This is starting to become one of my favorite channels. I genuinely feel excitement when I see that you've uploaded. You explain very complex concepts so simply and clearly. And I noticed those pauses throughout the video, giving us time to digest what you just said before moving on. Love it, and looking forward to the next vid!
Hey viewers, thanks for watching! Mathematics is all about precision, and in that spirit, there are a few clarifications/nit-picks we wanted to address regarding notation choices made for the video, choices which may lead to some confusion: 1) The third term in the titular equation, w x w x r, should be most precisely written as w x (w x r), with parentheses to indicate that the enclosed term should be evaluated first. This could lead to some confusion if one attempted to evaluate (w x w) first, which is zero. 2) The first term in the titular equation, 𝛿v0/𝛿t, is expressed as a partial derivative in the first half of the video. However, due to a production miscommunication, it becomes expressed as a regular derivative in the second half. In truth neither of these derivative expressions are quite correct to indicate the meaning of this first term. Indeed, the partial derivative symbolism typically communicates that there are multiple variables in play some of which are being held constant; however, in this case its use was intended to communicate that the change in the v0 vector is being evaluated within the K0 coordinate frame only. However, we failed to remain consistent with that intended use and switched back to the regular derivative in the second half of the video. Thus, the viewer should note that wherever the dv0/dt term appears in this video, whether expressed as a partial or regular derivative, its appearance only ever refers to the derivative which should be evaluated with respect to the K0 coordinate frame, and that it should not be confused with the "true" dv0/dt term which would be evaluated in the at-rest K frame and whose true value, as depicted towards the end of the video, is actually 𝛿v0/𝛿t + w x v0. 3) For expressing the equations of motion of the frame in non-cross product form, we introduce the omega-hat vector, which lies in the tangential direction. In other works this tangential unit vector is generally indicated by the theta-hat vector. However, since we did not introduce the angle quantity theta within the video itself, we avoided the use of theta-hat here, and moreover, since ω = dθ/dt, omega-hat and theta-hat actually lie in the same direction, and so its use seemed natural here. However, when working with cross-products, one must interpret the omega vector as pointing along the axis of rotation -- so this can lead to some confusion if one is not careful about distinguishing between the use of a cross-product form or non-cross product form.
It doesn't make the derivation simpler if you use geometric algebra, it's only when you use tensor calculus and have a good understanding of vectors that it's easier. It becomes so easy, you almost don't need intuition! Geometric algebra can be used with tensor calculus to make everything make more sense though as well.
This is well described and depicted, but I can't get past the notational choices. Between K and K0, I would choose K0 as the "rest" frame (with zero movement). Even better, use K for the rest frame and K' for the moving frame. Then use the subscript to indicate successive moments in time. x_0 defined as x at time t=0, x_1 defined as x at time t=t_1, etc. 23:36 omega_hat should be the direction of omega_vector. I call the circumferential direction theta_hat, the direction a vector moves when theta is increased.
There was a lot going on in this video, notional choices were difficult! The reason we avoided theta_hat is because we had not introduced theta anywhere as a quantity -- and remember that omega is simply d-theta/dt, so the omega-vector must also point in the same direction as the theta-vector. The confusion is of course that the theta/omega vector is also interpreted to be in the axial direction when the use of cross-products is implemented.
@@dialectphilosophy I think just using \hat{v} would have saved some confusion here. Also, the acceleration should be written ω × (ω × v) instead of ω × ω × v. Loved the video though
One of the rare clear treatments of the Coriolis terms, especially the factor 2. Looking forward to connections to Lorentz force and eventually interpretations of GR.
Yes. He addressed the 2 ω x r thingy ; the mystery which has always left unsolved by many of the students scratching their heads whilst looking at the Coriolis Force derivation
i thought it was going to be an elementary video that i'd skim through, ended up being something i never thought about. the quality is over the roof. i can't wait for your future videos
I am a high school student from italy and i loved your explaination and the animations! I found the video understandable and quite easy to follow. Keep up with your videos, you are becoming one of my favorite channels
The approach here is really amazing!!! Especially the interpretation portion at the end. I’ve seen and read numerous approaches to this topic, but no one has ever actually ever adequately explained where the “two” comes from in the Coriolis force before… very incredible.
I've already studied all this but HOLY HELL dude you made it come ALIVE. If this were to be the way people were taught physics I think it'd be everyone's favorite subject.
Trying to understand rotations without bivectors is like trying to understand english text written with chinese characters - it's unnecessary overcomplicated. Watch the «Swift Introduction to Geometric Algebra». You will cry that you haven't learned it sooner.
@@РайанКупер-э4о My opinion is to just use whatever methods available to solve a problem accurately and quickly, so there's less chance to make mistakes. Tensors are just arrays of numbers, they can be a 1d array like a vector, a 2d array like a matrix, and so on, although 2d is usually all you need. If I were summarizing, it's like changing linear algebra into normal multiplication and sums. Tensor calculus is just doing calculus on those products and sums. It's important to note tensors don't inherently have any physical meaning, exactly like a list of real numbers, but you can make them have meaning by introducing a basis, which can be a vector basis, a bivector basis, and so on. Then, doing calculus (usually just derivatives) on both the components and basis gives you a physical model of the world. It's like trading the mental effort of intuition for the mental effort of applying math and physics definitions correctly. To each their own though, it's my opinion that all those definitions only build my intuition, because physics is not that intuitive to me.
It's the same thing in quantum mechanics. Pauli matrices? Complex numbers being somehow "essential" to the formalism? BS. They completely hide the geometrical intuition of quantum mechanics, and contribute to mysticism like "non-locality" and spin being "a completely quantum phenomenon" (=read, magic). I highly suggest Lasenby's introduction to GA for physicist.
@@РайанКупер-э4о it's my opinion to use whatever methods available to solve the problem as accurately and quickly as possible to reduce possible mistakes, sometimes intuition is part of that too. Hopefully this is a good explanation. Tensors are just arrays of (real) numbers, they can be 1d like a vector, 2d like a matrix, and so on. Just as vectors need basis vectors for their components to mean anything, tensors also only have meaning in a basis. If I could summarize tensor calculus, it would be doing like linear algebra while being able to keep track of every component, and making sure changing your coordinates(basis) doesnt change the underlying math or physics. This just means strategically placing indicies, sums, and products, and then doing calculus, usually differentiation on them, where you can use product rule and so on. Luckily there are some guiding principles i found apply everywhere in physics as far as I've studied: 1. Physical units must line up on both sides, and units in exponents are ALWAYS dimensionless. 2. A change in coordinate system doesn't change the physical quantities involved (invariance of velocity, force, angular velocity, torque) 3. The number of total #indices on both sides should be the same. A scaler(0 index, rank 0 tensor) equals another scaler, a vector (1 index, rank 1 tensor) is equal to another vector, a matrix (2 index, rank 2 tensor) is equal to another matrix, and so on. 4. Both sides should have the same number of covariant and contravariant indicies, basically meaning they would transform the same way under a different basis. 5. With multivectors, you can always split up a multivector equation into it's "blades" so scalers are equal to scalers, vectors to vectors, bivectors to bivectors, trivectors to trivectors, and so on. (Note bivectors still only have 1 index, so it's different from 3.)
