed your thought process, and the human psychology involved in this. Wanted to chime in. As an engineer who's worked satellite thruster micro balances in the past, I'd say the rolling and sliding pivot contact, changing pivot point vs lever angle, and nonlinear fishing line spring are all adding too many challenges into your setup. They sell mechanical spring flex pivots ideal for this application, taking away a significant number of problems. Wish you luck
Glad the fishing line stuck out to you too. My first instinct seeing that was to swap it with the heaviest gauge of steel wire he can twist like a twist tie with a pair of pliers so he can get a really firm contact. Increase that reaction speed drastically and reduce the distance the lever rolls around on that contact surface. Those spring pivots are really nice though... a lot better than kludging.
Flex, deflection from the linear motion "that it ought to have", multiple things that intuitively might seem negligible, but in the end might leave too much wiggle room. In this case quite literally, since it makes something in the system wiggle a bit.
When you said that the experiences were the same that immediately felt wrong to me. I've worked construction a decent amount and I knew instinctually that was wrong somehow. But I couldn't figure out why. This was such a cool video. I love how you take intuition and convert it into understanding.
yeah I had the same thing, the 'black box' thing seemed wrong and it felt like you'd need to push harder or whatever with the longer lever, but when he said it I just assumed he was right and my intuition was just due to the fact that all real levers have their own mass
If you've used levers in construction you have almost certainly used one hand as the fulcrum and the other hand on the end of the lever. You would absolutely have noticed the difference between holding the lever in the middle vs holding it near one end.
I think what changes about the black box experiement under gravity is not the amount of FORCE the exposed part of the lever applies, but its SPEED when the mass is in freefall. The half mass at double the distance will still fall, in its place along the lever, accelerating at the same rate as any size mass anywhere along the lever, but the further the mass, the less the lever will spin around the pivot point.
Same. I’ve worked with my hands for 25 years and I knew the feel should be different. I have learned that experience can fine tune your intuition for certain things. It’s why classroom learning cannot replace hands on experience. You need both. Using a pulley to lift something does make it easier for someone with less strength. But for someone stronger it feels like racing in first gear.
Great video Steve! I love the thought process through the whole video. A simple Newton's cradle already requires solving multiple differential equations simultaneously while making major assumptions like non-dispersive hertzian springs. So when you introduced a lever to the whole thing I knew it was going to get complicated :)
Not gonna lie, I’ve watch so many ActionLab shorts that seemed to relatable and dementedly unhinged that I had to ask myself how you got into this gig in the first place. And then you go busting out real sets of physics modeling concepts and show that you know what you’re talking about after all😂 This actually makes my level of trust in your work go up tremendously. Even if you were to mess something up, if a peer who saw the mistake were to point it out it looks like you’d not suffer from the Dunning-Krueger effect and thus be able to self-correct.
I love the fact that you have the humility to admit you don't fully understand something and reach out to someone else to help out, and you put it on UA-cam.
I think he understands these things very well; you have to in order to set up an experiment to illustrate a phenomenon. but if he came out all "I am smarter than you" he would have a very small audience. So he replicates his learning experiences so that you can learn. It's just that he's already learned it.
This helps me understand why playing a grand piano feels very different in touch to an upright. One of the main differences in the action is that grand pianos have much longer keys (the black and white bits on the outside look the same but the pivot point and total length of the leavers are much longer in the grand piano). So although the down weight (minimum weight to depress the key) and the up weight (maximum weight for ley to go up) can be similar, the levers mean a grand piano feels very different at playing speeds. There are many other differences in the mechanism that help a grand act faster and repeat faster too. But key length has an impact and I think it is similar to the experiment in this video with waggling different levers.
A pianist friend told me it's also to do with the orientation of the hammers, horizontal vs vertical.
9 днів тому+55
This whole thing reminded me why I like Lagrange's formalism so much: It's hard to reason about forces as soon as the system becomes even a little bit complex, but it's much easier to reason about kinetic and potential energy.
I understand levers. Once I asked my father what this thing was and where wanted me to put it. He said it was a leeverite. I asked him what's a leeverite. He said, Leeeverite there.
A perfect example of how anything non-linear (in this case the sqrt(2) factor when doubling the leverage and halfing the mass) can become quickly confusing in terms of physics intuition. Well illustrated and explained, well done all of you guys!
Non-linear systems are fascinating and wildly unintuitive. The way I've always described it to less math/physics inclined people is that non-linearity is like the eldritch gods of the math world. I've spent so much brain power on trying to rationalize how we're able to simplify and make such on point assumptions about physical systems to force them to act linear in specific scopes, despite the fact that reality seems to favor non-linearity.
double the power sent to a speaker and the cone's amplitude doubles but to us the perceived sound volume barely increases... our ears are non-linear transducers making all sorts of things counter intuitive. most volume control knobs use logarithmic potentiometers to account for this. a linear potentiometer (same resistance per degrees of turning) is not v useful for this as first few degrees of travel act almost like an on/off switch and the rest make no difference in loudness. *it takes about 10x the power to 'double the volume'
@@duroxkilo Out ears have the highest dynamic range of any of our senses. We can literally detect many orders of magnitude difference with out sense of hearing.
I think there is a relatively simple and intuitive explanation for this which is that the mechanical advantage of the lever "applies twice". If you halve the mass and double the distance, the mass will accelerate the same amount as it did originally for a given applied force. This makes sense intuitively. The end you are holding on to, however, will accelerate at half the rate of the mass itself due to the mechanical advantage of the lever. That means that it will feel harder to move the mass that is small and further out. Due to this effect, if you double the length of the lever the apparent mass will go up by 4x, but the apparent strength of gravity will go down by 2x leading to a total increase in force of 2x. If you also halve the mass, it will then feel 2x as heavy as it did before instead if 4x, meaning that the force is the same, but the mass is doubled.
As far as system improvements: The single biggest thing will be increasing the rigidity of your pivot. Holding the anchor in a rubber jaw vice clamped to the table provides lots of opportunity for flex and thus damping. That thing needs to be attached rigidly to something very heavy. I am picturing fixing your pivot bar into a concrete block or some such to give it a solid base. It is like with blacksmithing anvils. You want it heavy and rigidly connected to the floor so the hammer rebounds and all the energy goes into the work piece. The fishing line / rocker pivot design is fantastic; large radius line contact with little movement and no gap. I might glue some magnets to the sides to replace the fishing line, but you are not going to do better than that line contact with any small ball bearing or shaft pivot. It might also be worth trying to make a curved lever, something that looks a bit like a recurse bow pointing toward the balls so that the pivot is in line with the contact faces, that would also make it possible to balance so it is not trying to tip forward.
I mean for the longest time blacksmithing anvils were the slightly larger then a fist , you just need a good base and having a smaller anvil helps keeping the piece you're working on straight , even though it sounds counter intuitive . Anvils are supposed to bounce the force back into the work piece , so if you hame a hammer which is smaller then an anvil , the anvil will bounce the energy up into your work piece thus making it curve up, this often happens when you're drawing out a piece .
I really like the curved lever setup to make it balance without the extra piece of fishing line. The steel lever is HSS to attempt to match the hardness of the ball bearings approximately (and reduce losses from deforming the lever in impact). The cutting of which would probably involve a water jet cutter, which I didn't have access to, or a lot of grinding. My argument was that because the steel is so stiff and if you get it right the movement of the lever is so minute that change in forces from something much less stiff like a piece of fishing line will be negligible. Well it may have been motivated by the day or two grinding high speed steel that would otherwise have been involved...
Surely the mass if the pivot must be considered? The lever needs to be non-flexing as does the anvil. A curved pivot changes the angle of reaction from the anvil. How about a moving ball on a a thin pivot beam that rotates 180 from the top row to the bottom row? - hard to describe
I’m a high school student from Asia and a passionate physics enthusiast. Here are some of my humble thoughts: I view a lever as a converter of equal torque. On one end, it inputs a unit torque, and on the other end, it outputs the same unit torque. As for rotational speed, it’s analogous to pushing a 1 kg object and a 2 kg object over a distance of 1 meter using a force of 1 newton. Pushing the 2 kg object takes more time because performing the same amount of work does not imply the same power during the process.( In rotational motion, the moment of inertia corresponds to inertial mass in translational motion.)
Even with the incorrect assumptions made about the black box, you could still tell. You could push both lever ends down to the same distance, and let go at the same time. One will take longer to fall than the other. I think this is identical to your explanation but i'm not entirely sure.
That reminds me of another neat physics “paradox”. If you have a broom lying on the floor, and you lift the handle by a foot or two (keeping the head of the broom on the floor) and let it drop again, the end of the broomhandle falls faster than you expect from gravity. The reason is that the broomhandle’s centre of gravity accelerates at almost 1g, so the tip falls at almost 2g (minus losses due to rotational kinetic energy, and some sideways acceleration if the broomhead sticks in place on the floor). You can even attach a cup to the handle, hold a ball next to it at the same height, drop them at the same time, and have the cup catch the ball.
What's funny is, the black box thing didn't "seem" right to me, it seems like you'd need more force to push the lever or it would accelerate more slowly or something, but I ignored that because I thought I was just thinking about the mass of the lever since any lever you would use IRL would have mass.
You got me confused in the first half, good job! I was thinking for your lever, I'm thinking a U shape lever with ends of the U at the center of balls would transfer energy best. Or perhaps it is another source of confusion! either way, worth a try! [edit] of course for U to work, it should be much lighter than the balls otherwise the mass-energy equations may cause similar issues.
Don't understand the U shaped bit! Why not a dumbbell shaped lever where the balls at either end are the same as the balls in the cradle, and the bar between them, weightless.
The u shaped element may act as a waveguide to make an elastic wave turn around. This is similar to what happens with the water hammer effect where a pressure wave can travel through the pipe and turn around at the elbows
Agree with the U-shaped device to change the direction of the compression wave. It isn't exactly *motion* that is traveling; it is a pressure wave at the speed of sound in steel and the actual physical deformation is probably only some microns.
As a car guy, this video reminds me of gearing in vehicles. The lever with the large weight close to your hand is like being in a low gear, and the lever with the weight far from your hand is like being in a high gear. You push with the same force in both scenarios like the engine pushes the car forward with the same force, but the weight (or car) accelerates differently. I dont do maths well, but I imagine the gear ratios in a transmission get closer together in the higher gears because of the square root like you mentioned.
I thought about transmissions too. When dealing with them you have to remember that power in ideal transmission is constant between the input and the output. Only torque and speed change with gears in reverse relation.
It probably has to do with torque too. the slow gear spins slower but transmits more torque, which is better to overcome the initial inertia of the car and get it going, or to climb inclines (which naturally is done slower). the fast gear has more velocity but less torque since the car is already moving at a certain speed, so it there's less energy spent on accelerating it. I would probably take a large amount of time trying to prove this mathematically, but my intuition leads me to this, and it sort of matches what Steve (and Henry) said.
This is completely false. The only reason you have gears is because the engine itself can deliver much more power in a very narrow "engine turning speed". The gears are so that this ADDITIONAL FORCE THE ENGINE PROVIDES can be applied at different "tire turning speeds".
@@TheMarcQEngines are completely different. Tge transmission is there because the Engine itself gives more power when it turns at a specific speed. The transmission allows the engine to stay within this "ideal zone" throughout vastly different car speeds.
What Steve is missing is time. Applying 1N for 1meter ignores the time factor. Applying 1N of force for 1m on a 50ton ship will take hundreds, of years, if not more. Applying 1N for 1 meter on a inflatable matress will take just a few seconds. Did I exert the same amount of work?
I think the lever problem in this Newton-thingie could come from the point off rotation. In the two scenarios this point changes and in both the lever isn’t straight, it’s at an angle. That might be why the distances don’t mach up.
@@Giantcrabz At around 11:19, he brings up the idea of starting a business tricking investors into backing a free energy scheme, which would be fraud. He says he won't do it, but if he did, he would use the sponsor to do so. Advertising how suitable it is for doing crime seems a bit odd.
@@Giantcrabz Steve suggested that if he were to start soliciting investors for his free energy device, he would use the sponsor of the video, Odoo, to manage the process. However free energy devices are a scam due to the immutable laws of physics, which Steve knows full well, so his suggestion is of course a joke. He would never do that (but if he did... he would use Odoo)
I'm afraid Steve has it the wrong way around. Levers and pulleys and inclined planes aren't weird. It's *gravity* that's weird, specifically, the equivalence principle! The root of the intuition described at 14:00 is that the force needed to counter act gravity's effect on an object is directly proportional to its inertia against acceleration. That's a really strange and fundamental part of physics which comes out of General Relativity (or, rather, is an ingredient that goes into its construction). Furthermore this constant is almost the same everywhere on Earth and for all objects. This gives us the wrong idea that the force required to start something moving is a good guide for how quickly it will move afterwards - but that's actually only true for vertical motion in a familiar gravitational field. All the examples given of pulleys, levers and inclined plane simply decouple the force needed to keep something steady with it's effective inertia (ie, the amount of acceleration caused by a given excess force). The reason that people's minds jumped to rotational system is because the relevant inertia there, the moment of inertia, is different to the gravitational mass. But there's nothing intrinsically rotational about that, it's actually the _generic_ case for dynamical systems. In other words, our intuition about dynamics is built around the singular exception to the rule! Generally, the force keeping something stationary is completely unrelated to it's inertia against acceleration, it's only vertical motion where the only force is gravity where the two are linked.
I was going to mention the equivalence principle actually! I thought it might be a good explanation for my wonky intuition. But I talked about it with Henry quite a bit and came to the conclusion that it wasn't the core of the issue. But I don't know, your comment is making me think! Thanks!
@@SteveMould Glad I could contribute! I'd love to be a fly-on-the-wall for those kind of discussions. To write it mathematically, consider _F = m a_ where the force is an applied thrust T opposed to an environmental force _R_ . Rearranging it, we get that the acceleration is _a = (T - R) / m_ . Which shows that there are two parameters at play here, a minimum force _R_ to overcome, and then an _m_ that determines how much acceleration is produced by the net excess force. To determine two parameters you need both to see how hard you have to push the lever to hold it steady, and how much resistance there is to wiggling it. In the case of simply lifting something, we have _R = m g_ and the acceleration simplifies down to _a = T/m - g_ . This _g_ is not an unknown parameter, because we know intuitively what it is, so we are left with only 1 free variable: which means that knowing the force required to keep it steady *does* tell us something about how quickly it would accelerate to a net force.. So I don't think it's *just* the equivalence principle, but the equivalence principle plus our familiarity with local gravity. After all, if you were on the Moon holding something in your hand so it was steady, and then pushed up with double that force, it would accelerate up at only 1.6m/s^2, substantially slower than you'd expect! Obviously, the follow up video should be shot on the Moon to test this.
