To Master Physics, First Master The Rotating Coordinate System

[@dialectphilosophy]

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.

[@maximilianoriveramuniz6060]

Una muy buena explicación

[@Twitledum9]

Pin this pls

[@nickcunningham6344]

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!

[@-_Nuke_-]

So true!

[@STONECOLDET944]

You have given me a very good idea even though I already knew the concepts. God bless the academic side of youtube

[@Deniz-le9xp]

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

[@dean532]

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

[@thstroyur]

I can give an even simpler explanation that requires no approximations or frame-shifting: it all boils down to seeing rotation as an _active_ transformation R in the 'lab' frame, with inverse R^-1 = R^T. Let the position of the rotated particle be given by the matrix equation Q = R . q; then, acceleration is simply the second derivative of that: d^2/dt^2 (Q) = d/dt (R . dq/dt + (dR/dt) . q) = R . [d^2/dt^2 (q) + R^T . d^2/dt^2 (R) . q + 2R^T . dR/dt . dq/dt] Do the last two terms in the right-hand side look familiar? Also - notice the factor of 2 in the third one?

[@federicosilla1453]

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

[@andrestomas7112]

I have youtube blocked off through so many barriers to not get distracted when studying. But the quality of this video made me remove all of them for a moment to give you a like and a "amazing video" comment. Keep up the great work!

[@vempatirahulreddy2158]

I wish more videos like this on classical mechanics, especially rigid bodies. It will greatly helpful and reduce the burden on highschool students

[@QuantumGravity-dv2xz]

This provides a better explanation for galaxy rotation curve without invoking dark matter. Keep up the good work!

[@imaginingPhysics]

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.

[@W.M.-]

Finally an awesome channel which has the real equations and visuals. Tired of these KZbin tutorials which make you feel as if you're understanding a concept but which are really extremely simple. Also great to see traditional parallelogram arguments used, keep up the good work!

[@spirko97]

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.

[@dialectphilosophy]

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.

[@frankjohnson123]

@@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

[@Lolwutdesu9000]

@@dialectphilosophy I would have also chosen K0 to be the rest frame. This is standard notation in pretty much all of science and math, where the 0 subscript indicates some original or initial state. Other than that, it was really well done!

[@aurelia8028]

​@Lolwutdesu9000 i don't think there's a standard notation here. Some books on relativity use S and S' instead. Kinda confusing. Just use two different letters ffs

[@scottcann9246]

​@@frankjohnson123 You mean to say w x (w x r), but agreed... w x w x r appears to take the cross of w and w which is a zero vector

[@thepolishguy7539]

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.

[@staticjpl]

I feel like these equations are super useful for network games specifically when dealing with players on moving platforms, which typically is very hand to sync and predict. In a sense you can treat the particle as the player and the platform as the Frame. Using these equations I suspect it would be easier to forward predict the position of the player on the moving platform as the moving reference frame. If my theory is correct the equations might make it simpler to compute any changes and better sync the server and client for these types of problems! Thanks for the wonderful video!

[@DemonetisedZone]

A more simple physical interpretation is exactly what i need to get a handle on this👍😉

[@РайанКупер-э4о]

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.

[@lih3391]

@@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.

[@PathfinderPhysics]

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.

[@lih3391]

@@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]

@@wargreymon2024, epicycles works too, they can describe motion of planets perfectly, but no one uses them now for some reason.

[@lih3391]

@@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.)

[@henrytzuo8517]

The best video I have ever seen for explaining this concept. Thank you so much Sir!👍👍👍

[@se7964]

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.

[@DevRajyaguru-lx8pi]

Thank you man! Saved me from unexpected errors in my understanding

[@Zxymr]

Very good visual explanation of Christoffel symbols.

[@lovishnahar1807]

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

[@vinestreet4031]

This is so nicely done. Congratulations. Something to be very proud of.

[@domg6041]

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.

[@entropyz5242]

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.

[@Dharun-ge2fo]

What are you doing now for a living.

[@entropyz5242]

@@Dharun-ge2fo robotics engineer

[@richardchapman1592]

Makes sense​@@entropyz5242since all robotics is relevant to the original system spec of the software.

