Thanks for your kind words and support!

Thanks, great to hear that it was a clear explanation. Back when I was a Physics undergraduate I never fully understood why dk'/dt = ω x k' and so on, so my hope is that this will help people who are now in a similar situation!

Thanks for your kind words, I'm glad the videos have been helpful!

Good to hear, thanks for watching!

Thanks for saying so!

Thank you!

Thanks for watching, I'm glad it helped!

Thanks for watching and I'm glad it was helpful!

You're welcome, I'm glad it was helpful!

Thank you for watching!

Hello and thanks for watching! With the ω x A term, what matters is that both vectors are expressed in the same basis. This could either be the basis of S (i, j, k) or S’ (i’, j’, k’) - whichever is more useful for the problem at hand. If A were constant in S’ and you wanted the time derivative in S, then you would indeed need to transform the components of A into frame S using a rotation matrix before taking the cross product with ω expressed in S. Perhaps the most common usage of the relation derived in the video, though, is to find the equation of motion of a particle in frame S’ - so here A is a position vector which is varying with time in S’ and we want to know how exactly it’s going to evolve over time. In this case it’s more useful to keep A in the S’ basis and express ω in that same basis. I think the key point to remember is that the vector ω x A exists independently of any basis, but if we want to write this vector out in component form then the components of ω and A must be expressed in the same basis. Hope this helps a little, there are some more videos later in my rotating frames playlist which might also be useful: kzfaq.info/sun/PLTntRzhyShSEugh4o6AARrJRS-PxxqjiI

@@DrBenYelverton Thank you so much! Yes, I continued to be tormented by the question since I posted the comment🙂. And came to the realization that I was actually conflating between "which frame a vector is with reference to" and "which coordinate system the vector may be expressed in" (as you mention above). My question had to do with the latter. I was able to make peace with it by assuming that both systems used a common Z axis, and freezing time at a multiple of 2pi/omega. Then the basis vectors would coincide in both systems, and all equations would go through smooth. In general, as you mentioned, A|S and A|S' are consistently oriented at any instant of time, no matter the bases, but if the actual cross product is to be computed then a common set of coordinate bases should be used (mapped if necessary). Thank you also for sharing the full playlist; I will certainly be watching the subsequent videos in the series.

Thanks for watching. Imagine writing out the equation in component form, so that you now have three separate equations in terms of the x, y and z components of all the vectors. Maybe the easiest way to see how to do this is just to write the vectors in column vector form. Each of the three individual equations now only involves scalars and you can differentiate as usual. After differentiating, write your three equations as a single equation again by switching back to vector notation and you'll arrive at the result in the video.

@@DrBenYelverton, if I understood properly, you mean this: d/dt (A i' + B j' + C k') = d/dt ( A(t) * [a(t), b(t), c(t)] + B(t) * [d(t), e(t), f(t)] + C(t) * [g(t), h(t), i(t)] ) Where a(t), b(t), ..., i(t) are the components of versors i', j', k', which are variable with time if examined in the fixed reference frame. And then you go with product rule, is it correct?

Yes, that's exactly right - it basically comes down to viewing your vector equation as three scalar equations, so you can then proceed with all the rules you know for scalars.

Thanks for watching!

@@DrBenYelverton Sir, I'm requesting you to Upload Bsc Physics videos please if you can. It really helps me understand.

@@hian77 Will do! I have many more undergraduate-level Physics videos planned.

@@DrBenYelverton that's great 😊

Sounds like an interesting exercise - though probably not something I'd be able to do right now as I haven't used Christoffel symbols since studying GR around 7 years ago! Thanks for watching.