@@mattwis86 The pulley and inclined plane result in similar equations and of course follow the same laws of physics. But for the lever the moment of inertia is the more appropriate model. When you break down the moment of inertia model down to the infitisimal volume element and very small angles it is basically the same as the point masses on pulleys or inclined planes. Of course the rockets in space system once again is different because the mass is not fixed to the lever and the movement of the mass is not following the rotation of the lever.
This, but I think the number of people who know of moment of inertia is limited to the few who took first year core-physics or engineering-physics, +- some. A tiny % of people.
@@TimLF I'm pretty sure it was part of the mandatory high school physics here, but it was covered in the first physics course at the university as well.
You're so close to discovering gears and gear ratios. If you rotate multiple levers of the same length around the center and connect them together, you get a gear.
I remember you asking me about this and getting initially stumped, followed by getting math sniped to 5am ahah, fun to see this video finally getting out there!! the way I saw this problem, was that there seems to be a mixup between input force vs output force, and/or input displacement vs output displacement, and/or an assumption about time taken to apply the energy being the same, when it's actually not assuming we constrain input energy to 1J and output end lever displacement to 1m, and input side rod length to 1m, then I got these results: 1kg ball, output rod length 1m: 1J output kinetic energy after √2s at √2m/s 1/2kg ball, output rod length 2m: 1J output kinetic energy after 1s at 2m/s which means energy is preserved as expected!
It's something that falls out due to mechanical advantage, which itself comes from W=F*d, which comes from the kinetic energy formula, which comes from the 2nd law of motion (F=ma), by including displacement. F_effective=(force/advantage)=ma. 10N/1 = 1kg * a 10N/2 = 0.5kg * a 10N/1/(1kg) = a = 10 m / s^2 10N/2/(0.5kg) = a = 10 m / s^2 You can also tell they accelerate at the same rate, because it takes the equal force to accelerate them both against gravity at a static position (which requires them to have the same F=ma, meaning your finger must experience the same mass, meaning the effective force yada yada) final_v = a * t But here we're applying the force for a certain distance, based on the kinematic equation: d = (1/2)at^2 t = sqrt(2d/a) therefore, final_v=a*sqrt(2d/a), which simplifies to sqrt(2ad) fv_a = sqrt(2 * 10m/s^2 * 2m) fv_b = sqrt(2 * 10m/s^2 * 1m) the first two terms cancel when divided, and poof (fv_a/fv_b) = sqrt(2) drops out. Generalizing, you get fv_a/fv_b=sqrt(d_a/d_b) It is because of mechanical advantage, which doubles the distance and halves the force. The issue is that we're accelerating the objects at the same rate but one travels a longer distance. It actually makes perfect sense if you think about your "finger force" as accelerating the mass at 9.8m/s^2 upward in the stationary example, in both cases. And both are traveling 0 distance, which is why they feel the same. The moment (no pun intended) you implement distance(d) > 0, the final_v=a*sqrt(2d/a) comes into play. Technically net acceleration is also 0 in the static case
Saw the profile pic and initially thought it was Freya Holmér. But then I saw the @ and didn't recognize it, and thought, "Oh, someone is using her pic as a profile pic," which was a surprise; something I had not expected to see. But then I checked Freya's @ and it is Freya, so Freya IS in the comments. This was mental roller coaster ride. LOL
I don’t think you can do it without the lever black box matching. Because if it black box matches, both momentum AND energy are conserved. A perfectly elastic collision! Anything else is inelastic… It’s the maximum power transfer theorem! I sent Steve a pic of what I Think will look incredible in slow motion!
I struggled with a similar thing recently when thinking about the energy associated with hydraulic mechanical advantage. I realized that when you try to calculate the energy associated with displacing a piston of area A1 with a force F1 by a distance d1 and rearranging the mechanical advantage equation you get F1 = (A1/A2)*F2 to isolate F1 so that you can multiply in d1 to arrive at the work you get F1*d1 = (A1/A2)*F2*d1. Then I realized that the other piston displacement is d2 = d1*(A1/A2), which makes sense. Say A2 is bigger (like a hydraulic jack ). You pump on the small area piston to multiply your force over a larger area, at the cost of displacement, and the energy is the same. Just thought it was funny I wrestled with something similar recently. Love your videos.
Levers are tricky because they convince us to think about rotational situations in translational terms. We can get away with that when the small angle approximation applies, but levers tempt us to extrapolate the approximation beyond its reasonable limits.
I'm halfway through the video and it seems like they are addressing this exact point, but with the opposite position, that it's less about rotation physics but more about mechanical advantage. Which is probably a good example of people thinking they understand levers, but don't understand them as well as they think. I'm including myself here.
This is a really intuitive explanation that every astrophotographer knows but doesn't understand. An equatorial mount functions better with it is balanced, better functioning means longer exposures meaning better photos. But mounts have a maximum weight that you can put on them. So to some people, it makes sense to put the weight as far down the counter arm as possible to use the least amount of weight. But actually, the better outcome is using more mass on the counter arm closer to the rotation point because the moment of inertia is lower. This makes a lot more sense now
When you set up the diagram of the two different levers in space my instant reaction was "wrong!" It took me a minute to articulate that "Steve, you've forgotten about the impulse. Force over time, Steve! The mechanical advantage is different so for the same force the impulse is different!" I couldn't have told you sqrt2 though.
Indeed. Just from using levers to lift and move objects in regular life, I knew it was possible to feel the difference in a black box scenario, though I had to think for a moment to find a physics terms explanation for my personal experience.
Yeah same thing here, it "seemed wrong" but since this guy is so smart I'm like "It seems wrong because of the moment of inertia or whatever, but I've never used a zero-mass lever so it's probably just counterintuitive."
I had a similar problem several years ago when I was designing a spring mechanism as a hood restraint. The spring had to deflect enough to slow the hood to a stop after having been initially flung open. What I found was that the amount of spring deflection didn't depend at all on how far away it was attached to the hood from the hood pivot axis -- it would deflect the same amount regardless. I was pretty surprised by this (and so was my boss), until I realized that the difference was how long it took to decelerate the hood to a stop. But basically it was an energy problem. No matter where the spring was attached, it had to absorb the same amount of energy of the rotating hood, so it would always deflect the same amount. Ultimately, the spring concept proved to be too clunky, and we didn't go with it at all. But it was a pretty interesting analysis.
As soon as he said you couldn't tell the difference, I was saying inertia as well. I didn't know the maths, but I knew that a different length would change the feeling of each for sure.
I felt to me like Steve was intentionally avoiding the word INERTIA and the word TORQUE. 😂 Eventually the video does mention "moment of inertia" a few times, but I don't think torque ever came up.
22:26 maybe hang the Newton's cradles next to each other instead of above and below, and the lever will swivel in the horizontal plane on a vertical axis? That way the pivot point could be a point instead of a line, minimizing complexity and friction. That said, I wonder about the "shockwave" model: does the shape of the level matter for the purposes of transmitting the shockwave? Especially since the shape of the lever is so different than the shape of the balls. 🤷♂️
What if it were a C shaped lever so that the balls were impacting on the ends of the bar, but then where do you place the pivot, on the middle outside of the C or in the very rotational centre of the C?
0:46 Buddy, You don't need to convince me that I don't understand levers. I will admit straight up, I have no clue how a lever works. I took physics in university and that only made things worse. My principle is: "Archimedes was tapped in, and big stick move heavy thing!"
@Slackker_ No you nitwit, I am saying physics is more than just memorizing a textbook answer. Like the whole video is proving.... Are you mentally well?
This is what I love about science and engineering videos: my knowledge on the subject is lower than a brick to understand it, but I can follow along because the way it’s explained makes sense at the moment
Moment of inertia is just a formalism to shorrcut some calculations. It doesn't explain what's going on, but rather gives you a fake feeling of unerstanding
@@borincod It may be a "shortcut" avoiding considering every single particle along the length of the lever having separate interactions, but for the purposes of this video it absolutely works! Halving the mass and doubling the radius does the same thing to the moment as Steve originally explained would hypothetically happen to kinetic energy, as the radius is squared. The entire idea of moments is based around this concept. It doesn't work for the pulleys as they don't have an equivalent analog for torque, but you could probably shortcut the acceleration calculation in a similar way if you used it often enough to make deriving the formulas worthwhile.
I have to confess, I was screaming "that's wrong" at the screen as soon as you said stuff about wiggling. But only because I made the same mistaken assumptions you did and then figured it out better later when designing - of all things - orchestral triangle beaters. Getting a nice balance feel and keeping them as nimble as possible is not intuitive. It was one of those waking up in the night moments - followed by trying to convince myself that my new intuition was right in the dark without pen and paper.
@@donperegrine922 thank you for your interest. While I am all for general education, I'm not currently much up for divulging specific applications which are, essentially, trade secrets and part of making my living. Maybe one day I'll write a book to collate all my little ideas, approaches and insights. However, I expect the audience for it would be very niche.
@@MattNolanCustom riiiiiggt gotcha. I'm an engineer myself (student) and I love reading and telling design stories. Moments of revelation. I bore some people who are being too polite lol
Your black box experiment made my brain fizz, because I'd done very close to that experiment in a different context. In high school physics, we learned about how 'weight' is acceleration due to gravity. Mass, on the other hand, doesn't need gravity. Our language is kind of terrible and we mix up weight and mass all the time. If you take a 1kg mass into space, it will have close to zero weight, but it will still have its mass. Your wiggle-box experiment immediately reminded me of the experiment we did in class, where you stuck a mass on the end of a flexible strip of metal that was fixed at the other end and gave it a nudge. The strip would act like a spring, and the mass would bounce back and forth. I think the period of the bounce told you the mass. Heavy -- er... Massive items would wobble slowly, while ligh-- (what's the opposite of 'massive'??) -- items with less mass would wobble quickly. It provided an answer to 'how do you weigh something in outer space?' I think your wobble box was exercising something similar.
While I had the advantage of knowing that the intuitive answer was incorrect, the first thing I thought of was acceleration - I was delighted when you announced that it was indeed the factor. To me, this shares the intuitional discrepancy with the fact that holding an object still against the force of gravity is not technically doing any "work" because there is no displacement (though that one might be more of an issue of semantics)
Throughout this video, I was reminded about pendulums. They work off a very similar concept, and one might be tempted to believe that a pendulum of a given weight dropped from a given height has the same period no matter the length, as it experiences the same acceleration at any angle along the curve. The problem is again clear when considering the distance: the acceleration may be the same, but a smaller pendulum has less distance to travel for the same amount of rotation.
Same here. The length of the pendulum determines it's period, independent of its weight. So if you try to wiggle the longer one at the same speed as the short one, you'll feel more resistance.
@@jakemensing6672In the real world? It probably would, as you can't perfectly drop something as unwieldy as a grandfather clock straight up and down. If it was dropped straight up and down, the pendulum wouldn't move, since all the forces will be in alignment with the pendulum as it slams into the ground.
@@nikkiofthevalley It doesn't matter if it's dropped straight up and down or completely sideways. In order for the pendulum to swing it would have to fall faster than the point is is attached to, and since both are being accelerated at the same speed by gravity there is no swing. The orientation of the clock doesn't change anything about how a pendulum operates. The only possible exception I can think of to this is if the clock, as a whole, has a lower terminal velocity than the pendulum. If so, and it fell long enough to reach that terminal velocity, then the pendulum would start to fall relative to the clock again and start swinging.
Pausing at 4:17 to point out that the lever would definitely not feel the same on the finger with half the mass at double the distance. You'd feel the same force in both situations, but the lever would accelerate differently in both cases, since both balls would fall with the same acceleration due to gravity. Therefore with double the distance, the lever would accelerate half as fast.
Exactly, I thought about something similar a while back, where depending on the pulley setup of a gym cable tower, it'd create different forces on the muscle during acceleration and deceleration.
@nonstop7243 that's a great example! Like elastic bands vs. Cable weights. Same weight but you can't swing the weight up from the easier part of the lift with bands because there's no inertia
Thank you for saving me from having to write a comment on this. He could argue, that you are not allowed to move, but the animation clearly implies that there is no way to know, even with movement.
My real life example, which I believe is the same concept. When we tow our cars on a trailer most of them are front engine cars with a heavy bias right at the front, when loading them you stand back and observe the levelness of the trailer and you're typically looking for it to be fairly level to choose how far forwards you load it. As we primarily tow front engine vehicles with a front weight bias, the whole car is usually backwards in relation to the axle, which in this case is obviously the pivot point, meaning there was more car behind the axle. However for a while we utilised a boat trailer with its axles much further back relative to the trailer frame due to the fact that inboard ski boats have a much more central mass with their engine in the centre. So we would load the car backwards on the trailer and to get the neutral balance on the trailer it meant having the engine just rearward of the axles, with the bulk of the car forward of the axles. While the static balance was the same, the fact that the mass behind the axle was dense and was very close to the pivot point gave amazing stability for towing as obviously it's such a dynamic situation where proposing and bouncing is a huge issue. As the vehicle is essentially the hand pushing down and controlling the mass on the other end of theever (behind the trailer axle) this seemed to dampen down a lot of the movement both side to side and up and down
I'm just an average electrical engineer who had mech eng service courses in statics and dynamics. I spotted the flaw as soon as you flipped up that first dual diagram.
Having said that, my intuition was that this was a dynamic situation and I was uneasy when time wasn't taken into account in that first graphic. Thus I would started looking for the flaw sooner, but if I had started from the double Newton's cradle, as you did, perhaps my intuition would have failed me. Hmm... tricky problem.
Electrical systems are about different forms of energy and we don't combine energy into just 'joules' so we tend to understand different energy types in a system. We also deal with waves, and they can be pretty important.
As he described "there is no way to proof which one has more mass" my first thought was "Wonder what happens if you wiggle it?". Because it's just a real life observation, that a long pole is more unwieldy than a short one, even when the longer one is lighter.
I just love the way you guys keep coming up with these demonstrations of just how much more subtle ABSOLUTELY EVERYTHING is than you would think. It's just pure joy!
You need to try mounting your lever on a ball bearing. Make it so that the balls strike it perfectly along the axis of spin. You'll probably have to provide more vertical gap between the two Newton's cradles so that you'll have room to counterbalance the strike plate. This setup would allow for the best transfer of power with minimal losses. You're losing way too much energy from your lever setup.
yeah, the clip of the through hole lever had too much play in it. so it wasn't pivoting cleanly along the axis. but then again that also is an issue of not having a machining set up to get a tight fit bearing in the lever with proper tolerance.