@@РайанКупер-э4о it's my opinion to use whatever methods available to solve the problem as accurately and quickly as possible to reduce possible mistakes, sometimes intuition is part of that too. Hopefully this is a good explanation. Tensors are just arrays of (real) numbers, they can be 1d like a vector, 2d like a matrix, and so on. Just as vectors need basis vectors for their components to mean anything, tensors also only have meaning in a basis. If I could summarize tensor calculus, it would be doing like linear algebra while being able to keep track of every component, and making sure changing your coordinates(basis) doesnt change the underlying math or physics. This just means strategically placing indicies, sums, and products, and then doing calculus, usually differentiation on them, where you can use product rule and so on. Luckily there are some guiding principles i found apply everywhere in physics as far as I've studied: 1. Physical units must line up on both sides, and units in exponents are ALWAYS dimensionless. 2. A change in coordinate system doesn't change the physical quantities involved (invariance of velocity, force, angular velocity, torque) 3. The number of total #indices on both sides should be the same. A scaler(0 index, rank 0 tensor) equals another scaler, a vector (1 index, rank 1 tensor) is equal to another vector, a matrix (2 index, rank 2 tensor) is equal to another matrix, and so on. 4. Both sides should have the same number of covariant and contravariant indicies, basically meaning they would transform the same way under a different basis. 5. With multivectors, you can always split up a multivector equation into it's "blades" so scalers are equal to scalers, vectors to vectors, bivectors to bivectors, trivectors to trivectors, and so on. (Note bivectors still only have 1 index, so it's different from 3.)
A video very well done. You gave a very intuitive perspective on the matter, as for the visuals. Rather than showing that the visuals are a result of the mathematics, you have shown that the mathematics are a result of the visuals (as physics should work, contrary to my theoretical physics class) - and with such ease! Subscribed.
I am enjoying the videos' presentations. It has been a while since I have even looked into mathematics, and it is a shame since it was one of the few languages I found success with, considering my dyslexia. A dam is about to burst in our understanding of our universe, and I want to be fully prepared. I genuinely believe it isn't a coincidence that I am being recommended content like yours and many of the *conspiratorial* videos that speak about potential misunderstandings (to put it lightly) of electromagnetism. I wouldn't consider it benevolent as much as a necessary trickle as more of the dam springs leaks. It's uncanny and while I appreciate being able to view content like this it does make me question why now if ever and for what is this content preparing me for. Hopefully I am able to connect those dots.
Dynamics was my toughest class in undergrad but I had a good teacher. Years back coming into this video and i understand everything. Makes me realize how much of a great teacher he was and how well ingrained the principles are in my brain.
Dear Dialect channel colleagues! My father Prof. Dr. Tolga Yarman warns me that the correct notation for the acceleration in the linear equation a = (v0' + vf' - v0 - vf) / dt [at 3:17] SHOULD INVOLVE infinitesimal velocities, otherwise the balance of the equation cannot be maintained. You can see it by carrying the 1/dt on the RHS to the LHS to achieve adt = (dvdt / dt) = dv = v, which does not hold. This likewise reflects to all the other related equations in rotational frame as well. But I personally like your idea that the rotating frame involves infinite overlapping diminutive Cartesian coordinate layouts separated by radially dependent different angular velocities. Thank you for directing us through this journey! Please note that our QTG2 paper to Annals of Physics is under re-evaluation. We would like to hear from you on especially this line of investigation, where the anticipated bridge between the end results of general relativity and quantum mechanics was realized by Tolga Yarman and his team.
@@OzanYarman there is an implicit limit that v0' goes to v0. This is just the context and definition of v0 and v0' in the video. Haven't you studied the definition of the derivative? v0'-v0 and delta t both go to 0 in the limit, and their ratio results in the time derivative of v0 at some arbitrary time and position. If there was no limit, the expression for acceleration really would go to infinity. But obviously it doesn't right?
i think the video is good but if you would have distinguished between accelerating and non accelerating frames then it would have been much easier. Also instead of calling that "alteration" you could just say that instead of velocity being constant due to acceleration that also changes, this is regarding Vo and Vo' and new Vo' where the new Vo' is because the translation is altering but you could have said it is accelerating (at 12:34 ). Overall it was an outstanding video best i have ever seen.
Nice work. Just one nitpick: defining omega-hat as perpendicular to omega may cause confusion. Universally, the hat symbol for a vector means the unit vector along that vector: \hat{a} = a / |a|
Yes, unfortunately there is some confusion and difficulty with this subject. Since omega is just the rate of change of the coordinate angle, the "true" direction of omega should be the tangential one; but for the purposes of the use of cross-products it is also interpreted to lie along the axis of rotation. The problem fundamentally is that one quantity is utilized for multiple purposes.
@@dialectphilosophy the angular velocity vector has to point along the axis of rotation - that's the only direction that makes sense for many reasons, not the least of which is that omega is the angular velocity of an entire coordinate system here, not just one point we happen to single out in that system. Same for a rotating solid body, star, galaxy, etc. Nevertheless, great job on the video and the animations. I must remember to check out some more videos on your channel.
Another amazing video 🙏 🤔 So K° = Expansion of Universe And K = Movement of Local Group objects bound and clustered by gravitation (this is where my mind has been lately - I keep hearing about the universe expanding and everything moving away from each other, BUT also galaxies stay bound in attraction, and so I wonder how does one distinguish the "true" motion of locally bound objects from the "motion" of the expansion of the universe?)
All about physics also released an updated video about rotation. Both of those are goated videos. Also, this is like the perfect time this video and I am so ready for this. 😁
If you prefer GA over linear algebra, use the rule that a vector resulting from a cross product in linear algebra is just the dual of the the corresponding bivector. In other words, put a unit pseudoscalar next to any cross product to get the bivector equation. The order in which you multiply by the pseudoscalar determines your chirality convention.
