Hidden Beauty in a Rolling Wheel
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- Опубліковано 11 лип 2024
- This video takes an in-depth look at a rolling wheel, and demonstrates that the point on the wheel that's in contact with the ground is instantaneously at rest. In addition, this point acts as the instantaneous center of rotation, which means that all points on the wheel are (instantaneously) rotating about the point in contact with the ground. In my opinion, the fact that the contact point is the instantaneous center of rotation is probably the most interesting aspect of a rolling wheel. And of course, if you're going to talk about a rolling wheel, it would be criminal not to mention that the path of a point on the periphery of wheel traces out a cycloid.
Special thanks to my partner in crime, Marc Renault, for helping get the video footage of a speeding car. Thanks also to Jonathan Barrick, for making the beautiful wheel, and to Noah Lape for helping record the intro/outro clips.
Music credit for the car scene:
Stock Media provided by AudioSphere / Pond5
Background music for the rest of the video:
Music by Vincent Rubinetti
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/album/1dVyjw...
The wheel graphic was adapted from github.com/sparshg/animations, and was used in a similar rolling motion video at • Rolling motion animati... .
I think you just made me understand why the Scrambler at a carnival feels the way it does. Great video!
Glad you enjoyed it!
Great video! Your talent for explaining such topics is remarkable and your use of animations to draw attention to certain parts of what’s on the screen is excellent!
Thanks! Glad you like it!
What a nice and well explained video about the non slipping rolling wheel phenomenona. In my times as student all was abstract black and white books. This kind of audio visual material make all more intuitive, I showed your video to my students which help them to understand this topic.
Great to hear. I will eventually be doing a lot of videos that I think will be really useful to students.
Your videos have the same energy as old physics videos from the 1900s (in a good way) we used to watch while studying physics. Your passion is really enjoyable!
Wow, thanks....I think! :)
Holy moly. I learned something while sitting in the train. ❤❤❤
Awesome!!
Even cooler is that on a train the part of the wheel rim below the top of the track is moving backwards
@@RickReid-nh6gm Yes, that may very well be cooler. I thought about going into this, but thought there was already enough (perhaps too much) in this video. Believe it or not, this concept comes back in the Square Orbits video (Part 1).
The amount of work done for these videos is insane. This channel is so detailed and I love how the explanations are both intuitive and detailed.
Glad you like them! And yes, they are a lot of work!
Amazing video, I’ve never before had a concrete grasp on what rolling motion is, but when you described it as rotational and translational motion it clicked immediately
Fantastic! Glad it helped!
Incredible video.. Extremely good explanation.. awesome animation.. Totally loved it.. Definitely subbed and would wait for your next video.. Keep up the great work.. I must say the Animation is superb..
Thanks so much for the kind words. I tried to make the animations both useful and pretty!
@@AllThingsPhysicsUA-cam Could you please share how you made the animations.. maybe a tutorial video.. That would be great too.. and very helpful.
@@AmitKumar-xw5gp Some of the animations were done using standard video editing software, but most of them were made using a mathematical animation engine (programming package) called manim. Manim was developed (and is under continual development) by Grant Sanderson for making the animations used on his 3blue1brown UA-cam channel. There are a number of manim tutorials already available, and as I am not a manim expert I will probably not delve into making manim tutorials, at least for the time being.
@@AllThingsPhysicsUA-cam So, did you outsourced the manim part to someone..?
@@AmitKumar-xw5gp No, I did it all myself, but I am still learning as I go. I could probably do a manim tutorial, but for now I want to focus on making videos for AllThingsPhysics.
Great Video! It's crazy to think about a wheel rotating around its contact point with the ground.
That's my favorite aspect of a rolling wheel!
It’s actually easier if you imagine a square (or n-gon in general).
Such a shape would actually rotate around the contact point before instantly switching to the next one.
@@fullfungo I hadn't thought of that, but you're right, that does make it easier to think about. Thanks!
@@fullfungo Rarely do I find such insight in youtube comments, that's an incredible way to visualise what's occurring!
Also, the dynamics of a rigid body (all points always at the same relative distance to each other) only allows for rotations and translations. Thus, if a point is instantaneously at rest, then the only possible motion for a rigid body is an instantaneous rotation around that point.
This the highest gift one can offer for the love of such a wonderful subject Physics. All your videos are phenomenal and your are an amazing communicator. Thank you!!!
Thank you so much for the kind words!
The greatest tesla adv that can exist XD
Amazing work, as all your videos I've seen so far )
Thank you! Please feel free to share with others who might be interested!