[@arunsinghamahapatra2918]

Thank you so much Sir for explaining very well. Regards 🙏

[@100iqgaming]

the difference in quality between A level and degree physics youtube is INSANE

[@larrybryant4827]

Nice and through explanation. Thanks !

[@robertbelongia6887]

Best explanation and visualization on the net!

[@Zonnymaka]

Truly an amazing video, chapeu!

[@solenoideardilloso738]

when I studied physics at school and university I was always frustrated by the amount of equations and deductions drawn from complex analyses and interpretations. After learning robotics and the concepts of rotations and frame translations I realized that they turn physics into something meaningful, elegant and understandable, after that I understood why among the first elementary chapters of physics are vectors.

[@Duskull666]

Just in time for my introduction to general relativity test :)

[@KarTandir]

Hey, incredible videos as always. I wanted to tell you that putting subtitles into the video, or setting up youtube's subtitles would make non-native speakers like myself's job a ton easier. These topics are already hard to understand as what they are, trying to listen to the speaker and make up sentences inside the head while looking at an visualisation makes it even harder. Nonetheless, thank you!

[@dialectphilosophy]

Hey there, thank you for watching and for providing feedback. We will definitely look into it!

[@purabimondal6270]

Make more such intuitive explanations on mechanics and electromechanics For information on circular motion, Let a particle be undergoing circular motion and the angular position of the particle at an instant be θ. The position of the particle at any instant is given by polar coordinates: r = r( cos θ i + sin θ j)(i,j are unit vectors along x and y axes respectively). We can finally obtain by simple calculus that acceleration vector of the particle at any instant t, a = -ω²r(cos θ i+ sin θ j) + r(dω/dt) (-sin θ i + cos θ j) Clearly , the components of this acceleration are centripetal acceleration (magnitude ω²r=(v²/r) and directed towards origin) and the tangential acceleration (magnitude r(dω/dt) = dv/dt where v, equal to rω, is the SPEED of the particle at any instant.

[@yash1152]

0:59 the production is stellar so far

[@bide2505]

Cool it helped me in radial nodes. And in rotational kinetics

[@JakobWierzbowski]

Just awesome. If only your videos had been around during my undergrad time 🤣

[@jawaharbabuadapa]

This is exactly what I need to succeed in my life, now I shall succeed

[@cosmicraysshotsintothelight]

as long as you do not vote for Trump. (if American)

[@Ma_X64]

Well, Maxwell's equations describe movements of the ideal fluid because of Faraday perceptions of electricity as ideal fluid flow.

[@primenumberbuster404]

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. 😁

[@mikip3242]

You mean "All Things Physics" right? Yeah, awesome channel

[@markszlazak]

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

[@TheYurubutugralb]

Yeah, only $61 to download the pdf🤑

[@markszlazak]

@@TheYurubutugralb Ouch. Try z-library. Everything there is free and no strings attached.

[@stefanlicanin9485]

Thank you Dialect for your work. I have learned a lot about physics watching your videos.

[@bozydarziemniak1853]

Thats how our gravity works. Bravo. First person who found it out in despite me.

[@kenetmartinez369]

Just as an advice, I wouldn't use that "small arc length" stuff. Actually, no matter how large the angle is, the arc length remains the same: s = theta*r. You could prove this via the integral arc length formula. I think that is better to say, look, when the angle is very small, there is no difference between the arc and a straight line, so despite the displacement being curve, we can still use vectors, which represent straight lines, to represent our dr, and the magnitude will be theta*r precisely. The last rule actually come from calculus, using the cosine law: Because we are over a circle, we have an isosceles triangle with both sides equal to r. By law of cosines, x^2 = r^2 + r^2 - 2*r*r*cos(θ) = 2r^2 - 2r^2cos(θ) = 2r^2(1-cos(θ)) = 4r^2((1-cos(θ))/2 = 4r^2 sin^2(θ/2) {USING THAT sin^2(x) = (1-cos(2x))/2 }, so x= 2rsin(theta/2), but, because the angle is arbitrarily small, sin(theta/2) ≈ theta/2, obtaining that x = 2*r*theta/2 = r*theta, which is precisely the arc length equation, so basically we have said that the arc length is aproximately a straight lines for SMALL ANGLES, not for small arc length. Remember that this thing holds up to 13.99°, so if the radius is very large, we can easily find that the arc is not that small. That intuitive thought find its validation via this sin(theta/2) ≈ theta/2 thing, which come from the taylor series. Thats why we can use it! Without the previous argument we can easily say the first thing, and its equally valid and surely not that obvious just by reading the name you gave.