This goes for the sin/cos representations of the equations as well. When the dot product is computed as cos(x), the cross product can be computed as i*sin(x). Multiplying by a pseudoscalar gives i*i*sin(x) = -sin(x) or -i*i*sin(x) = sin(x) (depending on the orientation of the pseudoscalar). You can even normalize by changing the magnitude of the pseudoscalar to match the ratio of the dilation/contraction of z wrt the x,y plane
I am surprised how much the little background swooshes adds to the animation. It's actually improving understandability when you use different sounds for different transformations.
FYI: Here is a simple understanding of the derivation of cross-products and dot-products from a linear combination of vectors. "The linear combination of vectors implies the existence of the cross and dot products" by Jose Pujol. International Journal of Mathematical Education in Science and Technology Volume 49, 2018 - Issue 5
Understanding rotations is essential to also dispel mysticism like non-locality in quantum mechanics. I went over it in my channel if anyone's interested.
Well that's where quantum mechanics comes in, see? The universe simulation doesn't have to render every atom or particle that isn't being observed, so it just keeps track of where the particle is _likely_ to be at, only rendering it in when it has to.
You are still looking at it as if it is a particle with a singular location that the universe has to render instead of us rendering a computation based on the data we receive, based on our limited computational power and sensory power. A computer doesn't render a frame based on the data in the entire simulation; it only renders what is in the field of view. Look at how frame rendering becomes more challenging the more comprehensive the field of view. If you allow that thought process, you realize we create the matrix.
10:00 the velocity and displacement vectors have different units, so it doesn't really make sense to compare their relative lengths. A given velocity might be numerically larger than a given displacement in one unit system and smaller in another.
The velocities may not always be larger that is true; it's just most likely in the case of rotational motion they would be. Regardless, equating the velocities and displacements helpfully allows one to keep track of what the particle is doing on a physical level. One can always properly resize the vectors at the end anyhow.
When you graphically represent vectors that don't have a pure length magnitude, you always choose a proportionality constant for those vectors, usually implicitly. You might choose to say that, say, a 6cm long arrow represents a force vector with a magnitude of 60N, meaning that you have a proportionality constant of 1000 kg s^(-2). In the video, the proportionality constant was explicitly chosen as dt, such that the length of the arrow representing a velocity vector v would have length vdt = dx.
How to master thing you don't understand by watching thing you don't understand. People who understand thing: "This is actually a great way to conceptualize thing! I totally understand thing now. Well, I understood thing before, but I can totally retrace my steps by watching this video you've made. Good job!"
Sorry to hear the video was difficult for you, but thank you for the feedback. Can you explain for us which parts of the video you were unable to follow/understand?
@@dialectphilosophy Thank you for your feedback on my feedback. Your videos are well-made and their explanations carefully considered. It's simply that years of dedicated study are required to understand these subjects. People make the mistake of watching videos like this when they've yet to learn mathematics beyond a high school level. They will say, "Wow, this is really interesting, what else isn't Big Science telling us?" but lack anything beyond a cursory understanding of the math and physics involved. So it's just eye candy for them. It serves no educational value. For people who understand physics and math exceptionally well, videos like this are pointless, also not educational. But people "on the spectrum" tend to derive some pleasure out of seeing their knowledge visualized by others. Those are for whom videos like this are created, I assume, as very few people have the precise amount of knowledge and ignorance to truly learn anything from such a presentation.
@@AmericanPatriot1812dude, seriously? there’s plenty of comments on here saying this video helped them understand the topic. It certainly helped me. The creator seemed to have been considerate enough to ask you specifically what you had trouble with understanding, and instead of answering with anything useful you just gave an extraordinarily arrogant-sounding attack of videos “like this one”, an attack which seemed more interested in discrediting and throwing suspicion on the creator’s motivations and intentions than critiquing anything about the video specifically. Indeed I haven’t read a comment so pretentious or so desperate to imply its authors own intellectual superiority as this one in a while. So what specifically DID you have trouble with understanding? Because this video certainly can be approached with just high school math. And if you can’t answer that question, then at best you are extraordinarily disingenuous, and at worst you have a raging narcissistic complex.
@@se7964 I do like your channel. I'm a subscriber, actually. It's merely that the "curse of knowledge" makes it difficult for those who lack insight and empathy to effectively communicate their ideas to lay people. We all have complex schema in our heads describing things that others can not immediately understand. For a simple example, we young people have memorized a lot of internet acronyms (ROFL, LOL) that old people do not know the meaning of. So we could tell them a story and have its meaning be ambiguous to everyone but ourselves, "My friend Ralph went ROFL, which made me LOL! IDEC anymore." The semantics of that story make perfect sense to us. As a result, it may seem that we are conveying useful information. However, those who do not know what those acronyms mean will be left with an ambiguous story. In the case of mathematics, "acronyms" are made up of other acronyms that are made up of other acronyms, so the difficulty of telling a story that conveys useful information is compounded. Even a great, empathetic teacher will accidentally include material his students will not be familiar with in attempting to teach them something else they are not familiar with. You may argue that allowing students to deduce things for themselves embodies the truest sense of "teaching." But that isn't teaching. That's an invitation to become an autodidact. If you have to read twenty Wikipedia articles to understand a lecture, the lecture was incomplete. Lay people, by the way, are the main demographic of these videos. And they will not understand how to work with three-dimensional vectors, no matter how snazzy the visuals your channel produces are. Multivariable calculus is the domain of people obsessed with mathematics. To effectively use the information this video teaches, one already has to know a not-insignificant amount of mathematics. The who lack that knowledge will just be left feeling stupid and inadequate. Those who have a lot of mathematical knowledge will find these videos trivial and pointless. Feel free to call me names now.
@@AmericanPatriot1812I would pay money to simple observe you in real life. America is a heretical creation of Cromwell protestants and you are a prime example of its well-deserved decay. 😂
I just want to point out that cross product is not associative. Meaning that in general, (a × b) × c ≠ a × (b × c). Whenever this video has "ω × ω × r", did you actually mean ω × (ω × r)?
Yes. To have been precise we should have included those parentheses, and we apologize if it confused you. (It was ultimately an aesthetic choice, we felt the parentheses cluttered up the equation 🤷♂️)
@@dialectphilosophyI would also add that *ω* itself (via the R.H.R) points in the positive z-axis, and "ω hat" could have caused some vector confusion, although its usage is implicit as to which direction its referring to
Are you reaching out to that the movement of electric field lines in sync with their associated charge is analogous to the behavior of a gravitational field extending outward from a mass?