This is great David
Super ! I suspected Fourier was the next logical step. 👍
This great. Complex but simply explained
Amazing Video
This is nice, David!!
Thank you!!! Great video and great explanation!
Glad you enjoyed it!
Absolutely excellent video, I loved the format and the pacing.
Thank you so much!
Tanks for another interesting and instructive video, and "it's a relief" to see that sometime theory and practice actually line up :)
Best regards.
I will never think about a rolling wheel the same again.
👍
Nice job!
I like your deep vision of things around you. "Dimensional view".
This video is a real beauty. Wonderful video and explanations. Great!!
Than you! Please consider subscribing and sharing the video with others!
Might just be the best physics videos I’ve ever watched. Thank you for your hard work on this, makes a lot of sense!
Thanks! I’ve been overly busy for a while, but should be making more videos soon. Stay tuned!
Is a great explanation. Thanks. It's more intuitive if you watch a bulldozer moving, the tracks are eerily motionless!
@@johnwakeling9233 Yes, I with I would have thought of a bulldozer when making the video. Such a great example!
Superb video.
Thanks! Please consider subscribing and sharing the video with others!
Mate I wish I had physics lecturers like you in Uni - my physics exams would have been a breeze as opposed to what I experienced !
You rock, dude.
Probably because I used to play in a progressive rock band! 😄
Amazing Video, Understood very well I hope you upload more because your content deserve more appreciation 🙏
Thank you. I’m about to make a new batch of videos, so stay tuned!
Fantastic
I wish I had a teacher explaining physics like that , I'd definitely became another Einstein .
I had enjoyed every second of this video .
Thank you
Cool. That's great to hear.
Nicely done! Will be using for my class!
Great! I hope it's helpful. And please feel free to share with others who might be interested!
An excellent presentation on vectors for a wheel in motion.
Glad you liked it!
I figured this out while riding my bicycle in 1975. Looking down on the wheel, I could see the axle was in focus, the ground and the rim in touch with the ground whizzing backward beneath me, while the top of the tire was whizzing in the opposite direction at an even greater speed (2X). I then sketched out the "cycloid" - a term I wasn't familiar with till now, plus the horizontal velocity of any point on the tire (a thumb tack) which is sinusoidal. Superimposing the two curves realy messes the mind - so much so that it created the first big rift with my then girlfriend (mathematician/engineer; we're still married). The whole excercise gave me some initial insight into relativity - i.e. motion and velocity are very much dependant on the position of the observer and/or participant. Thanks for the video (and flashback)!
Glad you enjoyed it!
Спасибо! Очень познавательно!
Is it worth doing a video on Aristotle's (not a) paradox? New to the channel, great work, many thanks, subscribed. 👍😀
Physics makes what seem like ordinary things seem so amazing!
Ordinary things are often amazing if you look closely!
Bravo
Although it would add to the length of this video it might be worth pointing out the advantages of the point on the very top of a rolling wheel --- noting that it basically is the end of a 2nd class lever with a fulcrum at the wheel's bottom. This fact allows one to push a car on a level surface with about half the force needed should one push from the rear bumper, making the task much easier. Also, it's why no matter what size glass plate you have in a rotating microwave oven, the glass plate will rotate at twice the angular velocity of the carousel wheel it rides upon. And why tank treads move at twice the tank's speed when running on the top as opposed to the ground, no matter the configuration.
Nice comment...some very interesting points indeed!
Although I understand the explanation, it is/has always miraculous to me how a wheel/car can moving while the point at the ground is motionless. I had also that same feeling when looking at the track of a moving tank. (didn't need a high speed camera for this, to see that wonder)
Yes, the tank example is a great way to understand this phenomenon!
35 yrs ago, the teacher of mechanics promised one degree better grade for those who can write a code that draws the path of a point of a rolling wheel on the schools Commoder 16s. We were not bad at coding and not bad at math, still we could not grasp the function that describes that motion although we knew it was called a cycloid.
Since then, this story came to my mind once in a while but I didn't put much energy in imagining it again and solving that good old task.
It was nice remembering it again and moving a step closer to the solution that waits for me to go on pension.
So glad I could bring that memory to you!
Math & Physics hippies are the best hippies.
Technically, the ground is not at rest because it is moving, we just do not realize it because it is not moving relatively to us.
Excellent video! I'd liken your videos to a physics version of 3blue1brown videos. Fascinating and incredibly well taught concepts! I'm amazed your channel only has a few thousand subscribers.