4:35 about no experiment, the inertia of a 1 kg mass is higher than that of a 1/2 kg mass, so I would expect we can determine the mass by feeling how it reacts to inertia
I think if you moved the lever down at a known speed, fast enough to toss the weight in the air, you can work out how fast it was moving upwards by how long it took to come back down. There’s only one part of the lever that moved at that speed so you have the distance, and from there you can get the mass by division? Commenting at my own peril before finishing the video
also commenting at around 435 but yeah when holding still you couldnt tell but the moment you let off the thing and mass drop you would be able to tell
Engineer here, related to the lever Newton's cradle, check the concept of Center of Percussion. Percussion dynamics are very unintuitive and it's why this might not be working as expected. When the ball hits the lever it wants to translate and rotate at the same time, so mass and inertia are interlinked.
i think a good way to get a (correct) intuition is to think about it in terms of *acceleration* exerted over distance, rather than force exerted over distance: the small mass is experiencing one meter per second of acceleration over a distance of two meters, whereas the big mass experienced that same acceleration over a distance of one meter. by the time the small mass has finished traversing the first meter, it's already moving, so the acceleration it experiences while traversing the second meter is less, since it takes less time. the confusion comes because normally when we think about acceleration, we're talking about a fixed *time* spent accelerating, so we're not used to thinking about it in terms of distance.
In game design, there's some interesting things you have to account for when you're trying to model a physics engine, and it comes down to how a dynamic system works being very different to static ones. A snapshot in time (which is what you render to the screen after you calculate the position of objects to be rendered for that frame) is a very different beast to varying conditions over time, and things like acceleration play a huge part in how you have to calculate how an object might move between frames. What this thought experiment shows is the sum of a bunch of moments where an event starts at a specific point, goes through some process, and has a final state (a moving rocket and a moving weight). You're only interested in the start and end picture, but there is an acceleration curve that both weights go through between them, that has an impact on how that all plays out. Getting to the bottom of these investigations comes with an understanding that physics is a very deep rabbit hole, even at a fundamental level. I feel like with the lever in your Newton's cradle idea, it probably has a lot more to do with losses through transferring that energy than it does with some kind of flaw of the idea itself. I think it would be possible with more development. A cool idea nonetheless.
I figured this out by using different cable machines in my gym. Some have an extra pulley and the weights are twice as heavy but feel slightly easier than the ones with half the weight and no pulley. I noticed that at the bottom of each rep, the machines without the the pulley felt harder in the transition to lifting up again. Pulleys operate with the same force multiplication properties as levers, so I knew as soon as you said waggling it wouldn't help you differentiate that something was off.
@@launchpadmcquack98 you said "the weights are twice as heavy" and you are sitting here telling other people they are wrong? the weights all weigh the same, the distance they move is what changes smart one
@bmxscape You're misunderstanding what I'm saying. The physical weights on the double pulley racks are twice as heavy in order to achieve the same static resistance at the handle. That's how pulleys work. Double the weight with double the effective leverage on the weight results in the same static load, but I bet you felt real smart typing that reply...
When both sides of a lever are equal, there is no change, as opposed to just directly pushing it; these levers are only used to change the applied force in a convenient direction. Levers in which the load arm is longer than the effort arm are used for gain in speed. It is sometimes hard to understand what a gain in speed means in the equations we solve since we make assumptions. we can separate levers by there MA into tree types MA=1 Effort arm=Load arm (Change in direction) MA>1 Effort arm>Load arm (Gain in energy) (But loss in speed) MA
Here's something I find puzzling which might be related: Suppose you go ride a bike today. Initially a friend pushes you to get you up to speed. Then you exert a constant force let's say 100N for 100s, and the air resistance exerts an equal and opposite force so you don't accelerate at all during that time. Let's say you travel 100m. So the work you did was 100*100=10kJ. Tomorrow you go ride the bike again. Again your friend initially pushes you up to speed, and you start exerting a constant force of 100N for 100s. But this time there is a headwind, and the speed at which the air resistance is equal and opposite to your force is slower. This time you only travel 50m. So you exerted 50*100 = 5kJ. Your subjective experience, I think, was about the same on the two days. But on the second day you did half as much work. What's the deal?
The important to remember about the W=f*d equation we're using is that 'f' is the Net Force on the object. In your first scenario you've actually done 0J of work once your friend let go - as you said the wind force exactly cancels your pedaling, so you might as well be an object floating through space. The headwind day is the exact same equation, it just feels different because while you're thinking about it in terms of ground speed, your forces are concerned with air speed (which is the same both days - enough for 100N of air resistance).
An important factor is also very likely the loss of energy through the lever set up, newtons cradles are held in suspension so the force has nowhere to go but through the balls in contact. The extra bits of metal and fishing line attached to a vice grip and the table are a good culprit for how quickly the system stops moving, even with the moments of impact on the lever set up right
Yeah, also thought about it. So it's not about static problem, it's dynamic, and this is where simple law of lever stops working, and laws of rotation dynamics appear.
10:20 Isn't this kind of similar to how gear ratios work? When you shift into a higher gear, you gain torque but you lower your RPM. In a similar sense the longer the lever is (with equivalent ratio of weight at end), the longer it takes to push the lever down. I think the difference is probably that a gear is more like making the lever longer without adjusting the weight. Longer lever = more torque for a given weight, but each revolution takes longer, same as with gears.
He's measuring acceleration across distance, distance travelled given acceleration is d = (1/2)at^2, so time is t = sqrt(2d/a). Since both masses accelerate at the same rate, the one is accelerated for longer due to this. You can see they have the same acceleration in the static example, where the same force is applied and both accelerate against gravity at the same rate (10m/s^2 in the example).
The distance doubles, so no free energy. Im sure you discuss this later on in the video, but as someone who routinely uses levers to move things like concrete blocks, think of levers like you'd think of a gearbox. Your rocket has to travel 2m to affect 1J on the 1kg mass.
Also, I think I'm right that an object at rest will stay at rest too. So there's a chance that the mass difference could be..... And the video says that's a thing. Lol
20:45 Looks like you nailed the setup, and the reason it doesn't bounce very long is your lever is flexing and that is eating some of the energy. Try using a more rigid lever like a harder metal, or something like carbon fiber.
@@guustflater9232 I recommend air bearings on the pivot, because it is so much easier to hide the energy consumed by the air compressor when demonstrating my perpetual motion machines. Oh wait... Don''t read that, O.K.?
I'm only at 6:31, but shouldn't the 1/2 kg rocket move slower? In this situation, the 1/2 ball effectively gets 2 J of energy. So, either the math is wrong, or the assumption that the rocket must experience the same force is incorrect. The rocket would push harder in this case. If it's pushing with 1 N, it should have a harder time turning the lever, which means it would move slower. It's probably not half the speed, but like 20-30% slower. Most values stay the same in a 1:1 situation, but yeah, levers are weird indeed. That's what my gut feeling would say-no mathematician here, hehe EDIT: 7:45 lol. Anyway, I was thinking about the different feeling you'd get in a gym when lifting a weight 1:1 versus through a pulley. Even if it's half the weight, it feels more draggy and resistant to movement. EDIT2: Ah Okay so actually 41% of the speed
4:27 - Being "clever" (read: smartass), very technically as the black box was drawn there IS an static experiment you could perform to determine the mass of the object hiding in the black box. Simply remove your finder and let the lever end, hidden in the box, touch the table. The angle of the lever and height of the pivot will let you work out the length of lever hidden past the pivot and with that information (and the static force from before you removed your finger) you can work out the mass. ;)
I say the box goes far enough down that you can't do that, but you can still tell due to the mechanical advantage's inertia. The end of your lever simply won't accelerate as fast with a weight a longer distance away
Physics tutor here. You are correct that this is very similar to an impedance matching situation, that second piece of fishing line that you introduced, is actually functioning as an elastic storage and turning the lever into a harmonic oscillator. In terms of your original paradox, if I act on the lever with a waggling force mg + A cos(ω t), the mass m at distance L feels this force and due to F = m a, the first lever responds as y(t) = A/(m ω²) cos(ω t). The mass ½ m at 2L, feels half this force due to its mechanical advantage, but also has half the mass, so it actually describes the exact same y(t)! But your finger at distance L, travels half the distance for that same y(t). Now here's where it gets interesting for me: I think that the frequency ω chosen is independent of the load, you just have a preferred frequency that you want to shake your hand at. Since you are not tuning this frequency, you have no way to know that this isn't a harmonic oscillator, e.g. a rebar that is stuck in the ground. You can tell that based on comparing low frequency and high frequency jitters, how they move the thing, but it's my claim that none of the people you ran the experiment on, actually did that. “same force, half the motion” then _unintentionally reads_ as, “this feels like a stiffer piece of rebar.” If that's correct, then if you repeat it with ½ m at √2 L, you can do the inverse experiment! You give the levers oriented vertically to someone, ask “are these the same,” they will jiggle them and say “yep!!” ... Then you will invite them to just push them down to the same distance and hold them both down in parallel and they will say “oh, this bar is 30% lighter than that one!!” and be appropriately amazed.
Im sure you are that "clever" person, Steve was talking about in the beginning. And besides the big ass text you still had the urge to tell us that you are some tutor.
My intuition about fishing line is that normal monofilament line is 1) pretty stretchy and 2) doesn't spring back instantly after stretching, more like it's measured in seconds to minutes. This intuition leads me to think the line is acting not just as a spring but also introduces damping and therefore energy loss. Nevertheless, I guess it's possible that my intuition about the line is actually wrong, confused by som other phenomenon of the mechanics of trying to pull my bait loose from some rock. If otoh my intuition is correct, then trying other line materials (dyneema?) might provide some "pretension" for the lever with less spring- and dampening effects?
I was immediately thinking about the wiggling as a source of defeating the "black box", thank you for framing that up so succinctly! I agree with the interesting inverse experiment, and this is somewhat along the lines of the "source of unintuitiveness" discussed in the video, with other hypothetical setups.
@@simon7719 you are mostly correct, the line will be stretched out a bit at equilibrium so it does spring back both ways, but it's definitely not a great material for energy storage. In mechanical watches you get thin metal bars coiled into spirals to store energy, which is overkill for this build but would look so cool.
Okay, I'm going to guess right now, at 5:00, that there's something wrong with this idea of "moving" the bottom part of the lever "one meter." The whole thing would be rotating, not going straight, and if the weight flies off the end of the lever, then it can't have really gotten the 1N of force the whole time.
Revisiting the black box at 7:40, not having seen the rest of the video: Sure, the force is the same, but the acceleration won't be! The moment of inertia of the half kilogram configuration is double that of the one kg. The finger exerts the same force, and the same torque, on the lever in both cases, but that's in static equilibrium. Once you try accelerating the mass, the moment of inertia of the longer lever resists the increase in angular velocity more than the shorter, and you'll notice that you need to push harder on the longer lever to pivot around the fulcrum at the same rate. The work equation is blind to the *rates* of transfer. It takes longer for the same force to transfer the same amount of energy through the longer lever. You can imagine trying to push against the black box levers in both cases. It's hard to apply a consistent force, so you might be tempted to move your end of the lever at the same rate for the longer lever, but this requires a larger torque to overcome the larger moment of inertia for the longer lever, so you'll need more force, and you'll work harder. This may seem strange when you consider that there is indeed no difference in your experience as long as the lever remains stationary. Rotational dynamics are not quite intuitive! The rockets confuse the issue because they presumably thrust for the same time, but one will encounter more resistance in its path than the other, and will have failed to rotate the lever as much before it ceases firing, thereby imparting less energy into the mass. (Remember that the fulcrum is fixed in place; if the second rocket were trying in vain to push aside the fulcrum, it would successfully transfer zero energy to the mechanical system, which should come as no surprise. This is like that, but there's a spectrum to how much the fulcrum is able to impede the motion of the rocket, depending on the size of your lever.) Instead, because the rocket's leftward velocity doesn't get as large, its propellant's rightward velocity is larger on average over the whole thrust, and that's where the missing energy goes.
My first thought while working this out is that mechanical advantage is analogous to transformers, so if you have an advantage of N, then the impedance on the other side is not scaled by N, but N^(2) For the example you gave with a distance of 2 (N=1/2), the mass that would feel the same is 1/4 the original mass. This is equivalent to what you mentioned about reducing the distance by sqrt(2) to feel the same
me too. Levers are mechanical transformers. I clearly remember myself having this "hey, what value does a resistor feel like from behind a transformer,... i guess it's multiplied by the ratio" thought, but then something else didn't quite line up, and i thought this through and came to the n^2 ratio. With that already ironed into my brain, i was instantly able to point out where Steve's initial explanation went wrong. But that is indeed not immediately intuitive.
I was thinking about moment of inertia and rotation the entire time.. you can't imagine the grin that came on my face when you said that was wrong!!! I LOVE getting to the part of a problem where the last theory you have is finally gone and your only option is to hunker down and be humbled with new knowledge
I don't know if this will come up later in the video, but the "black box" assumption at the start is just wrong: The both configurations with different masses at different distances from the lever point such that the torque (m×d) is the same do not have the same moment of inertia (m×d²). This means the finger can distinguish between them, if it is allowed to push and feel how the lever moves after pushing (as is suggested by the animation. And this is exactly what the rocket experiment is doing. In particular, the rockets take different amounts of time for their 1J-push at 1N, because the moment of inertia that they are pushing against is different.
yep this is the first thing I flagged as wrong - if the finger is completely still, it feels the same (same static force), but if you're allowed to wiggle your finger and feel the dynamic response you can tell the difference
Yeah and that's why his intuition was wrong. But moment of inertia doesn't apply to the pulley example, so you have to do some different math. It's something that falls out due to mechanical advantage, which itself comes from W=F*d, which comes from the kinetic energy formula, which comes from the 2nd law of motion (F=ma), by including displacement. F_effective=(force/advantage)=ma. 10N/1 = 1kg * a 10N/2 = 0.5kg * a 10N/1/(1kg) = a = 10 m / s^2 10N/2/(0.5kg) = a = 10 m / s^2 You can also tell they accelerate at the same rate, because it takes the equal force to accelerate them both against gravity at a static position (which requires them to have the same F=ma, meaning your finger must experience the same mass, meaning the effective force yada yada) final_v = a * t But here we're applying the force for a certain distance, based on the kinematic equation: d = (1/2)at^2 t = sqrt(2d/a) therefore, final_v=a*sqrt(2d/a), which simplifies to sqrt(2ad) fv_a = sqrt(2 * 10m/s^2 * 2m) fv_b = sqrt(2 * 10m/s^2 * 1m) the first two terms cancel when divided, and poof (fv_a/fv_b) = sqrt(2) drops out. Generalizing, you get fv_a/fv_b=sqrt(d_a/d_b) It is because of mechanical advantage, which doubles the distance and halves the force. The issue is that we're accelerating the objects at the same rate but one travels a longer distance. It actually makes perfect sense if you think about your "finger force" as accelerating the mass at 9.8m/s^2 upward in the stationary example, in both cases. And both are traveling 0 distance, which is why they feel the same. The moment (no pun intended) you implement distance(d) > 0, the final_v=a*sqrt(2d/a) comes into play. Technically net acceleration is also 0 in the static case
@@refindoazhar1507 Yes it is. And you should explain why the pulley example has the same problem as an exercise for yourself (ignore my other comment about it thx)
The answer lies in: Torque vs horsepower Force vs power And trying to conserve ENERGY! Momentum match Kinetic energy match. Totally elastic collision. Maximum power transfer theorem.