The reason rotations don't commute is because they comutate or co-mut... As a thing that is rotating is rotated, the direction it is rotated from or to changes. There's also two different types of rotation... There's internal rotation such as a rocket rotated by its engines applying torque to itself where as it rotates the engines are also rotated to change the effect of rotation direction... And there's external rotation as in picking up a toy rocket ship in your hands and rotating it which then the axis that it's being rotated by changes differently based on its rotation.
Your work is superb, 10x better than any textbook i've came across. I hope both science and education will move forward, eventually, from textbooks and papers into forms of communication such as this.
Thật ra không có rotation chỉ có breathing of expanding and contraction because when eath rotate it vibrate and that vibrations mean alternating of time so we actually after birth we move back and forth in time line and that time line is rotating and so our existence map out three rings inner , outer and center and those rings if we stay in one place is relatively stay the same and if we do nothing it may narrow and merge to 1 and that mean paradise of living daed but if we move around it map out all kind of universes . that is why Buddha say maximum 49 days if we stationary we will die certain dead but if we move around we became living in borrowed time shared life with othef spirit floating called holy spirits so what is capitalist or communists when we can not survive by individual self
Like endless other ‘explanations’ of physics’ math a fundamental error exists, in this case that a a third, or another Kframe in which K andK ko are being measured. Motion of Frame relative to what? K is at rest relative to what. Any frame of reference cannot know if it is at rest or not, but only in reference to some ‘not it’, which may a singular or multiple other Frames…
Particles that are moving in line only move in their frame they don't move in addition to their frame. Otherwise they're not in that frame they're in another frame that's moving relative to that frame and you could have thousands and billions of frames until you get to the final particle frame but it's still not moving within its frame
A frame is arbitrary and can be given any state of motion we like. We could for instance, construct a frame that is always co-moving with the particle, no matter what the particle's motion. In physics, the frame will generally represent a system of measurement from which the observer is making their observations.
@@dialectphilosophy then it wouldn't be co-moving it would be an intermediate frame with its own motion. If there's a frame moving that's neither the observer nor the observed then it's a different observable or observer, and not relevant to the motion of the observable. the intermediate frame with undefined properties (like say 1/2 of the observables motion) does not help with any of this... .it is bordering on how quaternions are treated, since the math for them involves theta/2.... but even that doesn't actually have to be; using axis-angle and Rodrigues' composite rotation formula, could use trig substitutions and make it just rotations by theta; this breaks being able to place it in a matrix, but there's no absolute requirement to form a matrix to rotate things anyway... so it's merely a convenience of the math structure chosen, and is just to support making a quaternion cross product... But rotation formulas themselves are just the cross product of the axis unit vectors scaled by sin/cos of the angle of rotation, and doesn't have to be angle/2. 2sin(a/2)cos(b/2) is just sin(a+b) instead. still have to compute 4 terms, sin(a+b), sin(a-b), cos(a+b) and cos(a-b) instead of sin(a/2) ,cos(a/2), sin(b/2), and cos(b/2)... but does simplify some of the subsequent multiplications. My video on rotations from 3 years ago has drifted back to like 20ish back on my channel.... (just saying it that way because I'm assuming I can't post links in comments). So my argument is just that the whole basis from the beginning of this is kind of irrelevant to the situation mentioned in the title... making even watching past a few minutes quite a chore.
an awful lot of talk of fictitious forces and "truly moving frames" for a dialect video. I assume it's just used for teaching purposes here. Anyway, to be honest, I got confused in the second half of the video. I imagine this might be good for undergrads but I feel like, just taking derivatives using the usual rules would've been clearer to me.
You have given me a very good idea even though I already knew the concepts. God bless the academic side of youtube
This is starting to become one of my favorite channels. I genuinely feel excitement when I see that you've uploaded. You explain very complex concepts so simply and clearly. And I noticed those pauses throughout the video, giving us time to digest what you just said before moving on. Love it, and looking forward to the next vid!
So true!
Hey viewers, thanks for watching! Mathematics is all about precision, and in that spirit, there are a few clarifications/nit-picks we wanted to address regarding notation choices made for the video, choices which may lead to some confusion:
1) The third term in the titular equation, w x w x r, should be most precisely written as w x (w x r), with parentheses to indicate that the enclosed term should be evaluated first. This could lead to some confusion if one attempted to evaluate (w x w) first, which is zero.
2) The first term in the titular equation, 𝛿v0/𝛿t, is expressed as a partial derivative in the first half of the video. However, due to a production miscommunication, it becomes expressed as a regular derivative in the second half. In truth neither of these derivative expressions are quite correct to indicate the meaning of this first term. Indeed, the partial derivative symbolism typically communicates that there are multiple variables in play some of which are being held constant; however, in this case its use was intended to communicate that the change in the v0 vector is being evaluated within the K0 coordinate frame only. However, we failed to remain consistent with that intended use and switched back to the regular derivative in the second half of the video. Thus, the viewer should note that wherever the dv0/dt term appears in this video, whether expressed as a partial or regular derivative, its appearance only ever refers to the derivative which should be evaluated with respect to the K0 coordinate frame, and that it should not be confused with the "true" dv0/dt term which would be evaluated in the at-rest K frame and whose true value, as depicted towards the end of the video, is actually 𝛿v0/𝛿t + w x v0.
3) For expressing the equations of motion of the frame in non-cross product form, we introduce the omega-hat vector, which lies in the tangential direction. In other works this tangential unit vector is generally indicated by the theta-hat vector. However, since we did not introduce the angle quantity theta within the video itself, we avoided the use of theta-hat here, and moreover, since ω = dθ/dt, omega-hat and theta-hat actually lie in the same direction, and so its use seemed natural here. However, when working with cross-products, one must interpret the omega vector as pointing along the axis of rotation -- so this can lead to some confusion if one is not careful about distinguishing between the use of a cross-product form or non-cross product form.
Me when i refuse to use geometric algebra:
Is that a solo leveling pfp i see?
It doesn't make the derivation simpler if you use geometric algebra, it's only when you use tensor calculus and have a good understanding of vectors that it's easier. It becomes so easy, you almost don't need intuition! Geometric algebra can be used with tensor calculus to make everything make more sense though as well.