Cool, thanks! Please feel free to spread the word, I'd love it if a few thousand subscribers became a few hundred thousand!
So would a picture taken not show the point of contact being sharp image, whilst at top it is vey blurry?
That would be a convincing demonstration for me. Like your explanation and your animation (watched it without audio/subtitles, you may have discussed it)
Yes it would, and it's in the video. Watch it again, that's one of the most convincing parts!
I love the text animation how did you make it 😊
I use a program called manim (a Mathematical ANIMation engine), written by Grant Sanderson of @3Blue1Brown. If you're interested, I give a shoutout to Grant in this video: ua-cam.com/video/mq7j5jKxV-0/v-deo.html.
Enjoy!
From the way you analyze things in the few videos of yours that I've watched so far, I suspect you would also find the Acceleration of points on the wheel interesting. That motionless point at the bottom is undergoing acceleration. . .
Indeed it is!
Why didn't you show the motion of a point halfway between the center and the outer edge?
Just because I didn't want the video to get too long and complicated. But if you watch the square orbit video (part 1) you will see that I do exactly that!
Very nice presentation :-). If you need ideas for future videos: how is it possible that the friction between the ground and a wheel can propel a car. This has kept me awake at night as I just haven't been able to wrap my head around it. The point of the wheel at which the friction is acting upon is at rest (v=0), thus the power produced by the friction force (F*v) must be zero. So are car wheels in reality slipping a bit? What is going on?!
You ask a great question, and I do plan on addressing this question. There are (at least) two more rolling wheel topics I want to address, but It won’t be until after the next couple of videos. But you are correct, the power produced by the friction is zero! Stay tuned.
Kinda like watching a tank track. The lower part of the track in contact with the ground doesn't seem to move. The upper track seems to move twice as fast as the tank itself.
Yes indeed! I hadn’t thought of that!
That's the first thing I thought about when he asked the question. When I was a kid, watching a parade, I was surprised to see that the part of the tank tracks that were touching the ground didn't move at all. It's not that they didn't SEEM to move. They actually don't move. I seems to me that they do APPEAR to be moving, especially from a distance. But up close, as a kid watching a parade, it was clear to me. What was less clear at the time was that the top of the track is moving at TWICE the speed of the tank, as you mentioned, and as the video mentioned about wheels also.
@@johningram2153 On second thought, the tracks are constantly moving.... relative to the tank :P
@@fredsalter1915 yeah, but I meant relative to the ground.
@@johningram2153 I had not thought of a tank (or bulldozer) when I was making this video. Wish I had, I would have included that as an example!
This is all from the point of view of the observer attached to the ground. An observer attached to the axel would argue no points on the wheel are at rest. And an observer attached to a point on the wheel would likely feel no movement, only a force, proportional to the wheels rotation speed, in a direction away from the axel.
Yes…frame of reference is the ground. But if you’re on the axle, wouldn’t the wheels center look to be at rest? And if you’re on the wheel itself, I definitely think you’d feel movement…I mean, you’d get dizzy as hell (unless you happened to be at the center of the wheel), wouldn’t you?
@@AllThingsPhysicsUA-cam If your reference was the axle then there would be a point at the wheel's centre of rotation that doesn't change its position relative to you, but it would just be a point, not an actual area. Every single atom in the wheel would be rotating and tracing a circle around that point, and if there was an atom that was absolutely perfectly aligned with that centre of rotation then it would not be moving, but it would still be rotating and therefore not at rest.
I think of being on the wheel as the Hermes spacecraft in that movie The Martian, where they create an artificial gravity by spinning up a circular part of the space station. You might get dizzy if you hang out in the centre of the wheel as you would be approaching a point where you're just spinning on the spot. But otherwise you would just be pressed against your surroundings; either the other atoms in the wheel if you're actually a part of the wheel, or just pressed against the circumference of you were an object inside the tire.
@@AntonBurnsRed You are correct that it is only a mathematical point that would be truly at rest at the center of the wheel. And yes, in whatever frame YOU are in, you would appear to be at rest (to yourself).
13:02 can there be "motion at one instant of time"? I can only understand passing of time as an integral part of motion, meaning:no time elapsed=no distance travelled.
Assume something is moving with a constant velocity. Does it move at every instant of time? I think so. You may not be able to *calculate* the speed at a single instant of time, and based upon that single instant you might not know it's moving, but that doesn't mean it *can't* be moving.
4:23
Quick question: how is omega a vector? What is its direction?
The direction is perpendicular to the plane of circular motion, with the direction given by the right-hand rule (if the fingers of your right hand curl in the direction of circular motion, then your thumb gives the direction of the angular velocity vector.