22:00 - What if they were side by side instead of on top of each other? This would eliminate the elasticity of the fishing line and your forces on both sides would be equal.
At first I thought you had misunderstood the point of the experiment but on second thought I think that's a great idea. Very creative. I hope Steve tries it
@genxjack72 obviously swingsets don't exist because if two swings were next to eachother the chains would cross paths and get tangled up /s You can place two newton's cradles next to eachother without there being any overlap, they don't have to share a stand or whatever you were imagining. In the video, its clear that he has 2 basic newton's cradles each with their own frame that are just held in place with a 3d printed stand, so it's as simple as removing the 3d printed parts and placing both frames next to eachother
I suppose it would depend on whether the suspension strings need to be at a specific angle for them to work properly and if the impact point still needs to be a specific distance from the pivot point.
Have you pondered the idea of not making a lever at all, but using a fixed piece of steel. If you say that the shockwaves (as mentioned in the Action Lab video) are a possible explanation of the force behind the Newton Cradle, then a piece a steel that is fixed and has some internal flexibility in it, let's say springsteel, there is a chance that the 'shockwave' will propagate through the steel and drive the second newton cradle. In essence your got to stay very still to move 😉A bit like when you hit a hamer on a steel block, it bounces off really hard...
It is the same with electronic technology. Get this: when you use a transistor to amplify signals, it always looks like you are getting more energy out than you are putting in. The energy, however, is coming from a dc voltage source which, along with resistors, is used to bias a transistor into the "active" region, which is how it gets the energy to amplify the signal. A "tunneling" diode has a unique function where it provides "negative resistance", which put back energy which is lost by the resistive contact between a sensitive probe and an experimental sample. However, in order for the tunneling diode to work, a dc energy source has to bias the diode into a current-to-voltage quiescent point where the negative slope of the curve is located. So, we still cannot violate the laws of thermodynamics by using a transistor or a tunneling diode.
It is the same gear problem, when you have a magical transistor (no bias loss) your still get watts in equaling watts out because you halve the amps when you double the voltage.
While watching the "black box" explanation of the two levers, my thought was that while the force of the finger is the same, the reaction at the fulcrum and internal moment of the beam are different. This tangentially gets to the leverage discussion that was the solution, but I wasn't pausing to work through it all. Good stuff!
One idea about the position on the lever with the pivot point on the back (22:01): I would suspect that the width of the lever plays a role here. Because it is quite thick, I would argue that striking the front of the lever at a certain height is not the same as striking it this exact distance from the pivot point: rather you are actually striking it farther away. And because the distance relevant for the lever is the distance to the pivot point and in this configuration the width contributes a lot to this distance, the position seems to deviate a lot from the theoretical positions (which is of course the distance from the pivot point, not the height above the pivot point). I hope this makes sense, it is a bit hard to explain fro me without a drawing or something like that.
The theoretical levers, such as in the diagrams, always have their pivot in the center. The real world lever isn’t really pivoting, it is rotating around the pivot behind it. This definitely makes things more complicated to me.
You crack me up with your "evil mastermind" arguement for buying the Odoo management app. LOL! I'm still chuckling to myself 5 minutes later. Nice one.
This all really can be understood by realizing that rotational energy is also present in the system... since one lever has a greater rotational inertia, it will have a lesser rotational kinetic energy.
That makes sense. While you were laying out the logical steps before getting to the point where "hang on, did we just get in more energy than we put out?" and I realized, at least I think I did, that one of the assumptions made was incorrect. The mass does move across double the distance for the same applied force, but that doesn't mean it's traveling at double the speed. After all, the work equation is just "force x distance" and doesn't have a time component. So the half-mass-double-distance object would actually be traveling at √2 times the speed of the first example, thus preserving the known laws of thermodynamics. And it was pretty clever to point out earlier that that √2 would be useful later.
5:10 You claim that the acceleration of the rockets will be the same, but it wouldn't. It is pushing on a greater moment of inertia. I bet that is what the rest of the video is going to be about.
My thoughts as of 6:40 - A lever wouldn't operate as depicted in space since the pivot isn't fixed in place. A force would need to be exerted at some additional point along the lever in order for it to operate as depicted, and this force is the source of the extra energy.
Oh! That’s a good point. I was feeling like these difference at this point is a lever in space doesn’t have gravity pulling on it, so maybe levers only work how we imagine when they are flat against the earth. Which would explain why he had an unexpected problem when trying to use one sideways.
I know what you're trying to say but I'm not sure that exrra force is imparting extra kinetic energy into the setting because it's not moving. Its like pushing against a house. It doesn't matter how hard you push, it doesn't increase KE because it doesn't move. I want to be proved wrong if i am
there is extra force. in space, this setup would not move as shown unless you had a rocket engine pushing the fulcrum rightward at a tuned magnitude to the interaction with the rocket.
that's exactly what I was puzzled about, when I was calculating optimal balance weight and shape on crankshaft of combustion engine. you need certain amount out m*d to kinda cancel out forces, but if you look into racing, you want the engine to spin up faster- less inertia. you cannot make counterweight directly lighter, because you throw it out of balance. And this gave me the insight to spot your "mistake" . AND because of this I think quite a lot of engine builders/tuners shave off weight not optimally to keep balance but to reduce inertia.
Oddly, the distance that seems to work well for long lever matches root 12 which matches the moment of inertia of a spinning rod *spinning from its end*. So it's as if we're matching the moment of inertia of just one side of the rod. That doesn't sit right with me though. Hmmm. The sponsor is Odoo: click here to try it for free www.odoo.com/r/aykZ
Doesn't the pivot point matter here? Doesn't it have to be able to handle the mass being pushed, regardless of the mass? It doesn't seem like the variable here is the mass or the force being applied by your finger. It's how the pivot point is anchored and how much mass it can take being applied to it, Doesn't it have to be able to take the forces applied to it in order to move the ball? Doesn't the lever have to deal with these forces on the point of contact with the pivot point?
P.S - I'm a stupid person, so I apologize if none of that makes sense.
The shape of the object is equivalent to "simple pendulum" I = m•R^2
Pshhh, everything stated in this video is so obvious...
I'd like to point out that your lever isn't really pivoting around its center, but rather rolling on the thing you attached it to. I don't know how important that is, but it might partly account for the difference between the theory and practice.
Also, wouldn't a horizontal lever on a vertical axle, with side by side lines of balls, be easier to fine tune? At least it wouldn't be affected by gravity.
'root 12 which matches the moment of inertia of a spinning rod *spinning from its end*.' is wrong, its (ML*2)/3, its (ML*2)/12 for a rod spinning about its centre. just wanted to let u know🤗
After watching the video, now i understand levers less
so i guess you convinced me that i didn’t understand levers from the start
The true goal of education communicators - to get people just far enough up the dunning kruger curve so they realise how little they actually know.
yeah, if you move half the distance then you did less work and thus less energy. what a wacky video to come to this conclusion am i right?
First step of learning not knowing
Dunning Kruger's cradle. Pull back on that first ball to show us that we don't know 💩
All those physics test questions I got full score on, were wrong.
Good old Steve explains something, I go "aah yes, makes sense" and then he's like "yeah, but that's absolutely not how it works"
He's like Tom Scott - whenever he says something in his authoritative voice I instinctively believe him
now I'm sad hearing Tom's name again 😢 Hope he's living life at its fullest.@abigailcooling6604
Possibly one of THE MOST important reason to do Science(TM) to things is to test things against our intuition. "Of course it works this way, it's obvious, it just makes intuitive sense!" is an extremely limiting and often wrong way to understand the world.
@@crawley6957 It's like that one student in every class
student: "What if we do [thing] this way?"
teacher: "Intuitively it doesn't work"
student: "yeah but what happens if we do it anyways?"
and the other word isn't unintuitive or anti-intuitive or something you would think with a standard Latin prefix for no or the opposite.
counter intuitive... it must be important that they really needed the word counter. because that's not what you would expect... lol
There is such an urge to treat dynamic systems as purely a series of still frames. This beautifully shows the danger in that.
It beautifully shows me that had I signed up for 2 paid years of Brilliant, I would have been no further ahead in physics _intuition_ than when I started.
In high school like 22 years ago this dude, Peter F....... said exactly the same thing in a classroom discussion involving dynamics... The classic pendulum schwang, and then weather patterns and predictions, in a math class of all things! But we were all kinda taken aback when he said those words... "Why are we observing, and recording a static image of a dynamic system?" And our teacher made the point of being able to record a data point, but then acknowledging the need for changing the approach of teaching and studying dynamic everythings in her classrooms! When Mrs. Garrison told us to "just take a few minutes..." We knew some shit was changing her gray matter!
Mythbusters was teaching that 20 years ago.
Every mechanical engineering student knows that shit gets real once you need to start account for inertial forces.
@@TheTechnopider lol yeah. the option for me to take dynamics (as an EE) was so nice for understanding when static forces are enough or i need to go a step further.
This topic comes up a lot in tennis rackets. There's a measurement called "swing weight" (unit is kg/m^2). It represents how hard it is to accelerate (swing) a racket rather than how hard to hold it still horizontally. Two rackets can have the same weight and balance point but different swing weights. The one with smaller mass near the tip will be harder to accelerate than the one with larger mass near the handle despite "mass x distance" being the same.
Moment of inertia.
Wouldn't the one with smaller mass at the tip be the same one that had larger mass at the handle? What is the mass distribution that makes them different? I would think a larger mass at the tip would be harder to move (like how it's easier to balance something with the heavy part on top and the light part below because inertia makes the top part react more slowly to changes and you can readjust with the more responsive light bottom mass.
it’s also super important in any fencing/sword fighting sport, especially the ones using historical swords (i.e. not olympic fencing). The balance of the sword has a tremendous impact on how the sword handles, how fast it moves, how stable it is, how present in the bind it is, how much weight/power the strikes have. the balance is far more important than overall weight, and i’ve held 2 kg swords (quite heavy by sword standards) that feel lighter than 1.3 kg swords, simply because the poiof balance was closer to the hands.
That reminds me of this modern classic: Steve Smith identifying his bats blindfolded based on his impressive sense of the bat's inertia and weight. ua-cam.com/video/RaOCuDdBn90/v-deo.html
@beaudjangles this video is wild.
This video reminds me of the famous quote: “Aristotle said a bunch of stuff that was wrong. Galileo and Newton fixed things up. Then Einstein broke everything again. Now, we’ve basically got it all worked out, except for small stuff, big stuff, hot stuff, cold stuff, fast stuff, heavy stuff, dark stuff, turbulence, and the concept of time”.
Aristotle said some stuff that was spot on, too. He was pretty much wrong about all the science stuff, but some of his ideas about rhetoric and politics still hold true today.
@13donstalos This is not a criticism on Aristotle. Also, the quote does not say all of his stuff was wrong - only a bunch of them. Also-also, the quote is not meant to be taken seriously. :)
sounds like nonsense to me.
just a bunch of words for a sake of words. for some sleeping minds "may sound cool" - the only purpose of this givberish. may also be used to impress girls of illegal age.
@@zloidooraque0 it is called a joke, it is for the sake of laughter.
@@13donstalos we are considering physics only for this qoute
You may want to look up the term "reflected inertia". It explains why the inertia does not scale linearly with mechanical advantage, but quadratically. And actually, it can be generalized to reflected impedance, as all mechanical impedance scales quadratically with mechanical advantage. So this includes stiffness and damping. This is very important in gearboxes for instance. Also, the same principle has been used in theater equipment that makes you fly over the podium, to counteract gravity without adding much inertia.
This is the correct answer. Reflected Inertia. 💯
5head
I understand all these words but not in this order or context
This comment should be pinned.
@@dominicparker6124 I can imagine, lots of technical terms in there. I'd like to look at reflected inertia like this:
In straight motions, inertia is also called mass. So let's talk about mass. Then, as we learn from Newton, mass defines the relation between force and acceleration (F=ma). So the mass you experience (the reflected mass) is all about how much acceleration you get, given a certain force you apply. Now the funny thing is that the force and acceleration go through the lever in different directions. Here is what I mean with that:
Suppose you have a lever such that the actual mass is moving twice as fast as your hand. This means that the force on that mass is half of the force you apply. So the acceleration of that mass is half of F/m =0.5F/m. Next, this acceleration goes through the lever in the opposite direction. Accelerations are twice as low on the side of your hand. This means that the acceleration of your hand is half of 0.5F/m = 0.25F/m =F/(4m).
The term 4m is what is called the reflected mass, or reflected inertia. Although the lever ratio is 1:2, the mass ratio is 1:4.
With the same reasoning, quadratic relations can be found for stiffness (springs) and damping (viscous friction).
I hope this clarifies the terms a bit.
So, as a civil engineering student (25 years ago), I took a lot of semesters of statics and dynamics and so on in uni. Apparently I remembered enough of them to scoff at your "black box" step and mutter "surely the inertia moments of the two systems is different so they behave differently in a dynamic system", but other than that I almost followed your logic as well. I think the intuition fail when discussing levers (and pulleys and inclined planes...) is that the way we're taught about them (at around 10-12 years old in most countries, I believe) is always in a static setup, and the intuition that's drilled into our brains is about their behaviour at equilibrium so we're always reaching for that intuition before thinking about conservation of energy. Not sure what a good framing would be to help shift the viewer intuition that dynamic problems behave differently than static ones. In uni I've been taught the virtual work principle to analyze dynamical equilibrium, not sure what a good explanation would look like.
Unrelated, at some point you touch about how we perceive forces in a somewhat indirect way: I'd point out that 1kg feels WAY heavier if you hold it at an arms length so the brain is doing some sort of proxy measurement there to estimate the force (my engineer's brain would reach for the virtual work concept again, but maybe it's wrong).
greater difficulty moving the lever PROVED the half kg mass DID HAVE MORE KINETIC ENERGY, because the difficulty was in reversing the direction NOT in the initial movement.
seriously, how can't people see the whole conclusion of this video is BACK TO FRONT ?
i'm pretty happy that i was suspicious of that black box step as well, even though I have never formally studied dynamics
Yes, I was already skeptical at 4:20 when our host proclaimed that you couldn't tell the two systems apart. Exactly because kinetic energy grows quadratically with speed and impulse grows linearly, and the parts of the system in the box conserve both impulse and energy. (The fulcrum is outside the box.)