This is well described and depicted, but I can't get past the notational choices. Between K and K0, I would choose K0 as the "rest" frame (with zero movement). Even better, use K for the rest frame and K' for the moving frame. Then use the subscript to indicate successive moments in time. x_0 defined as x at time t=0, x_1 defined as x at time t=t_1, etc.
23:36 omega_hat should be the direction of omega_vector. I call the circumferential direction theta_hat, the direction a vector moves when theta is increased.
There was a lot going on in this video, notional choices were difficult! The reason we avoided theta_hat is because we had not introduced theta anywhere as a quantity -- and remember that omega is simply d-theta/dt, so the omega-vector must also point in the same direction as the theta-vector. The confusion is of course that the theta/omega vector is also interpreted to be in the axial direction when the use of cross-products is implemented.
@@dialectphilosophy I think just using \hat{v} would have saved some confusion here. Also, the acceleration should be written ω × (ω × v) instead of ω × ω × v. Loved the video though
One of the rare clear treatments of the Coriolis terms, especially the factor 2. Looking forward to connections to Lorentz force and eventually interpretations of GR.
Yes. He addressed the 2 ω x r thingy ; the mystery which has always left unsolved by many of the students scratching their heads whilst looking at the Coriolis Force derivation
why u didnt assigned this video for SoMe organised by 3b1b it pure gold, i never thought i would ever have this clear explaination of these topics
i thought it was going to be an elementary video that i'd skim through, ended up being something i never thought about. the quality is over the roof. i can't wait for your future videos
A more simple physical interpretation is exactly what i need to get a handle on this👍😉
I am a high school student from italy and i loved your explaination and the animations! I found the video understandable and quite easy to follow. Keep up with your videos, you are becoming one of my favorite channels
The approach here is really amazing!!! Especially the interpretation portion at the end. I’ve seen and read numerous approaches to this topic, but no one has ever actually ever adequately explained where the “two” comes from in the Coriolis force before… very incredible.
I wish more videos like this on classical mechanics, especially rigid bodies. It will greatly helpful and reduce the burden on highschool students
I've already studied all this but HOLY HELL dude you made it come ALIVE. If this were to be the way people were taught physics I think it'd be everyone's favorite subject.
Thank you for the kind words and support ☺️
Trying to understand rotations without bivectors is like trying to understand english text written with chinese characters - it's unnecessary overcomplicated. Watch the «Swift Introduction to Geometric Algebra». You will cry that you haven't learned it sooner.
@@РайанКупер-э4о My opinion is to just use whatever methods available to solve a problem accurately and quickly, so there's less chance to make mistakes. Tensors are just arrays of numbers, they can be a 1d array like a vector, a 2d array like a matrix, and so on, although 2d is usually all you need. If I were summarizing, it's like changing linear algebra into normal multiplication and sums. Tensor calculus is just doing calculus on those products and sums. It's important to note tensors don't inherently have any physical meaning, exactly like a list of real numbers, but you can make them have meaning by introducing a basis, which can be a vector basis, a bivector basis, and so on. Then, doing calculus (usually just derivatives) on both the components and basis gives you a physical model of the world. It's like trading the mental effort of intuition for the mental effort of applying math and physics definitions correctly. To each their own though, it's my opinion that all those definitions only build my intuition, because physics is not that intuitive to me.
It's the same thing in quantum mechanics. Pauli matrices? Complex numbers being somehow "essential" to the formalism? BS. They completely hide the geometrical intuition of quantum mechanics, and contribute to mysticism like "non-locality" and spin being "a completely quantum phenomenon" (=read, magic). I highly suggest Lasenby's introduction to GA for physicist.
@@РайанКупер-э4о it's my opinion to use whatever methods available to solve the problem as accurately and quickly as possible to reduce possible mistakes, sometimes intuition is part of that too. Hopefully this is a good explanation.
Tensors are just arrays of (real) numbers, they can be 1d like a vector, 2d like a matrix, and so on. Just as vectors need basis vectors for their components to mean anything, tensors also only have meaning in a basis. If I could summarize tensor calculus, it would be doing like linear algebra while being able to keep track of every component, and making sure changing your coordinates(basis) doesnt change the underlying math or physics. This just means strategically placing indicies, sums, and products, and then doing calculus, usually differentiation on them, where you can use product rule and so on.
Luckily there are some guiding principles i found apply everywhere in physics as far as I've studied:
1. Physical units must line up on both sides, and units in exponents are ALWAYS dimensionless.
2. A change in coordinate system doesn't change the physical quantities involved (invariance of velocity, force, angular velocity, torque)
3. The number of total #indices on both sides should be the same. A scaler(0 index, rank 0 tensor) equals another scaler, a vector (1 index, rank 1 tensor) is equal to another vector, a matrix (2 index, rank 2 tensor) is equal to another matrix, and so on.
4. Both sides should have the same number of covariant and contravariant indicies, basically meaning they would transform the same way under a different basis.
5. With multivectors, you can always split up a multivector equation into it's "blades" so scalers are equal to scalers, vectors to vectors, bivectors to bivectors, trivectors to trivectors, and so on. (Note bivectors still only have 1 index, so it's different from 3.)
@@wargreymon2024, epicycles works too, they can describe motion of planets perfectly, but no one uses them now for some reason.
@@РайанКупер-э4о it's my opinion to use whatever methods available to solve the problem as accurately and quickly as possible to reduce possible mistakes, sometimes intuition is part of that too. Hopefully this is a good explanation.
Tensors are just arrays of (real) numbers, they can be 1d like a vector, 2d like a matrix, and so on. Just as vectors need basis vectors for their components to mean anything, tensors also only have meaning in a basis. If I could summarize tensor calculus, it would be doing like linear algebra while being able to keep track of every component, and making sure changing your coordinates(basis) doesnt change the underlying math or physics. This just means strategically placing indicies, sums, and products, and then doing calculus, usually differentiation on them, where you can use product rule and so on.
Luckily there are some guiding principles i found apply everywhere in physics as far as I've studied:
1. Physical units must line up on both sides, and units in exponents are ALWAYS dimensionless.
2. A change in coordinate system doesn't change the physical quantities involved (invariance of velocity, force, angular velocity, torque)
3. The number of total #indices on both sides should be the same. A scaler(0 index, rank 0 tensor) equals another scaler, a vector (1 index, rank 1 tensor) is equal to another vector, a matrix (2 index, rank 2 tensor) is equal to another matrix, and so on.
4. Both sides should have the same number of covariant and contravariant indicies, basically meaning they would transform the same way under a different basis.
