Time derivatives in a rotating frame of reference

Here's how to derive a very useful operator relation linking time derivatives in rotating and inertial frames. We'll use this relation to show how fictitious forces arise in rotating frames in my next video.

About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university.

#physics #maths #math #mechanics #dynamics #fictitiousforces #coriolis #centrifugal #euler #forces #rotation #rotatingframes #inertialframes #calculus #vectors #differentiation #operators #particle #motion #circularmotion

[carlhenry]

I finished Differential EQ and Linear Algebra a year ago, you've made it very simple to follow, good job 👍

[huseyinguven]

Excellent, sir. Given your current number of subscribers, it's far below what you deserve. My wish is for your recognition to increase. 👌

[naivaidyavijayvargiya]

woow i found an underrated teacher i mean you can really go to any famous private institute or university and become their main teacher sir thanks for this effort for teaching here

[darksideng]

Excellent!!! Simple and direct to the point.

[cacostaangulo]

Excellent. In almost one slide the whole explanation. I really enjoyed watching your video.

[Forever._.curious..]

Amazing 🤩 . It's interesting and yr explaination is intuitive

[lordmandarin]

This video was very explicative and interesting. I always tried to obtain the derivative relation you have shown at the beginning by using row, columns and matrices notation. Putting the symbols i', j, ' k' like you did makes everything easier to understand. Thank you.

[heidarsafari]

Thank you for your excellent explanations and stating details in derivation .
🙏🙏🙏🌹🌹🌹

[AhmedMohamed--]

Great video and excellent explanation!

[giack]

Hello, thank you for the very clear video. I wanted to ask: at minute 5:24 we make: d/dt (A i' + B j' + C k'). But why this derivative follows the common rules of derivation of product as it was a product between scalar functions? It is the derivative of a linear combination of scalars and vectors..

[Musiclover]

Hello Dr. Yelverton, thank you so much for a lucid description on this topic. However I have one source of confusion which is bothering me (as I have been experiencing with many other videos addressing this topic as well). Referring to the second term of the last expression at 17:30 min, when you cross omega with the vector A, the latter has to be expressed in/converted to its time varying form in the inertial reference frame S, by applying coordinate transformation to the corresponding prime components in the rotating frame S', right? You cannot directly cross omega with the stationary prime components? If we make things a bit simpler by making the vertical axes of the two frames coincident, then the components in the S domain will be sums of components in the prime domain multiplied with Cos(wt), Sin(wt), etc. ? In the general 3D case shown this will be more involved with, e.g., qaternion rotations? Thank you for any advice to clarify my thinking.

[deeptochatterjee]

Or you could calculate the christoffel symbols in this new frame and find the covariant time derivative... Jk this was great, but it is an interesting idea to use the covariant derivative to verify this

[DJ-yjvg]

That's the first time I've seen how dihat/dt=w x ihat derivation