Air is compressed and the tier is bended, and it acts more like caterpillar
mathmatical proof that slamming into something stops you cold and momentum will make the rest of you move.
I know the two are totally unrelated, but is the blurring of the round dots @ 2:45 caused by a similar phenomenon or measurement uncertainty that makes position and momentum of quantum objects probabilistic instead of deterministic?
No, this is simple motion blur. The dots are moving while the camera shutter is open; the more they move the more they are blurred.
This is relative to the ground. Relative to the center of the wheel, the bottom of the wheel is moving backwards and the top is moving forward faster than the center. The front AND rear are not moving at all. Motion is relative, in this case I think the relative is middle sibling.
earth is flat and therefore wheels are rectangles.... jokes by side, cool video :P good visual presentation of the concept =)
I'm actually thinking of making a square-wheels video.
@@AllThingsPhysicsUA-cam u mean canadian wheels? :D
What happens when the wheel rolls on a treadmill?
Could you explain how friction causes a wheel to begin rolling forward?
If there were zero friction, then the wheel would be totally unaffected by any horizontal forces from the ground. Thus, if it was not spinning at all, it would remain "not spinning" while sliding along the ground (think of really slippery ice). But if there is friction with the ground, then the ground will impart a horizontal force acting at the point of the wheel in contact with the ground, and this force will cause a torque about the center of mass, which will lead to an angular acceleration about the center of mass. The result is that the wheel's rotational velocity will change. If it is not rotating initially it will begin to rotate due to the friction force from the ground.
Hope that helps!
@@AllThingsPhysicsUA-cam Thank you for your reply! I would like to know how friction makes a wheel roll forward or backward instead of just spinning in place. I understand that friction provides the force to make the wheel roll, but I'm unsure about the specifics of how this happens. I have an explanation, but I'm not sure if it is correct. Could you please take a look at it? Here is the link: ua-cam.com/users/shortslxwDwGvLbP0?feature=share (UA-cam will delete my comment if I it has external links, so I change the picture to a video, and put text in the comment).
@@cosmosben6726 The mechanism of how a spinning wheel becomes a rolling wheel is discussed in detail in this video: ua-cam.com/video/auJPuzKigGA/v-deo.htmlsi=n-2dwlVCTXjbzvB7.
how about , 'rolling wheel' ; a continuous falling mass overcoming friction by circular motion , momentum and or any means of external force ?
can i roll the wheel at the speed of light (299792458 m/s) ?
You can try! 😂
Not even the mathematical construct at the very center of the wheel is stationary because it is both rotating and moving laterally with the rest of the wheel.
This can say that even though the point is covering 2πr distance in time period T but then also it isn't covering exactly 2πr/t distance in unit time
Or the velocity isn't constant .......🤷
the non rotating centre of wheel is there for real, not just mathematically. it is however impractical to observe with current experimental technology.
wow, that's exactly what i was guessing before you showed it, that a wheel rolling on a surface moves its' centre of rotation, to impart the movement.
I think it's debatable whether the true center of the wheel exists physically. I mean, you can always zoom in more and more and you will continue to see that everything is rotating about some ever smaller region, and this can go on forever!
@@AllThingsPhysicsUA-cam : it's no different to trying to show the gravitational centre of two bodies. the point really does exist but, we are limited in being able to point it out, as measurement doesnt allow infinite precision.
would you say you cannot find the centre of a 40cm ruler? because the same ruler can be spun around centrepoint to scribe a perfect circle at ruler ends.
@@Chris-op7yt Correct, I would say I cannot find the center. I agree that there IS a center, but finding the true center point physically doesn't seem possible. 😉
It is a trick based on the wording. You first say that at "each instant of time" and does not mention that in every instant it is a different point. If you don't catch the significance of "each instant of time" it leads one to think that there is a single point that is not moving. But given that a tyre distorts when it has weight on it, it is not an instant (ie Delta t =0) it would actually be a measure time and instead of a point it is a segment.
I’m assuming a perfect situation, with only a single point of contact, even though this is surely not realistic.
The setup felt similar to ua-cam.com/video/PWvIYU_Z8z8/v-deo.html lol, great video and explanation!
Hello. Yes, I made use of (and adapted) the wheel graphic from your video (thank you); it is a very nice image that allowed for a seamless connection to the car scene and the white wheel I was using in the lab.