5. With multivectors, you can always split up a multivector equation into it's "blades" so scalers are equal to scalers, vectors to vectors, bivectors to bivectors, trivectors to trivectors, and so on. (Note bivectors still only have 1 index, so it's different from 3.)
Very good visual explanation of Christoffel symbols.
A video very well done. You gave a very intuitive perspective on the matter, as for the visuals. Rather than showing that the visuals are a result of the mathematics, you have shown that the mathematics are a result of the visuals (as physics should work, contrary to my theoretical physics class) - and with such ease!
Subscribed.
Thank you so much Sir for explaining very well.
Regards 🙏
This is so nicely done. Congratulations. Something to be very proud of.
0:59 the production is stellar so far
I am enjoying the videos' presentations. It has been a while since I have even looked into mathematics, and it is a shame since it was one of the few languages I found success with, considering my dyslexia.
A dam is about to burst in our understanding of our universe, and I want to be fully prepared. I genuinely believe it isn't a coincidence that I am being recommended content like yours and many of the *conspiratorial* videos that speak about potential misunderstandings (to put it lightly) of electromagnetism.
I wouldn't consider it benevolent as much as a necessary trickle as more of the dam springs leaks. It's uncanny and while I appreciate being able to view content like this it does make me question why now if ever and for what is this content preparing me for.
Hopefully I am able to connect those dots.
Dynamics was my toughest class in undergrad but I had a good teacher. Years back coming into this video and i understand everything. Makes me realize how much of a great teacher he was and how well ingrained the principles are in my brain.
What are you doing now for a living.
@@Dharun-ge2fo robotics engineer
Dear Dialect channel colleagues! My father Prof. Dr. Tolga Yarman warns me that the correct notation for the acceleration in the linear equation a = (v0' + vf' - v0 - vf) / dt [at 3:17] SHOULD INVOLVE infinitesimal velocities, otherwise the balance of the equation cannot be maintained. You can see it by carrying the 1/dt on the RHS to the LHS to achieve adt = (dvdt / dt) = dv = v, which does not hold. This likewise reflects to all the other related equations in rotational frame as well. But I personally like your idea that the rotating frame involves infinite overlapping diminutive Cartesian coordinate layouts separated by radially dependent different angular velocities. Thank you for directing us through this journey! Please note that our QTG2 paper to Annals of Physics is under re-evaluation. We would like to hear from you on especially this line of investigation, where the anticipated bridge between the end results of general relativity and quantum mechanics was realized by Tolga Yarman and his team.
Am I dumb
@@vijay32570lol
v0'-v0 is an infinitesimal value, and the same goes for vf.
@@lih3391 That is incorrect. The difference of two finite difference quantities cannot ever furnish an infinitesimal value.
@@OzanYarman there is an implicit limit that v0' goes to v0. This is just the context and definition of v0 and v0' in the video.
Haven't you studied the definition of the derivative?
v0'-v0 and delta t both go to 0 in the limit, and their ratio results in the time derivative of v0 at some arbitrary time and position.
If there was no limit, the expression for acceleration really would go to infinity. But obviously it doesn't right?
Gone over my mathematical head a little with this one lol
I'll wait for the next video and punch line :P
Just in time for my introduction to general relativity test :)
i think the video is good but if you would have distinguished between accelerating and non accelerating frames then it would have been much easier. Also instead of calling that "alteration" you could just say that instead of velocity being constant due to acceleration that also changes, this is regarding Vo and Vo' and new Vo' where the new Vo' is because the translation is altering but you could have said it is accelerating (at 12:34 ). Overall it was an outstanding video best i have ever seen.
Your animation is awesome. I wanted to know, Which software did you use to make this animation specifically the Formulation.
I'd guess Blender
Me too. I guess it can be done with Blender, but how long it would take... or if there is a library which people can use to speed up things?
@@APaleDot but how the Scientific notation? I started learning Manim but is there any easy way?
@@LearnScienceThroughPhysicist
I'd say Manin is the easy way. Unless you just want to screenshot LaTeX.
Nice work. Just one nitpick: defining omega-hat as perpendicular to omega may cause confusion. Universally, the hat symbol for a vector means the unit vector along that vector: \hat{a} = a / |a|
Yes, unfortunately there is some confusion and difficulty with this subject. Since omega is just the rate of change of the coordinate angle, the "true" direction of omega should be the tangential one; but for the purposes of the use of cross-products it is also interpreted to lie along the axis of rotation. The problem fundamentally is that one quantity is utilized for multiple purposes.
@@dialectphilosophy the angular velocity vector has to point along the axis of rotation - that's the only direction that makes sense for many reasons, not the least of which is that omega is the angular velocity of an entire coordinate system here, not just one point we happen to single out in that system. Same for a rotating solid body, star, galaxy, etc. Nevertheless, great job on the video and the animations. I must remember to check out some more videos on your channel.
@@dialectphilosophy You could've used \hat{\theta}
Just awesome. If only your videos had been around during my undergrad time 🤣
Please continue with a folloow up video on ficticious Centrifugal and Coriolis accelerations
That is the plan!
Another amazing video 🙏
🤔 So K° = Expansion of Universe
And K = Movement of Local Group objects bound and clustered by gravitation
(this is where my mind has been lately - I keep hearing about the universe expanding and everything moving away from each other, BUT also galaxies stay bound in attraction, and so I wonder how does one distinguish the "true" motion of locally bound objects from the "motion" of the expansion of the universe?)
Is the universe expanding, or is everything inside it shrinking?
Very good video please make one video filled with visual examples with different refrence frame in rotating body
When I was six, spinning on a rotating turntable as shown at the start did not make me dizzy at all. We were at Bear Nountain State Park
You may have superpowers 🦸 👀
All about physics also released an updated video about rotation. Both of those are goated videos. Also, this is like the perfect time this video and I am so ready for this. 😁
You mean "All Things Physics" right? Yeah, awesome channel
If you prefer GA over linear algebra, use the rule that a vector resulting from a cross product in linear algebra is just the dual of the the corresponding bivector. In other words, put a unit pseudoscalar next to any cross product to get the bivector equation. The order in which you multiply by the pseudoscalar determines your chirality convention.
This goes for the sin/cos representations of the equations as well. When the dot product is computed as cos(x), the cross product can be computed as i*sin(x). Multiplying by a pseudoscalar gives i*i*sin(x) = -sin(x) or -i*i*sin(x) = sin(x) (depending on the orientation of the pseudoscalar). You can even normalize by changing the magnitude of the pseudoscalar to match the ratio of the dilation/contraction of z wrt the x,y plane
I am surprised how much the little background swooshes adds to the animation. It's actually improving understandability when you use different sounds for different transformations.