[@dougr.2398]

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

[@dialectphilosophy]

You may have superpowers 🦸 👀

[@anassbellachehab9821]

I have a feeling that your next video will on some kind of "Eulerian view" of Maxwell's equations. E&M field as a flow of geodesics in the ether. For that you will need an appropriate definition of covariant derivative.

[@dan-valentin3023]

Please continue with a folloow up video on ficticious Centrifugal and Coriolis accelerations

[@dialectphilosophy]

That is the plan!

[@axle.student]

Gone over my mathematical head a little with this one lol I'll wait for the next video and punch line :P

[@jaw0449]

Man, I wish I had something like this years ago! Trying to do it in your head or 2D graphs, or program it yourself was hard

[@ParadesiJoel]

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.

[@Mr_Kyle_]

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?)

[@matthewhall6288]

Is the universe expanding, or is everything inside it shrinking?

[@UnrealogyTutorials]

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.

[@dialectphilosophy]

Thank you for the kind words and support ☺️

[@crazyengineer101]

Amazing video!

[@UNI2VERSE369]

Very good video please make one video filled with visual examples with different refrence frame in rotating body

[@LearnScienceThroughPhysicist]

Your animation is awesome. I wanted to know, Which software did you use to make this animation specifically the Formulation.

[@APaleDot]

I'd guess Blender

[@CorteLeo]

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?

[@LearnScienceThroughPhysicist]

@@APaleDot but how the Scientific notation? I started learning Manim but is there any easy way?

[@APaleDot]

@@LearnScienceThroughPhysicist I'd say Manin is the easy way. Unless you just want to screenshot LaTeX.

[@Ash-bc8vw]

Simply amazing

[@pankajk.r2448]

Underrated channel

[@OzanYarman]

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.

[@Bigchickenburger]

Am I dumb

[@TS-jm7jm]

​@@Bigchickenburgerlol

[@lih3391]

v0'-v0 is an infinitesimal value, and the same goes for vf.

[@OzanYarman]

@@lih3391 That is incorrect. The difference of two finite difference quantities cannot ever furnish an infinitesimal value.

[@lih3391]

@@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?

[@lokhimcheung9262]

Maxwell equations... EXACTLY why i was looking this up

[@richardchapman1592]

If we made an acceleration function comprising rotation and direction as described by it's two unit basis vectors as a function of t,it would all still be based on the original Cartesian frame.

[@PathfinderPhysics]

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.

[@dialectphilosophy]

Interesting channel! We've never found Bell's Theorem to be compelling... consider sharing your work on our discord server.

[@PathfinderPhysics]

@@dialectphilosophy i certainly will. I must stress that it's not my work, but Joy Christian's.

[@mescwb]

but how could get the "final" particle speed if its referential frame is moving relative to other, slower referential frame (one frame moving in a direction atop another slower / moving in different direction)? :)

[@BenAlternate-zf9nr]

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.

[@dialectphilosophy]

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.

[@robinbernardinis]

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.

[@vinniepeterss]

exceptionally done!

[@willo7734]

Our universe simulation must have some really huge processors to handle all this math for every atom on a constant basis.

[@nickcunningham6344]

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.

[@mikkel715]

If we were a simulation, small scale physics would reveal strange results...

[@domg6041]

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.

[@darrennew8211]

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.

[@dialectphilosophy]

Thank you, we appreciate the feedback on that!