The speed is zero, but the acceleration is not. It's like when tou throw a rock straight up in the skies. At its highest point the speed will be zero, but the acceleration is not. I didn't know you can call accelerating things "at rest". That just sounds weird to me, language wise, even if the speed is zero.
Yes, I debated long and hard over using the phrase "at rest" and tried to always qualify it with something like "there's always a point when it's at rest" to imply that it is only instantaneously at rest.
I like to imagine it as a vector field of speed and as a vector field of acceleration. At the zero speed point the speed is zero but the acceleration is not, so the next instant the speed will be bigger than zero, because of this axeleration. As a result, the point will move around the tire, but at that that specific time (instantaneous) when the point in the tire touches the ground the velocity is zero. Who wants to know more: The direction of acceleration at that "zero velocity" time is ⬆️ up from the ground.
And the speed is zero the acceleration is not, made it click for me.
The math is handy to know, but to my knowledge we have no proof of the concept of a single point in space or time. It's possible that space and time are quantum phenomena that increment in non-infinitesimal quantities, making the instant of time and space of that "contact point" impossible.
think of the wheel as a bunch of sticks bound at the center point. remove all but one stick.
Wait a second, ok, this is a year old, but did I hear you correctly? You said that a rolling non-slipping wheel, that every point on the wheel has the same translational speed.
Isn't the point at 12 noon going to 3 o'clock going faster than the point that was at 3 o'clock and going to 6 o'clock? The 12 o'clock would be going faster and the 3 o'clock point would be going slower....(?)
I don't think you heard it correctly. You can think of a rolling wheel as having a combination of a purely translational velocity, in which every point moves with the same translational speed, plus a purely rotational velocity, in which every point rotates about the center. The actual motion of a rolling wheel is the sum of these two motions. So yes, ultimately the point at 12 O'clock is moving faster than any other point on the wheel.
Does that make sense?
Dont all wheels roll?
Depends on what you mean by "roll." Some wheels "roll" without slipping, and some "roll" while slipping.
@@AllThingsPhysicsUA-cam so basically wheels that are road safety hazards are the ones that slip
This is another really cool video. It's neat to revisit these mechanics topics. I don't know if Relativity will ever be a subject that you address, but if it is I hope you can tackle a question for which I have never been able to find an answer. So far as I know, empty space does not impose a drag force on material objects that move through space. So, if you threw a hammer in the most remote section of the Bootes Void, it would move in a straight line for a very long time -- no drag force to decelerate it [assuming perfectly empty space]. So if there is no frictional interaction between matter and space, why do the galaxies get carried along with space as it expands? What force is binding the galaxies to space so that the expansion of 3d space manifests as the movement of physical matter?
I'm homing in (hehe) on your use of my pet peeves. At 2:23 you say you used a "fast shutter speed", which is of course not true. You use a fast shutter. Or a high shutter speed. or a high speed shutter. But not a fast shutter speed, or fast speed shutter. It's funny how instinctively when we would say 'fast speed shutter' we know it's wrong but change the order to 'fast shutter speed' and suddenly - though still wrong - it sounds less wrong, probably because we've heard it (wrong) so often. Oh, and at 11:54 you mention a slow shutter speed.
On topic! If the top of the wheel is travelling at twice the translational speed of the wheel, would that mean a car could never go faster than half the speed of light as that would mean the top of wheel would exceed the speed of light?
Alternatively, could we have a loooong metal rod attached in the middle (like a propeller) to some extremely mega super powerful electromotor and floating somewhere in space where the rod itself has a length of c/(2*Pi) = say 48.000 km and have the electromotor drive the rod with a frequency of 1 Hz? Because that would mean the ends of the rod would move a distance of 2*Pi*R per second and exceed the speed of light? At least in the frame of reference of the electromotor. I've been thinking about that very question for decades.
It’s you again!! 😉. Yes, you are right about the (fast or slow) shutter speed, and happy to see you homed-in on it!
Regarding your more on topic question, I will have to punt. Relativity, especially when it comes to rotational motion, is very challenging to understand. So at the very least I’ll have to think more about this before attempting any kind of answer.
@@AllThingsPhysicsUA-cam Yeah, sorry, it's me indeed. I'm a physcist myself though not working in physics so all knowledge is buried somewhere deep down there. The relativity thing is a question I have been thinking about ever since I first learned about it in the 80's. Would love to see an episode on that topic!
@@edwinov I will eventually delve into some topics in relativity, but I've got a long list of other topics that I want to discuss first so it will likely be a while.
@@AllThingsPhysicsUA-cam "it will likely be a while"...
That's all relative.
@@edwinov 😂