Thank you, we appreciate the feedback on that!
@@dialectphilosophy For me the sounds are quite annoying and mostly unnecessary :-)
Truly an amazing video, chapeu!
Amazing video!
FYI: Here is a simple understanding of the derivation of cross-products and dot-products from a linear combination of vectors.
"The linear combination of vectors implies the existence of the cross and dot products" by Jose Pujol. International Journal of Mathematical Education in Science and Technology Volume 49, 2018 - Issue 5
Yeah, only $61 to download the pdf🤑
@@TheYurubutugralb Ouch. Try z-library. Everything there is free and no strings attached.
Understanding rotations is essential to also dispel mysticism like non-locality in quantum mechanics. I went over it in my channel if anyone's interested.
Interesting channel! We've never found Bell's Theorem to be compelling... consider sharing your work on our discord server.
@@dialectphilosophy i certainly will. I must stress that it's not my work, but Joy Christian's.
i would love to see the riemann curvature tensor covered on this channel
We're getting there! Almost finished with our coverage of the Christoffel Symbols, and then Riemann curvature is up next!
i m excited about when will im watching the video about constitutive relations in rotating systems
Thank you Dialect for your work. I have learned a lot about physics watching your videos.
Our universe simulation must have some really huge processors to handle all this math for every atom on a constant basis.
Well that's where quantum mechanics comes in, see? The universe simulation doesn't have to render every atom or particle that isn't being observed, so it just keeps track of where the particle is _likely_ to be at, only rendering it in when it has to.
If we were a simulation, small scale physics would reveal strange results...
You are still looking at it as if it is a particle with a singular location that the universe has to render instead of us rendering a computation based on the data we receive, based on our limited computational power and sensory power.
A computer doesn't render a frame based on the data in the entire simulation; it only renders what is in the field of view. Look at how frame rendering becomes more challenging the more comprehensive the field of view.
If you allow that thought process, you realize we create the matrix.
Oh you're going all the way aren't you? Nice.
10:00 the velocity and displacement vectors have different units, so it doesn't really make sense to compare their relative lengths. A given velocity might be numerically larger than a given displacement in one unit system and smaller in another.
The velocities may not always be larger that is true; it's just most likely in the case of rotational motion they would be. Regardless, equating the velocities and displacements helpfully allows one to keep track of what the particle is doing on a physical level. One can always properly resize the vectors at the end anyhow.
When you graphically represent vectors that don't have a pure length magnitude, you always choose a proportionality constant for those vectors, usually implicitly. You might choose to say that, say, a 6cm long arrow represents a force vector with a magnitude of 60N, meaning that you have a proportionality constant of 1000 kg s^(-2). In the video, the proportionality constant was explicitly chosen as dt, such that the length of the arrow representing a velocity vector v would have length vdt = dx.
Underrated channel
How to master thing you don't understand by watching thing you don't understand.
People who understand thing: "This is actually a great way to conceptualize thing! I totally understand thing now. Well, I understood thing before, but I can totally retrace my steps by watching this video you've made. Good job!"
Sorry to hear the video was difficult for you, but thank you for the feedback. Can you explain for us which parts of the video you were unable to follow/understand?
@@dialectphilosophy Thank you for your feedback on my feedback.
Your videos are well-made and their explanations carefully considered. It's simply that years of dedicated study are required to understand these subjects.
People make the mistake of watching videos like this when they've yet to learn mathematics beyond a high school level. They will say, "Wow, this is really interesting, what else isn't Big Science telling us?" but lack anything beyond a cursory understanding of the math and physics involved. So it's just eye candy for them. It serves no educational value.
For people who understand physics and math exceptionally well, videos like this are pointless, also not educational.
But people "on the spectrum" tend to derive some pleasure out of seeing their knowledge visualized by others. Those are for whom videos like this are created, I assume, as very few people have the precise amount of knowledge and ignorance to truly learn anything from such a presentation.
@@AmericanPatriot1812dude, seriously? there’s plenty of comments on here saying this video helped them understand the topic. It certainly helped me.
The creator seemed to have been considerate enough to ask you specifically what you had trouble with understanding, and instead of answering with anything useful you just gave an extraordinarily arrogant-sounding attack of videos “like this one”, an attack which seemed more interested in discrediting and throwing suspicion on the creator’s motivations and intentions than critiquing anything about the video specifically. Indeed I haven’t read a comment so pretentious or so desperate to imply its authors own intellectual superiority as this one in a while.
So what specifically DID you have trouble with understanding? Because this video certainly can be approached with just high school math. And if you can’t answer that question, then at best you are extraordinarily disingenuous, and at worst you have a raging narcissistic complex.
@@se7964 I do like your channel. I'm a subscriber, actually.
It's merely that the "curse of knowledge" makes it difficult for those who lack insight and empathy to effectively communicate their ideas to lay people.
We all have complex schema in our heads describing things that others can not immediately understand. For a simple example, we young people have memorized a lot of internet acronyms (ROFL, LOL) that old people do not know the meaning of. So we could tell them a story and have its meaning be ambiguous to everyone but ourselves, "My friend Ralph went ROFL, which made me LOL! IDEC anymore." The semantics of that story make perfect sense to us. As a result, it may seem that we are conveying useful information. However, those who do not know what those acronyms mean will be left with an ambiguous story.
In the case of mathematics, "acronyms" are made up of other acronyms that are made up of other acronyms, so the difficulty of telling a story that conveys useful information is compounded. Even a great, empathetic teacher will accidentally include material his students will not be familiar with in attempting to teach them something else they are not familiar with.
You may argue that allowing students to deduce things for themselves embodies the truest sense of "teaching." But that isn't teaching. That's an invitation to become an autodidact. If you have to read twenty Wikipedia articles to understand a lecture, the lecture was incomplete.
Lay people, by the way, are the main demographic of these videos. And they will not understand how to work with three-dimensional vectors, no matter how snazzy the visuals your channel produces are. Multivariable calculus is the domain of people obsessed with mathematics.
To effectively use the information this video teaches, one already has to know a not-insignificant amount of mathematics. The who lack that knowledge will just be left feeling stupid and inadequate. Those who have a lot of mathematical knowledge will find these videos trivial and pointless.
Feel free to call me names now.