>Unrelated, at some point you touch about how we perceive forces in a somewhat indirect way: I'd point out that 1kg feels WAY heavier if you hold it at an arms length so the brain is doing some sort of proxy measurement there to estimate the force (my engineer's brain would reach for the virtual work concept again, but maybe it's wrong).
>proxy measurement there to estimate the force
intuitive thinking moment: your brain knows exactly how much force there is because that's what you sense, you then translate THAT into the weight of the object. "if X strain on muscle then Y weight" but X is dynamic and Y isn't, so we have to rely on heuristics to guess the weight, which is only as accurate as the amount of data points we have.
I program physics games and it was the same step I stopped at, "surely inertia plays a factor here, I mean think of a fly wheel and the distribution of mass"
Enjoyed how you showed your thought process, and the human psychology involved in this. Wanted to chime in. As an engineer who's worked satellite thruster micro balances in the past, I'd say the rolling and sliding pivot contact, changing pivot point vs lever angle, and nonlinear fishing line spring are all adding too many challenges into your setup. They sell mechanical spring flex pivots ideal for this application, taking away a significant number of problems. Wish you luck
Glad the fishing line stuck out to you too. My first instinct seeing that was to swap it with the heaviest gauge of steel wire he can twist like a twist tie with a pair of pliers so he can get a really firm contact. Increase that reaction speed drastically and reduce the distance the lever rolls around on that contact surface.
Those spring pivots are really nice though... a lot better than kludging.
Flex, deflection from the linear motion "that it ought to have", multiple things that intuitively might seem negligible, but in the end might leave too much wiggle room. In this case quite literally, since it makes something in the system wiggle a bit.
When you said that the experiences were the same that immediately felt wrong to me. I've worked construction a decent amount and I knew instinctually that was wrong somehow. But I couldn't figure out why. This was such a cool video. I love how you take intuition and convert it into understanding.
yeah I had the same thing, the 'black box' thing seemed wrong and it felt like you'd need to push harder or whatever with the longer lever, but when he said it I just assumed he was right and my intuition was just due to the fact that all real levers have their own mass
If you've used levers in construction you have almost certainly used one hand as the fulcrum and the other hand on the end of the lever. You would absolutely have noticed the difference between holding the lever in the middle vs holding it near one end.
@@youtubeuser1052 Yes, that's my experience too ! Oh good 🙂
I think what changes about the black box experiement under gravity is not the amount of FORCE the exposed part of the lever applies, but its SPEED when the mass is in freefall.
The half mass at double the distance will still fall, in its place along the lever, accelerating at the same rate as any size mass anywhere along the lever, but the further the mass, the less the lever will spin around the pivot point.
Same. I’ve worked with my hands for 25 years and I knew the feel should be different. I have learned that experience can fine tune your intuition for certain things. It’s why classroom learning cannot replace hands on experience. You need both. Using a pulley to lift something does make it easier for someone with less strength. But for someone stronger it feels like racing in first gear.
Great video Steve! I love the thought process through the whole video. A simple Newton's cradle already requires solving multiple differential equations simultaneously while making major assumptions like non-dispersive hertzian springs. So when you introduced a lever to the whole thing I knew it was going to get complicated :)
Not gonna lie, I’ve watch so many ActionLab shorts that seemed to relatable and dementedly unhinged that I had to ask myself how you got into this gig in the first place. And then you go busting out real sets of physics modeling concepts and show that you know what you’re talking about after all😂
This actually makes my level of trust in your work go up tremendously. Even if you were to mess something up, if a peer who saw the mistake were to point it out it looks like you’d not suffer from the Dunning-Krueger effect and thus be able to self-correct.
I love the fact that you have the humility to admit you don't fully understand something and reach out to someone else to help out, and you put it on UA-cam.
Fr such a pathetic weakling. Real men keep insisting on what they said or claim they never did say anything wrong
I think he understands these things very well; you have to in order to set up an experiment to illustrate a phenomenon. but if he came out all "I am smarter than you" he would have a very small audience. So he replicates his learning experiences so that you can learn. It's just that he's already learned it.
and receive thousands of dollars
@@thomasmaughan4798 that's a valid way of teaching but I can see why somebody might feel tricked
@@hobrin4242 who gives him the dollars
This helps me understand why playing a grand piano feels very different in touch to an upright. One of the main differences in the action is that grand pianos have much longer keys (the black and white bits on the outside look the same but the pivot point and total length of the leavers are much longer in the grand piano). So although the down weight (minimum weight to depress the key) and the up weight (maximum weight for ley to go up) can be similar, the levers mean a grand piano feels very different at playing speeds.
There are many other differences in the mechanism that help a grand act faster and repeat faster too. But key length has an impact and I think it is similar to the experiment in this video with waggling different levers.
A pianist friend told me it's also to do with the orientation of the hammers, horizontal vs vertical.
This whole thing reminded me why I like Lagrange's formalism so much: It's hard to reason about forces as soon as the system becomes even a little bit complex, but it's much easier to reason about kinetic and potential energy.
Frist thing the came to my mind too. Maybe even Hamilton mechanics.
I understand levers. Once I asked my father what this thing was and where wanted me to put it. He said it was a leeverite. I asked him what's a leeverite. He said, Leeeverite there.
Dammit hahaha
badum tss
Whereas mine was a lever expert...
He still hasn't come back.
Ohhh, dangit I got here late. I was gonna make a similar joke with cantaloupe and cantilevers but yours was better -w-
This joke will convince me to pronounce lever wrong like you guys, good job :)
A perfect example of how anything non-linear (in this case the sqrt(2) factor when doubling the leverage and halfing the mass) can become quickly confusing in terms of physics intuition. Well illustrated and explained, well done all of you guys!
Non-linear systems are fascinating and wildly unintuitive. The way I've always described it to less math/physics inclined people is that non-linearity is like the eldritch gods of the math world.
I've spent so much brain power on trying to rationalize how we're able to simplify and make such on point assumptions about physical systems to force them to act linear in specific scopes, despite the fact that reality seems to favor non-linearity.
double the power sent to a speaker and the cone's amplitude doubles but to us the perceived sound volume barely increases... our ears are non-linear transducers making all sorts of things counter intuitive.
most volume control knobs use logarithmic potentiometers to account for this. a linear potentiometer (same resistance per degrees of turning) is not v useful for this as first few degrees of travel act almost like an on/off switch and the rest make no difference in loudness.
*it takes about 10x the power to 'double the volume'
Exposure in photography is about non-linear, square root of 2 values.
@@duroxkilo Out ears have the highest dynamic range of any of our senses. We can literally detect many orders of magnitude difference with out sense of hearing.
I don't know, I'm not sure if the non linearity is the reason for this peculiarity actually.
I think there is a relatively simple and intuitive explanation for this which is that the mechanical advantage of the lever "applies twice".
If you halve the mass and double the distance, the mass will accelerate the same amount as it did originally for a given applied force. This makes sense intuitively. The end you are holding on to, however, will accelerate at half the rate of the mass itself due to the mechanical advantage of the lever. That means that it will feel harder to move the mass that is small and further out.
Due to this effect, if you double the length of the lever the apparent mass will go up by 4x, but the apparent strength of gravity will go down by 2x leading to a total increase in force of 2x. If you also halve the mass, it will then feel 2x as heavy as it did before instead if 4x, meaning that the force is the same, but the mass is doubled.
As far as system improvements: The single biggest thing will be increasing the rigidity of your pivot. Holding the anchor in a rubber jaw vice clamped to the table provides lots of opportunity for flex and thus damping. That thing needs to be attached rigidly to something very heavy. I am picturing fixing your pivot bar into a concrete block or some such to give it a solid base. It is like with blacksmithing anvils. You want it heavy and rigidly connected to the floor so the hammer rebounds and all the energy goes into the work piece.
The fishing line / rocker pivot design is fantastic; large radius line contact with little movement and no gap. I might glue some magnets to the sides to replace the fishing line, but you are not going to do better than that line contact with any small ball bearing or shaft pivot.
It might also be worth trying to make a curved lever, something that looks a bit like a recurse bow pointing toward the balls so that the pivot is in line with the contact faces, that would also make it possible to balance so it is not trying to tip forward.
I would be inclined to investigate flexures for the pivot: either standard flexures or the rolling tape type.
Perhaps BYU could offer some advice.
I mean for the longest time blacksmithing anvils were the slightly larger then a fist , you just need a good base and having a smaller anvil helps keeping the piece you're working on straight , even though it sounds counter intuitive .
Anvils are supposed to bounce the force back into the work piece , so if you hame a hammer which is smaller then an anvil , the anvil will bounce the energy up into your work piece thus making it curve up, this often happens when you're drawing out a piece .
I really like the curved lever setup to make it balance without the extra piece of fishing line.
The steel lever is HSS to attempt to match the hardness of the ball bearings approximately (and reduce losses from deforming the lever in impact). The cutting of which would probably involve a water jet cutter, which I didn't have access to, or a lot of grinding.
My argument was that because the steel is so stiff and if you get it right the movement of the lever is so minute that change in forces from something much less stiff like a piece of fishing line will be negligible.
Well it may have been motivated by the day or two grinding high speed steel that would otherwise have been involved...
One thing I thought is that on one you are pivoting on the balance point or closer to it and on the other you are not.
Surely the mass if the pivot must be considered?
The lever needs to be non-flexing as does the anvil.
A curved pivot changes the angle of reaction from the anvil.
How about a moving ball on a a thin pivot beam that rotates 180 from the top row to the bottom row? - hard to describe
"Lever comment"
Clever
@@pahissonni C "lever" comment
@@PIGEON5265DAMN thats a pun just waiting to strike at a moments notice
Leevah
@@oliver1784 to strike at a MOMENTs notice
I’m a high school student from Asia and a passionate physics enthusiast. Here are some of my humble thoughts: I view a lever as a converter of equal torque. On one end, it inputs a unit torque, and on the other end, it outputs the same unit torque. As for rotational speed, it’s analogous to pushing a 1 kg object and a 2 kg object over a distance of 1 meter using a force of 1 newton. Pushing the 2 kg object takes more time because performing the same amount of work does not imply the same power during the process.( In rotational motion, the moment of inertia corresponds to inertial mass in translational motion.)
Even with the incorrect assumptions made about the black box, you could still tell. You could push both lever ends down to the same distance, and let go at the same time. One will take longer to fall than the other. I think this is identical to your explanation but i'm not entirely sure.
Good point. I think they're the same explanation.
That reminds me of another neat physics “paradox”. If you have a broom lying on the floor, and you lift the handle by a foot or two (keeping the head of the broom on the floor) and let it drop again, the end of the broomhandle falls faster than you expect from gravity.
The reason is that the broomhandle’s centre of gravity accelerates at almost 1g, so the tip falls at almost 2g (minus losses due to rotational kinetic energy, and some sideways acceleration if the broomhead sticks in place on the floor). You can even attach a cup to the handle, hold a ball next to it at the same height, drop them at the same time, and have the cup catch the ball.
@@jaapsch2 very cool! it has a similar vibe to those falling slinky experiments
excellent testing procedure
What's funny is, the black box thing didn't "seem" right to me, it seems like you'd need more force to push the lever or it would accelerate more slowly or something, but I ignored that because I thought I was just thinking about the mass of the lever since any lever you would use IRL would have mass.
You got me confused in the first half, good job! I was thinking for your lever, I'm thinking a U shape lever with ends of the U at the center of balls would transfer energy best. Or perhaps it is another source of confusion! either way, worth a try!
[edit] of course for U to work, it should be much lighter than the balls otherwise the mass-energy equations may cause similar issues.
Don't understand the U shaped bit! Why not a dumbbell shaped lever where the balls at either end are the same as the balls in the cradle, and the bar between them, weightless.
The u shaped element may act as a waveguide to make an elastic wave turn around. This is similar to what happens with the water hammer effect where a pressure wave can travel through the pipe and turn around at the elbows
Agree with the U-shaped device to change the direction of the compression wave. It isn't exactly *motion* that is traveling; it is a pressure wave at the speed of sound in steel and the actual physical deformation is probably only some microns.
That's actually a brilliant idea. We all knew his lever wasn't optimized, but that seems like a very simple way to accurately direct the forces.
Assuming the lever is the correct weight it should absorb all of the energy and very little should dissipate as a wave. Ball guy was right... I think
As a car guy, this video reminds me of gearing in vehicles. The lever with the large weight close to your hand is like being in a low gear, and the lever with the weight far from your hand is like being in a high gear.
You push with the same force in both scenarios like the engine pushes the car forward with the same force, but the weight (or car) accelerates differently.
I dont do maths well, but I imagine the gear ratios in a transmission get closer together in the higher gears because of the square root like you mentioned.
I thought about transmissions too. When dealing with them you have to remember that power in ideal transmission is constant between the input and the output. Only torque and speed change with gears in reverse relation.
It probably has to do with torque too. the slow gear spins slower but transmits more torque, which is better to overcome the initial inertia of the car and get it going, or to climb inclines (which naturally is done slower). the fast gear has more velocity but less torque since the car is already moving at a certain speed, so it there's less energy spent on accelerating it.
I would probably take a large amount of time trying to prove this mathematically, but my intuition leads me to this, and it sort of matches what Steve (and Henry) said.
This is completely false.
The only reason you have gears is because the engine itself can deliver much more power in a very narrow "engine turning speed".
The gears are so that this ADDITIONAL FORCE THE ENGINE PROVIDES can be applied at different "tire turning speeds".
@@TheMarcQEngines are completely different. Tge transmission is there because the Engine itself gives more power when it turns at a specific speed. The transmission allows the engine to stay within this "ideal zone" throughout vastly different car speeds.
What Steve is missing is time. Applying 1N for 1meter ignores the time factor. Applying 1N of force for 1m on a 50ton ship will take hundreds, of years, if not more. Applying 1N for 1 meter on a inflatable matress will take just a few seconds. Did I exert the same amount of work?
I think the lever problem in this Newton-thingie could come from the point off rotation. In the two scenarios this point changes and in both the lever isn’t straight, it’s at an angle. That might be why the distances don’t mach up.
11:50 "My sponsor is great, you could even start a scam business with them" 😂
🍯
that *is* pretty much what he said 😅
@@SpydersByteoof this stuff is over my head, what's going on?
@@Giantcrabz
At around 11:19, he brings up the idea of starting a business tricking investors into backing a free energy scheme, which would be fraud. He says he won't do it, but if he did, he would use the sponsor to do so. Advertising how suitable it is for doing crime seems a bit odd.