[@vasekbrezina2801]

@@dialectphilosophy For me the sounds are quite annoying and mostly unnecessary :-)

[@Raja-c8t]

Oh what a Wonder full chain 🎉🎉🎉

[@eamon_concannon]

11.50 the coord velocity Vo means the velocity of a particle relative to rotating frame. Right? If so, and coord velocity is constant then vector Vo = vector Vo', right? Notation is very confusing

[@panos21sonic]

Slept thru the lecture where the teacher proved this (fckn 8am lectures...). Doubt he explained it better than this. That being said, my head still feels like itll explode

[@aesmon]

i would love to see the riemann curvature tensor covered on this channel

[@dialectphilosophy]

We're getting there! Almost finished with our coverage of the Christoffel Symbols, and then Riemann curvature is up next!

[@HuxleysShaggyDog]

Oh you're going all the way aren't you? Nice.

[@givemeArupee]

What do you mean by coordinate velocity ? Is it calculated wrt to K frame (rest frame) or K0 frame (rotating frame) ?

[@dialectphilosophy]

Coordinate velocity as used here refers to the velocity calculated with respect to the K0 frame, i.e. the rotating frame. Though mathematically it makes little sense to distinguish between coordinative and actual velocity (all velocity would be coordinative by definition, and one should rather say, velocity with respect to a given frame), in physics, rotating frames are non-inertial and as such, their rotation is regarded as 'real'. Thus the velocity of objects within such frames are only 'apparent', or 'coordinative'. This distinction becomes important when tackling fictitious forces.

[@AJ-et3vf]

Awesome video! Thank you!!!

[@usman.hqu1]

i m excited about when will im watching the video about constitutive relations in rotating systems

[@marc-andredesrosiers523]

Keep it up 🙂

[@rockapedra1130]

Awesome video!!!!

[@MwilimaIan]

I have mastered this equation.

[@SphereofTime]

2:39 new coordi

[@vincenzegreisingel2429]

Coriolis effect for gunnery

[@AmericanPatriot1812]

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!"

[@dialectphilosophy]

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?

[@AmericanPatriot1812]

​@@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.

[@se7964]

@@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.

[@AmericanPatriot1812]

​@@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.

[@PepeNuclear]

@@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. 😂

[@Nixontheman]

Love this channel ‼️‼️‼️

[@jayyoo906]

Nature say more difficult ones. Track a fly flight pathway, mathmathise the trace and predicts next moving.

[@liammccreary2941]

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.

[@liammccreary2941]

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

[@lyugaoyueyang8017]

For the last example, why is the frame acceleration 0 not -w^2r r_hat? Thank you

[@victortiempo-to5il]

What about the applied equation for any moving particle that experience heat and pressure as it travels through various dimensional conditions

[@mikkel715]

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?

[@dialectphilosophy]

Nothing to be said for certain at the moment, but there are certainly a number of intriguing similarities!

[@gizachewbayleyegn4309]

thank you

[@مرادمحمدصبري]

Thanks a lot

[@chuckjls]

May be a dumb question. How do rotating coordinate systems relate to motor control and the Park transform?

[@griffgruff1]

The brackets are missing in the cross-product term: WxWxr . It should be written as Wx(Wxr).

[@ibrahiymmuhammad4773]

Someone tried the rocking chair 🎉

[@fahimalizai6442]

WHAT helps to learn quantum physics?

[@dialectphilosophy]

We hope to have an answer to that one day.

[@xinpingdonohoe3978]

Feynman lectures can be useful.

[@Sasham4]

Thanks!

[@dialectphilosophy]

Thank you so much!! 🤗

[@SherriMSDRML-qm1pe]

Thank you thank you 🧠🤠🤖🇱🇷🇮🇳🇮🇳🇮🇳

[@gekkkoincroe]

Woah I understood nothing, I'll open my highschool book to see how this relates to newton's motion and rotational mechanics Although that was hard too

[@wargreymon2024]

This is gold

[@ayashione7743]

Hey could I ask in what editor do you make this videos, or are you using multiple programming languages?

[@bio_for_neet]

Can you please tell me what tools you use for animation?

[@empireempire3545]

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.

[@null-0x]

No. Textbooks and Papers need to stay.

[@Christopher-e7o]

Time bends place and time,mass and speed over gravity,----^

[@natico-w812]

this is some good physics