@@AmericanPatriot1812I would pay money to simple observe you in real life. America is a heretical creation of Cromwell protestants and you are a prime example of its well-deserved decay. 😂
Thank you thank you 🧠🤠🤖🇱🇷🇮🇳🇮🇳🇮🇳
Coriolis effect for gunnery
Hey could I ask in what editor do you make this videos, or are you using multiple programming languages?
I just want to point out that cross product is not associative. Meaning that in general, (a × b) × c ≠ a × (b × c). Whenever this video has "ω × ω × r", did you actually mean ω × (ω × r)?
Yes. To have been precise we should have included those parentheses, and we apologize if it confused you. (It was ultimately an aesthetic choice, we felt the parentheses cluttered up the equation 🤷♂️)
@@dialectphilosophyI would also add that *ω* itself (via the R.H.R) points in the positive
z-axis, and "ω hat" could have caused some vector confusion, although its usage is implicit as to which direction its referring to
exceptionally done!
thank you
I'm here before scienceclic praise the quality of the video.
We appreciate you 🙂
What about the applied equation for any moving particle that experience heat and pressure as it travels through various dimensional conditions
Keep it up 🙂
Watching this during breakfast
Thanks!
Thank you so much!! 🤗
I watch this for breakfast
2:39 new coordi
Bro uploaded the video on th same day my school started the chapter class 11 kv no.1 afs agra
Love this channel ‼️‼️‼️
Are you reaching out to that the movement of electric field lines in sync with their associated charge is analogous to the behavior of a gravitational field extending outward from a mass?
Nothing to be said for certain at the moment, but there are certainly a number of intriguing similarities!
But the distance of the space flowing inwards isn't added into the equation..?
Someone tried the rocking chair 🎉
The reason rotations don't commute is because they comutate or co-mut... As a thing that is rotating is rotated, the direction it is rotated from or to changes. There's also two different types of rotation... There's internal rotation such as a rocket rotated by its engines applying torque to itself where as it rotates the engines are also rotated to change the effect of rotation direction... And there's external rotation as in picking up a toy rocket ship in your hands and rotating it which then the axis that it's being rotated by changes differently based on its rotation.
There are even better examples of how perversely some scientists can think. But the complication of things preserves jobs.
Perfect 100.
This is gold
Nature say more difficult ones. Track a fly flight pathway, mathmathise the trace and predicts next moving.
Your work is superb, 10x better than any textbook i've came across. I hope both science and education will move forward, eventually, from textbooks and papers into forms of communication such as this.
No. Textbooks and Papers need to stay.
WHAT helps to learn quantum physics?
We hope to have an answer to that one day.
Feynman lectures can be useful.
Which rotation all goes back to axis angle.
what animation software do you use?
Amazing🎉🎉
What is this new genre of animation education???
Thật ra không có rotation chỉ có breathing of expanding and contraction because when eath rotate it vibrate and that vibrations mean alternating of time so we actually after birth we move back and forth in time line and that time line is rotating and so our existence map out three rings inner , outer and center and those rings if we stay in one place is relatively stay the same and if we do nothing it may narrow and merge to 1 and that mean paradise of living daed but if we move around it map out all kind of universes . that is why Buddha say maximum 49 days if we stationary we will die certain dead but if we move around we became living in borrowed time shared life with othef spirit floating called holy spirits so what is capitalist or communists when we can not survive by individual self
Newton's going like YAY!
Like endless other ‘explanations’ of physics’ math a fundamental error exists, in this case that a a third, or another Kframe in which K andK ko are being measured. Motion of Frame relative to what? K is at rest relative to what. Any frame of reference cannot know if it is at rest or not, but only in reference to some ‘not it’, which may a singular or multiple other Frames…
Im in highschool should I study this I am curious
Yes, you'll impress your teachers :-) Hit us up on our discord if you need help or have questions.
This made my imaginary frame hard and my real frame spin faster
Taylor Charles Hall Joseph Jones Jose
Good
What a great video!
wow!
This video might be a JoJo reference
Valeu!
Thank you for your support! ☺
Oooh a seesaw is a better sim with more stable design
❤❤❤
Particles that are moving in line only move in their frame they don't move in addition to their frame. Otherwise they're not in that frame they're in another frame that's moving relative to that frame and you could have thousands and billions of frames until you get to the final particle frame but it's still not moving within its frame
This actually reverses the direction of the cross product so instead of a cross b the other is b cross a
A frame is arbitrary and can be given any state of motion we like. We could for instance, construct a frame that is always co-moving with the particle, no matter what the particle's motion. In physics, the frame will generally represent a system of measurement from which the observer is making their observations.
@@dialectphilosophy then it wouldn't be co-moving it would be an intermediate frame with its own motion. If there's a frame moving that's neither the observer nor the observed then it's a different observable or observer, and not relevant to the motion of the observable. the intermediate frame with undefined properties (like say 1/2 of the observables motion) does not help with any of this... .it is bordering on how quaternions are treated, since the math for them involves theta/2.... but even that doesn't actually have to be; using axis-angle and Rodrigues' composite rotation formula, could use trig substitutions and make it just rotations by theta; this breaks being able to place it in a matrix, but there's no absolute requirement to form a matrix to rotate things anyway... so it's merely a convenience of the math structure chosen, and is just to support making a quaternion cross product... But rotation formulas themselves are just the cross product of the axis unit vectors scaled by sin/cos of the angle of rotation, and doesn't have to be angle/2. 2sin(a/2)cos(b/2) is just sin(a+b) instead. still have to compute 4 terms, sin(a+b), sin(a-b), cos(a+b) and cos(a-b) instead of sin(a/2) ,cos(a/2), sin(b/2), and cos(b/2)... but does simplify some of the subsequent multiplications.
My video on rotations from 3 years ago has drifted back to like 20ish back on my channel.... (just saying it that way because I'm assuming I can't post links in comments).
So my argument is just that the whole basis from the beginning of this is kind of irrelevant to the situation mentioned in the title... making even watching past a few minutes quite a chore.
It’s all Greek to me.
Nothing better for my saturnday breakfast
Didn't understood much but commenting for the all might The Algorithm.
yaz
nifty
mega cross star in a cornet system:-\
❤❤
an awful lot of talk of fictitious forces and "truly moving frames" for a dialect video. I assume it's just used for teaching purposes here.
Anyway, to be honest, I got confused in the second half of the video. I imagine this might be good for undergrads but I feel like, just taking derivatives using the usual rules would've been clearer to me.
Any jee aspirant here ?
Yeah, a question of this type was asked in 2016.