@@Giantcrabz Steve suggested that if he were to start soliciting investors for his free energy device, he would use the sponsor of the video, Odoo, to manage the process. However free energy devices are a scam due to the immutable laws of physics, which Steve knows full well, so his suggestion is of course a joke. He would never do that (but if he did... he would use Odoo)
I'm afraid Steve has it the wrong way around. Levers and pulleys and inclined planes aren't weird. It's *gravity* that's weird, specifically, the equivalence principle! The root of the intuition described at 14:00 is that the force needed to counter act gravity's effect on an object is directly proportional to its inertia against acceleration. That's a really strange and fundamental part of physics which comes out of General Relativity (or, rather, is an ingredient that goes into its construction). Furthermore this constant is almost the same everywhere on Earth and for all objects. This gives us the wrong idea that the force required to start something moving is a good guide for how quickly it will move afterwards - but that's actually only true for vertical motion in a familiar gravitational field.
All the examples given of pulleys, levers and inclined plane simply decouple the force needed to keep something steady with it's effective inertia (ie, the amount of acceleration caused by a given excess force). The reason that people's minds jumped to rotational system is because the relevant inertia there, the moment of inertia, is different to the gravitational mass. But there's nothing intrinsically rotational about that, it's actually the _generic_ case for dynamical systems.
In other words, our intuition about dynamics is built around the singular exception to the rule! Generally, the force keeping something stationary is completely unrelated to it's inertia against acceleration, it's only vertical motion where the only force is gravity where the two are linked.
This is the only correct answer.
Yeah, it's kinda wild that gravitational mass and inertial mass are the same (or at least, directly proportional) in all cases!
@@engineer_cat It's so wild, the equivalence principle is still an axiom in physics.
I was going to mention the equivalence principle actually! I thought it might be a good explanation for my wonky intuition. But I talked about it with Henry quite a bit and came to the conclusion that it wasn't the core of the issue. But I don't know, your comment is making me think! Thanks!
@@SteveMould Glad I could contribute! I'd love to be a fly-on-the-wall for those kind of discussions.
To write it mathematically, consider _F = m a_ where the force is an applied thrust T opposed to an environmental force _R_ . Rearranging it, we get that the acceleration is _a = (T - R) / m_ . Which shows that there are two parameters at play here, a minimum force _R_ to overcome, and then an _m_ that determines how much acceleration is produced by the net excess force. To determine two parameters you need both to see how hard you have to push the lever to hold it steady, and how much resistance there is to wiggling it. In the case of simply lifting something, we have _R = m g_ and the acceleration simplifies down to _a = T/m - g_ . This _g_ is not an unknown parameter, because we know intuitively what it is, so we are left with only 1 free variable: which means that knowing the force required to keep it steady *does* tell us something about how quickly it would accelerate to a net force..
So I don't think it's *just* the equivalence principle, but the equivalence principle plus our familiarity with local gravity. After all, if you were on the Moon holding something in your hand so it was steady, and then pushed up with double that force, it would accelerate up at only 1.6m/s^2, substantially slower than you'd expect! Obviously, the follow up video should be shot on the Moon to test this.
The concept is "moment of inertia" which determines the angular acceleration of a system.
Pendulum moment of inertia is proportional to square of the radius and linear over mass. Trivial stuff.
Brought up at 15:00-16:50, and isn't a full explanation, because the same situation can result from pulleys or inclined planes
@@mattwis86 The pulley and inclined plane result in similar equations and of course follow the same laws of physics. But for the lever the moment of inertia is the more appropriate model. When you break down the moment of inertia model down to the infitisimal volume element and very small angles it is basically the same as the point masses on pulleys or inclined planes.
Of course the rockets in space system once again is different because the mass is not fixed to the lever and the movement of the mass is not following the rotation of the lever.
This, but I think the number of people who know of moment of inertia is limited to the few who took first year core-physics or engineering-physics, +- some. A tiny % of people.
@@TimLF I'm pretty sure it was part of the mandatory high school physics here, but it was covered in the first physics course at the university as well.
Steve, before batteries were really a thing, did you know that we used Christmas lights and acid to make a shelf stable doppler radar in the 1940s?
You're so close to discovering gears and gear ratios. If you rotate multiple levers of the same length around the center and connect them together, you get a gear.
Really the teeth on the gear are just a lot of levers stacked atop each other
Circular levers?! Witchcraft!
😮😲🤯
This makes stupid amounts of sense! ⚙️
I was about to comment this on "how to improve".
Just using a gear with 2 extended rods as the arms of the lever.
wait what? gears are stacked levers, shut up i need a moment! :)
In this video, Steve gives us all the tools and knowledge necessary to commit large scale investor fraud. Solid video, 7.8/10
Claiming the government was suppressing the truth is a brilliant idea! He should patent that.
This is not a get rich quick video. It's a proven way to make money from willing people.
> solid video
i'd expect it to be a liquid video if it got a 7.8/10 !
I remember you asking me about this and getting initially stumped, followed by getting math sniped to 5am ahah, fun to see this video finally getting out there!!
the way I saw this problem, was that there seems to be a mixup between input force vs output force, and/or input displacement vs output displacement, and/or an assumption about time taken to apply the energy being the same, when it's actually not
assuming we constrain input energy to 1J and output end lever displacement to 1m, and input side rod length to 1m, then I got these results:
1kg ball, output rod length 1m:
1J output kinetic energy after √2s at √2m/s
1/2kg ball, output rod length 2m:
1J output kinetic energy after 1s at 2m/s
which means energy is preserved as expected!
It's something that falls out due to mechanical advantage, which itself comes from W=F*d, which comes from the kinetic energy formula, which comes from the 2nd law of motion (F=ma), by including displacement.
F_effective=(force/advantage)=ma.
10N/1 = 1kg * a
10N/2 = 0.5kg * a
10N/1/(1kg) = a = 10 m / s^2
10N/2/(0.5kg) = a = 10 m / s^2
You can also tell they accelerate at the same rate, because it takes the equal force to accelerate them both against gravity at a static position (which requires them to have the same F=ma, meaning your finger must experience the same mass, meaning the effective force yada yada)
final_v = a * t
But here we're applying the force for a certain distance, based on the kinematic equation:
d = (1/2)at^2
t = sqrt(2d/a)
therefore,
final_v=a*sqrt(2d/a), which simplifies to sqrt(2ad)
fv_a = sqrt(2 * 10m/s^2 * 2m)
fv_b = sqrt(2 * 10m/s^2 * 1m)
the first two terms cancel when divided, and poof (fv_a/fv_b) = sqrt(2) drops out. Generalizing, you get fv_a/fv_b=sqrt(d_a/d_b)
It is because of mechanical advantage, which doubles the distance and halves the force. The issue is that we're accelerating the objects at the same rate but one travels a longer distance.
It actually makes perfect sense if you think about your "finger force" as accelerating the mass at 9.8m/s^2 upward in the stationary example, in both cases. And both are traveling 0 distance, which is why they feel the same. The moment (no pun intended) you implement distance(d) > 0, the final_v=a*sqrt(2d/a) comes into play. Technically net acceleration is also 0 in the static case
Saw the profile pic and initially thought it was Freya Holmér. But then I saw the @ and didn't recognize it, and thought, "Oh, someone is using her pic as a profile pic," which was a surprise; something I had not expected to see. But then I checked Freya's @ and it is Freya, so Freya IS in the comments. This was mental roller coaster ride. LOL
I don’t think you can do it without the lever black box matching.
Because if it black box matches, both momentum AND energy are conserved.
A perfectly elastic collision!
Anything else is inelastic…
It’s the maximum power transfer theorem!
I sent Steve a pic of what I Think will look incredible in slow motion!
@@busimagen I really wish it just showed my profile name instead of handle lol
I struggled with a similar thing recently when thinking about the energy associated with hydraulic mechanical advantage.
I realized that when you try to calculate the energy associated with displacing a piston of area A1 with a force F1 by a distance d1 and rearranging the mechanical advantage equation you get F1 = (A1/A2)*F2 to isolate F1 so that you can multiply in d1 to arrive at the work you get F1*d1 = (A1/A2)*F2*d1. Then I realized that the other piston displacement is d2 = d1*(A1/A2), which makes sense. Say A2 is bigger (like a hydraulic jack ). You pump on the small area piston to multiply your force over a larger area, at the cost of displacement, and the energy is the same. Just thought it was funny I wrestled with something similar recently. Love your videos.
Levers are tricky because they convince us to think about rotational situations in translational terms. We can get away with that when the small angle approximation applies, but levers tempt us to extrapolate the approximation beyond its reasonable limits.
This
OTOH you can just replace levers with systems of pulleys and/or gears and obtain similar results without that issue.
this has nothing to do with small angle approximations
Yeah I though that was the problem for sure, only to later in the video realise that is super not the problem here.
I'm halfway through the video and it seems like they are addressing this exact point, but with the opposite position, that it's less about rotation physics but more about mechanical advantage. Which is probably a good example of people thinking they understand levers, but don't understand them as well as they think. I'm including myself here.
This is a really intuitive explanation that every astrophotographer knows but doesn't understand. An equatorial mount functions better with it is balanced, better functioning means longer exposures meaning better photos. But mounts have a maximum weight that you can put on them. So to some people, it makes sense to put the weight as far down the counter arm as possible to use the least amount of weight. But actually, the better outcome is using more mass on the counter arm closer to the rotation point because the moment of inertia is lower.
This makes a lot more sense now
When you set up the diagram of the two different levers in space my instant reaction was "wrong!" It took me a minute to articulate that "Steve, you've forgotten about the impulse. Force over time, Steve! The mechanical advantage is different so for the same force the impulse is different!"
I couldn't have told you sqrt2 though.
Indeed. Just from using levers to lift and move objects in regular life, I knew it was possible to feel the difference in a black box scenario, though I had to think for a moment to find a physics terms explanation for my personal experience.
you're yelling like in the meme where walter white is yelling at hank from a car lmao
Yeah same thing here, it "seemed wrong" but since this guy is so smart I'm like "It seems wrong because of the moment of inertia or whatever, but I've never used a zero-mass lever so it's probably just counterintuitive."
Thinking about it in terms of work vs. impulse was what made it all click for me.
I had a similar problem several years ago when I was designing a spring mechanism as a hood restraint. The spring had to deflect enough to slow the hood to a stop after having been initially flung open. What I found was that the amount of spring deflection didn't depend at all on how far away it was attached to the hood from the hood pivot axis -- it would deflect the same amount regardless. I was pretty surprised by this (and so was my boss), until I realized that the difference was how long it took to decelerate the hood to a stop. But basically it was an energy problem. No matter where the spring was attached, it had to absorb the same amount of energy of the rotating hood, so it would always deflect the same amount. Ultimately, the spring concept proved to be too clunky, and we didn't go with it at all. But it was a pretty interesting analysis.
The whole video, from first showing the problem to the end, I just sat here screaming "inertia" at the screen. lol
Yup. Moment of inertia of a mass m at a radius r from the center of rotation is mr^2, and everything is clear.
As soon as he said you couldn't tell the difference, I was saying inertia as well. I didn't know the maths, but I knew that a different length would change the feeling of each for sure.
I felt to me like Steve was intentionally avoiding the word INERTIA and the word TORQUE. 😂 Eventually the video does mention "moment of inertia" a few times, but I don't think torque ever came up.
The thing is, it is possible to tune the distance/mass to perfectly emulate the inertia, it just screws up the force @@Donn29
yep
22:26 maybe hang the Newton's cradles next to each other instead of above and below, and the lever will swivel in the horizontal plane on a vertical axis? That way the pivot point could be a point instead of a line, minimizing complexity and friction. That said, I wonder about the "shockwave" model: does the shape of the level matter for the purposes of transmitting the shockwave? Especially since the shape of the lever is so different than the shape of the balls. 🤷♂️
Pretty sure you nailed it with this suggestion, and I hope it's seen.
Yeah the horizontal variation might be the solution
I thought the same in the same moment of video 😋
What if it were a C shaped lever so that the balls were impacting on the ends of the bar, but then where do you place the pivot, on the middle outside of the C or in the very rotational centre of the C?
0:46 Buddy, You don't need to convince me that I don't understand levers. I will admit straight up, I have no clue how a lever works. I took physics in university and that only made things worse.
My principle is: "Archimedes was tapped in, and big stick move heavy thing!"
Big stick strong!
You're saying you didn't review angular momentum/moment of inertia in your university physics course? I find that hard to believe.
@Slackker_ No you nitwit, I am saying physics is more than just memorizing a textbook answer. Like the whole video is proving....
Are you mentally well?
@@Slackker_ Reviewing and being in class is not the same as learning :)
This is what I love about science and engineering videos: my knowledge on the subject is lower than a brick to understand it, but I can follow along because the way it’s explained makes sense at the moment
8:30 *silently screaming "moment of inertia! It's that darn capital I with weird formulas from college!"
16:00 Noooooooo I was wrong?!!!
I'm halfway through and was screaming "conservation of momentum!" Was I right?
Moment of inertia is just a formalism to shorrcut some calculations. It doesn't explain what's going on, but rather gives you a fake feeling of unerstanding
@@borincod It may be a "shortcut" avoiding considering every single particle along the length of the lever having separate interactions, but for the purposes of this video it absolutely works! Halving the mass and doubling the radius does the same thing to the moment as Steve originally explained would hypothetically happen to kinetic energy, as the radius is squared. The entire idea of moments is based around this concept. It doesn't work for the pulleys as they don't have an equivalent analog for torque, but you could probably shortcut the acceleration calculation in a similar way if you used it often enough to make deriving the formulas worthwhile.
@@BillieTheGoose No, you were right.
this feels like forgetting/not realizing you need the chain rule
I have to confess, I was screaming "that's wrong" at the screen as soon as you said stuff about wiggling. But only because I made the same mistaken assumptions you did and then figured it out better later when designing - of all things - orchestral triangle beaters. Getting a nice balance feel and keeping them as nimble as possible is not intuitive. It was one of those waking up in the night moments - followed by trying to convince myself that my new intuition was right in the dark without pen and paper.
Can you tell us the story about what the design problem was, what your epiphone was, and what your solution was?
@@donperegrine922 thank you for your interest. While I am all for general education, I'm not currently much up for divulging specific applications which are, essentially, trade secrets and part of making my living. Maybe one day I'll write a book to collate all my little ideas, approaches and insights. However, I expect the audience for it would be very niche.
@@MattNolanCustom riiiiiggt gotcha. I'm an engineer myself (student) and I love reading and telling design stories. Moments of revelation.
I bore some people who are being too polite lol
Your black box experiment made my brain fizz, because I'd done very close to that experiment in a different context. In high school physics, we learned about how 'weight' is acceleration due to gravity. Mass, on the other hand, doesn't need gravity. Our language is kind of terrible and we mix up weight and mass all the time. If you take a 1kg mass into space, it will have close to zero weight, but it will still have its mass.
Your wiggle-box experiment immediately reminded me of the experiment we did in class, where you stuck a mass on the end of a flexible strip of metal that was fixed at the other end and gave it a nudge. The strip would act like a spring, and the mass would bounce back and forth. I think the period of the bounce told you the mass. Heavy -- er... Massive items would wobble slowly, while ligh-- (what's the opposite of 'massive'??) -- items with less mass would wobble quickly.
It provided an answer to 'how do you weigh something in outer space?' I think your wobble box was exercising something similar.
While I had the advantage of knowing that the intuitive answer was incorrect, the first thing I thought of was acceleration - I was delighted when you announced that it was indeed the factor. To me, this shares the intuitional discrepancy with the fact that holding an object still against the force of gravity is not technically doing any "work" because there is no displacement (though that one might be more of an issue of semantics)
Throughout this video, I was reminded about pendulums. They work off a very similar concept, and one might be tempted to believe that a pendulum of a given weight dropped from a given height has the same period no matter the length, as it experiences the same acceleration at any angle along the curve. The problem is again clear when considering the distance: the acceleration may be the same, but a smaller pendulum has less distance to travel for the same amount of rotation.
Dude, reading your comment made me wonder...If you drop a grandfather clock off of a cliff, would the pendulum swing? I feel like it wouldn't.
And now that I think about it a little more, it would be like floating in space. So yeah, no it wouldn't work.
Same here. The length of the pendulum determines it's period, independent of its weight. So if you try to wiggle the longer one at the same speed as the short one, you'll feel more resistance.
@@jakemensing6672In the real world? It probably would, as you can't perfectly drop something as unwieldy as a grandfather clock straight up and down. If it was dropped straight up and down, the pendulum wouldn't move, since all the forces will be in alignment with the pendulum as it slams into the ground.
@@nikkiofthevalley It doesn't matter if it's dropped straight up and down or completely sideways. In order for the pendulum to swing it would have to fall faster than the point is is attached to, and since both are being accelerated at the same speed by gravity there is no swing. The orientation of the clock doesn't change anything about how a pendulum operates.
The only possible exception I can think of to this is if the clock, as a whole, has a lower terminal velocity than the pendulum. If so, and it fell long enough to reach that terminal velocity, then the pendulum would start to fall relative to the clock again and start swinging.
Pausing at 4:17 to point out that the lever would definitely not feel the same on the finger with half the mass at double the distance. You'd feel the same force in both situations, but the lever would accelerate differently in both cases, since both balls would fall with the same acceleration due to gravity. Therefore with double the distance, the lever would accelerate half as fast.
My thoughts exactly, you could measure the momentum and know which is a longer lever
Exactly, I thought about something similar a while back, where depending on the pulley setup of a gym cable tower, it'd create different forces on the muscle during acceleration and deceleration.
@nonstop7243 that's a great example! Like elastic bands vs. Cable weights. Same weight but you can't swing the weight up from the easier part of the lift with bands because there's no inertia
Thank you for saving me from having to write a comment on this. He could argue, that you are not allowed to move, but the animation clearly implies that there is no way to know, even with movement.
I had the same though, but you articulated it way better than I could have!
My real life example, which I believe is the same concept. When we tow our cars on a trailer most of them are front engine cars with a heavy bias right at the front, when loading them you stand back and observe the levelness of the trailer and you're typically looking for it to be fairly level to choose how far forwards you load it. As we primarily tow front engine vehicles with a front weight bias, the whole car is usually backwards in relation to the axle, which in this case is obviously the pivot point, meaning there was more car behind the axle. However for a while we utilised a boat trailer with its axles much further back relative to the trailer frame due to the fact that inboard ski boats have a much more central mass with their engine in the centre. So we would load the car backwards on the trailer and to get the neutral balance on the trailer it meant having the engine just rearward of the axles, with the bulk of the car forward of the axles. While the static balance was the same, the fact that the mass behind the axle was dense and was very close to the pivot point gave amazing stability for towing as obviously it's such a dynamic situation where proposing and bouncing is a huge issue. As the vehicle is essentially the hand pushing down and controlling the mass on the other end of theever (behind the trailer axle) this seemed to dampen down a lot of the movement both side to side and up and down
I'm just an average electrical engineer who had mech eng service courses in statics and dynamics. I spotted the flaw as soon as you flipped up that first dual diagram.
Having said that, my intuition was that this was a dynamic situation and I was uneasy when time wasn't taken into account in that first graphic. Thus I would started looking for the flaw sooner, but if I had started from the double Newton's cradle, as you did, perhaps my intuition would have failed me. Hmm... tricky problem.
Electrical systems are about different forms of energy and we don't combine energy into just 'joules' so we tend to understand different energy types in a system. We also deal with waves, and they can be pretty important.
@@jamoecw think maximum power transfer theorem.
As he described "there is no way to proof which one has more mass" my first thought was "Wonder what happens if you wiggle it?". Because it's just a real life observation, that a long pole is more unwieldy than a short one, even when the longer one is lighter.
I just love the way you guys keep coming up with these demonstrations of just how much more subtle ABSOLUTELY EVERYTHING is than you would think. It's just pure joy!
You need to try mounting your lever on a ball bearing. Make it so that the balls strike it perfectly along the axis of spin. You'll probably have to provide more vertical gap between the two Newton's cradles so that you'll have room to counterbalance the strike plate. This setup would allow for the best transfer of power with minimal losses.
You're losing way too much energy from your lever setup.
yh thats also my initial thought. there's probably so much friction and energy loss going on with current setup
yeah, the clip of the through hole lever had too much play in it. so it wasn't pivoting cleanly along the axis. but then again that also is an issue of not having a machining set up to get a tight fit bearing in the lever with proper tolerance.
There's no problem that can't be solved with more balls
4:35 about no experiment, the inertia of a 1 kg mass is higher than that of a 1/2 kg mass, so I would expect we can determine the mass by feeling how it reacts to inertia
I think if you moved the lever down at a known speed, fast enough to toss the weight in the air, you can work out how fast it was moving upwards by how long it took to come back down. There’s only one part of the lever that moved at that speed so you have the distance, and from there you can get the mass by division?
Commenting at my own peril before finishing the video
also commenting at around 435 but yeah when holding still you couldnt tell but the moment you let off the thing and mass drop you would be able to tell
Engineer here, related to the lever Newton's cradle, check the concept of Center of Percussion.
Percussion dynamics are very unintuitive and it's why this might not be working as expected.
When the ball hits the lever it wants to translate and rotate at the same time, so mass and inertia are interlinked.
i think a good way to get a (correct) intuition is to think about it in terms of *acceleration* exerted over distance, rather than force exerted over distance: the small mass is experiencing one meter per second of acceleration over a distance of two meters, whereas the big mass experienced that same acceleration over a distance of one meter. by the time the small mass has finished traversing the first meter, it's already moving, so the acceleration it experiences while traversing the second meter is less, since it takes less time. the confusion comes because normally when we think about acceleration, we're talking about a fixed *time* spent accelerating, so we're not used to thinking about it in terms of distance.
Leave her? I couldn't! I love her! Leave her!? NEVER.
She’d leave you in a second
Leave her Johnny, leave her 🎵🎶
i love you.
not like her.
not like you love her.
but still, i love you
Leaver her? I don't even know her.
@ awwwww
In game design, there's some interesting things you have to account for when you're trying to model a physics engine, and it comes down to how a dynamic system works being very different to static ones.
A snapshot in time (which is what you render to the screen after you calculate the position of objects to be rendered for that frame) is a very different beast to varying conditions over time, and things like acceleration play a huge part in how you have to calculate how an object might move between frames.
What this thought experiment shows is the sum of a bunch of moments where an event starts at a specific point, goes through some process, and has a final state (a moving rocket and a moving weight). You're only interested in the start and end picture, but there is an acceleration curve that both weights go through between them, that has an impact on how that all plays out.
Getting to the bottom of these investigations comes with an understanding that physics is a very deep rabbit hole, even at a fundamental level.
I feel like with the lever in your Newton's cradle idea, it probably has a lot more to do with losses through transferring that energy than it does with some kind of flaw of the idea itself. I think it would be possible with more development. A cool idea nonetheless.
Not losses, but the rotational inertia of the lever itself.
I figured this out by using different cable machines in my gym. Some have an extra pulley and the weights are twice as heavy but feel slightly easier than the ones with half the weight and no pulley. I noticed that at the bottom of each rep, the machines without the the pulley felt harder in the transition to lifting up again.
Pulleys operate with the same force multiplication properties as levers, so I knew as soon as you said waggling it wouldn't help you differentiate that something was off.
friction.
@곧곧곧 No, not at all.
Do not listen to these guys gymatics sensei. They wouldn’t understand
@@launchpadmcquack98 you said "the weights are twice as heavy" and you are sitting here telling other people they are wrong? the weights all weigh the same, the distance they move is what changes smart one
@bmxscape You're misunderstanding what I'm saying. The physical weights on the double pulley racks are twice as heavy in order to achieve the same static resistance at the handle. That's how pulleys work. Double the weight with double the effective leverage on the weight results in the same static load, but I bet you felt real smart typing that reply...
When both sides of a lever are equal, there is no change, as opposed to just directly pushing it; these levers are only used to change the applied force in a convenient direction. Levers in which the load arm is longer than the effort arm are used for gain in speed. It is sometimes hard to understand what a gain in speed means in the equations we solve since we make assumptions.
we can separate levers by there MA into tree types
MA=1 Effort arm=Load arm (Change in direction)
MA>1 Effort arm>Load arm (Gain in energy) (But loss in speed)
MA
18:45 had completely forgotten 😂
Here's something I find puzzling which might be related:
Suppose you go ride a bike today. Initially a friend pushes you to get you up to speed. Then you exert a constant force let's say 100N for 100s, and the air resistance exerts an equal and opposite force so you don't accelerate at all during that time. Let's say you travel 100m. So the work you did was 100*100=10kJ.
Tomorrow you go ride the bike again. Again your friend initially pushes you up to speed, and you start exerting a constant force of 100N for 100s. But this time there is a headwind, and the speed at which the air resistance is equal and opposite to your force is slower. This time you only travel 50m. So you exerted 50*100 = 5kJ.
Your subjective experience, I think, was about the same on the two days. But on the second day you did half as much work. What's the deal?
The important to remember about the W=f*d equation we're using is that 'f' is the Net Force on the object. In your first scenario you've actually done 0J of work once your friend let go - as you said the wind force exactly cancels your pedaling, so you might as well be an object floating through space.
The headwind day is the exact same equation, it just feels different because while you're thinking about it in terms of ground speed, your forces are concerned with air speed (which is the same both days - enough for 100N of air resistance).
Calm down before you break the simulation!
An important factor is also very likely the loss of energy through the lever set up, newtons cradles are held in suspension so the force has nowhere to go but through the balls in contact. The extra bits of metal and fishing line attached to a vice grip and the table are a good culprit for how quickly the system stops moving, even with the moments of impact on the lever set up right
Exactly the pivot absorbed most of it
9:28 Different moments of inertia
Yeah, also thought about it. So it's not about static problem, it's dynamic, and this is where simple law of lever stops working, and laws of rotation dynamics appear.
Thanks
I like the whole thought process behind this. It feels very relatable.
10:20 Isn't this kind of similar to how gear ratios work? When you shift into a higher gear, you gain torque but you lower your RPM. In a similar sense the longer the lever is (with equivalent ratio of weight at end), the longer it takes to push the lever down. I think the difference is probably that a gear is more like making the lever longer without adjusting the weight. Longer lever = more torque for a given weight, but each revolution takes longer, same as with gears.
A gear is just a bunch of tiny levers, and they're pushing on other tiny levers, rather than directly on the thing you want to move.
He's measuring acceleration across distance, distance travelled given acceleration is d = (1/2)at^2, so time is t = sqrt(2d/a). Since both masses accelerate at the same rate, the one is accelerated for longer due to this. You can see they have the same acceleration in the static example, where the same force is applied and both accelerate against gravity at the same rate (10m/s^2 in the example).
I wouldn't say similar, I would say identical, same exact systems and reasoning there.
The distance doubles, so no free energy. Im sure you discuss this later on in the video, but as someone who routinely uses levers to move things like concrete blocks, think of levers like you'd think of a gearbox. Your rocket has to travel 2m to affect 1J on the 1kg mass.
4:30, push it super fast. The bigger one will have more air resistance and feel heavier.
Also, I think I'm right that an object at rest will stay at rest too. So there's a chance that the mass difference could be..... And the video says that's a thing. Lol
8:14 matt parker is from the streets
24:07 "... stranger than they first appear, and so are police"
truer words...
Mechanical advantage is when you give an inch of your rights, and the pulley's force takes a mile.
pulleys
20:45 Looks like you nailed the setup, and the reason it doesn't bounce very long is your lever is flexing and that is eating some of the energy. Try using a more rigid lever like a harder metal, or something like carbon fiber.
Not only the lever, but also the pivot, the cradles en how these are connected.
Flexing should not be a problem as long as they return to the original shape without too much energy loss.
Think springs. (e.g. pogostick)
@@guustflater9232 I recommend air bearings on the pivot, because it is so much easier to hide the energy consumed by the air compressor when demonstrating my perpetual motion machines. Oh wait... Don''t read that, O.K.?
I'm only at 6:31, but shouldn't the 1/2 kg rocket move slower? In this situation, the 1/2 ball effectively gets 2 J of energy. So, either the math is wrong, or the assumption that the rocket must experience the same force is incorrect. The rocket would push harder in this case. If it's pushing with 1 N, it should have a harder time turning the lever, which means it would move slower. It's probably not half the speed, but like 20-30% slower. Most values stay the same in a 1:1 situation, but yeah, levers are weird indeed.
That's what my gut feeling would say-no mathematician here, hehe
EDIT: 7:45 lol. Anyway, I was thinking about the different feeling you'd get in a gym when lifting a weight 1:1 versus through a pulley. Even if it's half the weight, it feels more draggy and resistant to movement.
EDIT2: Ah Okay so actually 41% of the speed
4:27 - Being "clever" (read: smartass), very technically as the black box was drawn there IS an static experiment you could perform to determine the mass of the object hiding in the black box. Simply remove your finder and let the lever end, hidden in the box, touch the table. The angle of the lever and height of the pivot will let you work out the length of lever hidden past the pivot and with that information (and the static force from before you removed your finger) you can work out the mass. ;)
I say the box goes far enough down that you can't do that, but you can still tell due to the mechanical advantage's inertia. The end of your lever simply won't accelerate as fast with a weight a longer distance away
@@AirNeat All objects fall at the same rate... this is how pendulums work.
Physics tutor here. You are correct that this is very similar to an impedance matching situation, that second piece of fishing line that you introduced, is actually functioning as an elastic storage and turning the lever into a harmonic oscillator. In terms of your original paradox, if I act on the lever with a waggling force mg + A cos(ω t), the mass m at distance L feels this force and due to F = m a, the first lever responds as y(t) = A/(m ω²) cos(ω t). The mass ½ m at 2L, feels half this force due to its mechanical advantage, but also has half the mass, so it actually describes the exact same y(t)! But your finger at distance L, travels half the distance for that same y(t).
Now here's where it gets interesting for me: I think that the frequency ω chosen is independent of the load, you just have a preferred frequency that you want to shake your hand at. Since you are not tuning this frequency, you have no way to know that this isn't a harmonic oscillator, e.g. a rebar that is stuck in the ground. You can tell that based on comparing low frequency and high frequency jitters, how they move the thing, but it's my claim that none of the people you ran the experiment on, actually did that. “same force, half the motion” then _unintentionally reads_ as, “this feels like a stiffer piece of rebar.”
If that's correct, then if you repeat it with ½ m at √2 L, you can do the inverse experiment! You give the levers oriented vertically to someone, ask “are these the same,” they will jiggle them and say “yep!!” ... Then you will invite them to just push them down to the same distance and hold them both down in parallel and they will say “oh, this bar is 30% lighter than that one!!” and be appropriately amazed.
Im sure you are that "clever" person, Steve was talking about in the beginning.
And besides the big ass text you still had the urge to tell us that you are some tutor.
My intuition about fishing line is that normal monofilament line is 1) pretty stretchy and 2) doesn't spring back instantly after stretching, more like it's measured in seconds to minutes. This intuition leads me to think the line is acting not just as a spring but also introduces damping and therefore energy loss.
Nevertheless, I guess it's possible that my intuition about the line is actually wrong, confused by som other phenomenon of the mechanics of trying to pull my bait loose from some rock.
If otoh my intuition is correct, then trying other line materials (dyneema?) might provide some "pretension" for the lever with less spring- and dampening effects?
I was immediately thinking about the wiggling as a source of defeating the "black box", thank you for framing that up so succinctly! I agree with the interesting inverse experiment, and this is somewhat along the lines of the "source of unintuitiveness" discussed in the video, with other hypothetical setups.
@@simon7719 you are mostly correct, the line will be stretched out a bit at equilibrium so it does spring back both ways, but it's definitely not a great material for energy storage. In mechanical watches you get thin metal bars coiled into spirals to store energy, which is overkill for this build but would look so cool.
Okay, I'm going to guess right now, at 5:00, that there's something wrong with this idea of "moving" the bottom part of the lever "one meter." The whole thing would be rotating, not going straight, and if the weight flies off the end of the lever, then it can't have really gotten the 1N of force the whole time.
wtf
Revisiting the black box at 7:40, not having seen the rest of the video: Sure, the force is the same, but the acceleration won't be! The moment of inertia of the half kilogram configuration is double that of the one kg. The finger exerts the same force, and the same torque, on the lever in both cases, but that's in static equilibrium. Once you try accelerating the mass, the moment of inertia of the longer lever resists the increase in angular velocity more than the shorter, and you'll notice that you need to push harder on the longer lever to pivot around the fulcrum at the same rate.
The work equation is blind to the *rates* of transfer. It takes longer for the same force to transfer the same amount of energy through the longer lever. You can imagine trying to push against the black box levers in both cases. It's hard to apply a consistent force, so you might be tempted to move your end of the lever at the same rate for the longer lever, but this requires a larger torque to overcome the larger moment of inertia for the longer lever, so you'll need more force, and you'll work harder. This may seem strange when you consider that there is indeed no difference in your experience as long as the lever remains stationary. Rotational dynamics are not quite intuitive!
The rockets confuse the issue because they presumably thrust for the same time, but one will encounter more resistance in its path than the other, and will have failed to rotate the lever as much before it ceases firing, thereby imparting less energy into the mass. (Remember that the fulcrum is fixed in place; if the second rocket were trying in vain to push aside the fulcrum, it would successfully transfer zero energy to the mechanical system, which should come as no surprise. This is like that, but there's a spectrum to how much the fulcrum is able to impede the motion of the rocket, depending on the size of your lever.) Instead, because the rocket's leftward velocity doesn't get as large, its propellant's rightward velocity is larger on average over the whole thrust, and that's where the missing energy goes.
11:21 Ooh you should definitely talk about this with Mehdi from ElectroBoom 😂
Exactly my thought.
My first thought while working this out is that mechanical advantage is analogous to transformers, so if you have an advantage of N, then the impedance on the other side is not scaled by N, but N^(2)
For the example you gave with a distance of 2 (N=1/2), the mass that would feel the same is 1/4 the original mass.
This is equivalent to what you mentioned about reducing the distance by sqrt(2) to feel the same
me too. Levers are mechanical transformers. I clearly remember myself having this "hey, what value does a resistor feel like from behind a transformer,... i guess it's multiplied by the ratio" thought, but then something else didn't quite line up, and i thought this through and came to the n^2 ratio.
With that already ironed into my brain, i was instantly able to point out where Steve's initial explanation went wrong. But that is indeed not immediately intuitive.
Moment of Inertia: I'm gonna end this man's entire career!
I was thinking about moment of inertia and rotation the entire time.. you can't imagine the grin that came on my face when you said that was wrong!!! I LOVE getting to the part of a problem where the last theory you have is finally gone and your only option is to hunker down and be humbled with new knowledge
I don't know if this will come up later in the video, but the "black box" assumption at the start is just wrong: The both configurations with different masses at different distances from the lever point such that the torque (m×d) is the same do not have the same moment of inertia (m×d²). This means the finger can distinguish between them, if it is allowed to push and feel how the lever moves after pushing (as is suggested by the animation. And this is exactly what the rocket experiment is doing.
In particular, the rockets take different amounts of time for their 1J-push at 1N, because the moment of inertia that they are pushing against is different.
yep this is the first thing I flagged as wrong - if the finger is completely still, it feels the same (same static force), but if you're allowed to wiggle your finger and feel the dynamic response you can tell the difference
I understand levers
The entire video is basically "look at all my assumptions and how they turned out to be wrong"
Yeah and that's why his intuition was wrong. But moment of inertia doesn't apply to the pulley example, so you have to do some different math.
It's something that falls out due to mechanical advantage, which itself comes from W=F*d, which comes from the kinetic energy formula, which comes from the 2nd law of motion (F=ma), by including displacement.
F_effective=(force/advantage)=ma.
10N/1 = 1kg * a
10N/2 = 0.5kg * a
10N/1/(1kg) = a = 10 m / s^2
10N/2/(0.5kg) = a = 10 m / s^2
You can also tell they accelerate at the same rate, because it takes the equal force to accelerate them both against gravity at a static position (which requires them to have the same F=ma, meaning your finger must experience the same mass, meaning the effective force yada yada)
final_v = a * t
But here we're applying the force for a certain distance, based on the kinematic equation:
d = (1/2)at^2
t = sqrt(2d/a)
therefore,
final_v=a*sqrt(2d/a), which simplifies to sqrt(2ad)
fv_a = sqrt(2 * 10m/s^2 * 2m)
fv_b = sqrt(2 * 10m/s^2 * 1m)
the first two terms cancel when divided, and poof (fv_a/fv_b) = sqrt(2) drops out. Generalizing, you get fv_a/fv_b=sqrt(d_a/d_b)
It is because of mechanical advantage, which doubles the distance and halves the force. The issue is that we're accelerating the objects at the same rate but one travels a longer distance.
It actually makes perfect sense if you think about your "finger force" as accelerating the mass at 9.8m/s^2 upward in the stationary example, in both cases. And both are traveling 0 distance, which is why they feel the same. The moment (no pun intended) you implement distance(d) > 0, the final_v=a*sqrt(2d/a) comes into play. Technically net acceleration is also 0 in the static case
@@refindoazhar1507 Yes it is. And you should explain why the pulley example has the same problem as an exercise for yourself (ignore my other comment about it thx)
Alternate video title "Content Creator Discovers What Work Is"
A pretty cool video, still I'm disappointed that I didn't hear torque mentioned even once throughout the video.
Nah I liked it, made me feel smart for once
Or triangles/trig
I heard it, but only for a moment.
😉
The answer lies in:
Torque vs horsepower
Force vs power
And trying to conserve ENERGY!
Momentum match
Kinetic energy match.
Totally elastic collision.
Maximum power transfer theorem.
Holy shit - I loved that video - Please do more videos in the same style!!! I loved it from the start to the end!
22:00 - What if they were side by side instead of on top of each other? This would eliminate the elasticity of the fishing line and your forces on both sides would be equal.
This is also what I would liketo see
At first I thought you had misunderstood the point of the experiment but on second thought I think that's a great idea. Very creative. I hope Steve tries it
Don't think that could be done. The strings holding the bearings would cross each other.
@genxjack72 obviously swingsets don't exist because if two swings were next to eachother the chains would cross paths and get tangled up /s
You can place two newton's cradles next to eachother without there being any overlap, they don't have to share a stand or whatever you were imagining. In the video, its clear that he has 2 basic newton's cradles each with their own frame that are just held in place with a 3d printed stand, so it's as simple as removing the 3d printed parts and placing both frames next to eachother
I suppose it would depend on whether the suspension strings need to be at a specific angle for them to work properly and if the impact point still needs to be a specific distance from the pivot point.
Have you pondered the idea of not making a lever at all, but using a fixed piece of steel. If you say that the shockwaves (as mentioned in the Action Lab video) are a possible explanation of the force behind the Newton Cradle, then a piece a steel that is fixed and has some internal flexibility in it, let's say springsteel, there is a chance that the 'shockwave' will propagate through the steel and drive the second newton cradle. In essence your got to stay very still to move 😉A bit like when you hit a hamer on a steel block, it bounces off really hard...
Came here to suggest the same thing!
It is the same with electronic technology. Get this: when you use a transistor to amplify signals, it always looks like you are getting more energy out than you are putting in. The energy, however, is coming from a dc voltage source which, along with resistors, is used to bias a transistor into the "active" region, which is how it gets the energy to amplify the signal. A "tunneling" diode has a unique function where it provides "negative resistance", which put back energy which is lost by the resistive contact between a sensitive probe and an experimental sample. However, in order for the tunneling diode to work, a dc energy source has to bias the diode into a current-to-voltage quiescent point where the negative slope of the curve is located. So, we still cannot violate the laws of thermodynamics by using a transistor or a tunneling diode.
Damn the laws of thermodynamics. I've been trying to beat that damn law for the last 25 years...
It is the same gear problem, when you have a magical transistor (no bias loss) your still get watts in equaling watts out because you halve the amps when you double the voltage.
@@GoldenEDM_2018 If you cant beat it, join it, I guess
While watching the "black box" explanation of the two levers, my thought was that while the force of the finger is the same, the reaction at the fulcrum and internal moment of the beam are different. This tangentially gets to the leverage discussion that was the solution, but I wasn't pausing to work through it all. Good stuff!
23:15 it’s always the lagrangian
One idea about the position on the lever with the pivot point on the back (22:01): I would suspect that the width of the lever plays a role here. Because it is quite thick, I would argue that striking the front of the lever at a certain height is not the same as striking it this exact distance from the pivot point: rather you are actually striking it farther away. And because the distance relevant for the lever is the distance to the pivot point and in this configuration the width contributes a lot to this distance, the position seems to deviate a lot from the theoretical positions (which is of course the distance from the pivot point, not the height above the pivot point).
I hope this makes sense, it is a bit hard to explain fro me without a drawing or something like that.
The theoretical levers, such as in the diagrams, always have their pivot in the center. The real world lever isn’t really pivoting, it is rotating around the pivot behind it. This definitely makes things more complicated to me.
That's what I was thinking too!
moment of inertia!
You crack me up with your "evil mastermind" arguement for buying the Odoo management app. LOL! I'm still chuckling to myself 5 minutes later. Nice one.
Moment of Inertia. Just say Moment of Inertia. What haven't you said Moment of Inertia yet? Finally, at 15:10. That's your answer.
1:00 "I'm sure you'll lever comment..." 🎉
This all really can be understood by realizing that rotational energy is also present in the system... since one lever has a greater rotational inertia, it will have a lesser rotational kinetic energy.
That makes sense. While you were laying out the logical steps before getting to the point where "hang on, did we just get in more energy than we put out?" and I realized, at least I think I did, that one of the assumptions made was incorrect. The mass does move across double the distance for the same applied force, but that doesn't mean it's traveling at double the speed. After all, the work equation is just "force x distance" and doesn't have a time component. So the half-mass-double-distance object would actually be traveling at √2 times the speed of the first example, thus preserving the known laws of thermodynamics.
And it was pretty clever to point out earlier that that √2 would be useful later.
5:10 You claim that the acceleration of the rockets will be the same, but it wouldn't. It is pushing on a greater moment of inertia. I bet that is what the rest of the video is going to be about.
My guess was something to do with some forces coming from the pivot point.
Being absorbed by
My thoughts as of 6:40 - A lever wouldn't operate as depicted in space since the pivot isn't fixed in place. A force would need to be exerted at some additional point along the lever in order for it to operate as depicted, and this force is the source of the extra energy.
Oh! That’s a good point. I was feeling like these difference at this point is a lever in space doesn’t have gravity pulling on it, so maybe levers only work how we imagine when they are flat against the earth. Which would explain why he had an unexpected problem when trying to use one sideways.
I know what you're trying to say but I'm not sure that exrra force is imparting extra kinetic energy into the setting because it's not moving. Its like pushing against a house. It doesn't matter how hard you push, it doesn't increase KE because it doesn't move.
I want to be proved wrong if i am
there is extra force. in space, this setup would not move as shown unless you had a rocket engine pushing the fulcrum rightward at a tuned magnitude to the interaction with the rocket.
@@isaacyonemotoI believe this extra force that you are thinking of would be a bolt or bering at the fulcrum to fix it as this is just a 2d problem
that's exactly what I was puzzled about, when I was calculating optimal balance weight and shape on crankshaft of combustion engine. you need certain amount out m*d to kinda cancel out forces, but if you look into racing, you want the engine to spin up faster- less inertia. you cannot make counterweight directly lighter, because you throw it out of balance. And this gave me the insight to spot your "mistake" . AND because of this I think quite a lot of engine builders/tuners shave off weight not optimally to keep balance but to reduce inertia.