Equation of motion in a rotating frame: deriving the fictitious force terms
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- Опубликовано: 2 мар 2021
- Here's how to use the operator relation for time derivatives in a rotating frame to show how fictitious force terms (centrifugal, Coriolis and Euler) arise. It may be helpful to watch my previous video first: • Time derivatives in a ...
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.
My website: benyelverton.com
#physics #maths #math #mechanics #dynamics #fictitiousforces #coriolis #centrifugal #euler #forces #rotation #rotatingframes #inertialframes #calculus #vectors #differentiation #operators #particle #motion #circularmotion
Thank you for that derivation of all the fictitious forces, it was very elegant I thought.
I find it much simpler to solve for such rotational frames with Lagrangian mechanics.
Fair enough, perhaps a topic for a future video!
Notations are beautiful
Thank you!
I am electrical engineer, enjoying these videos alot 😍.
Great to hear, thanks for watching!
I'm also studying physics at cambridge, this is really helpful
Great to hear - good luck with the course!
@@DrBenYelverton I’m currently preparing for IB physics exams rn, the lectures are shockingly terrible. You think this channel would be a good substitute?
@@peterpoli2839 I have a couple of videos that are relevant to the IB course, but as a relatively new channel I don’t have anywhere near enough content yet for this to be a viable alternative to lectures. The best advice I can give for exam prep is just to do as many past papers as you can. I know it’s annoying that there are no mark schemes (even when I was supervising I didn’t have access to such things) but you can often get a good sense of whether you’ve answered a question correctly (e.g. many questions are “show that”; you can also check things like dimensions and whether the order of magnitude of your result is sensible). The way I always did things was just to try exam questions and look things up in the lecture notes when I didn’t know something, rather than try to learn all the theory first and then test myself. While the lectures are not always great, the lecture notes are generally pretty good and contain everything you need to know.
@@DrBenYelvertonWhat evidence is there against the geocentric model called the Neo-Tychonic model in which the planets revolve around the sun, but the sun revolves around the earth in the center?
@@moneyheist_- so much 😂
I just read for the first time: The same result could also have been obtained with the Euler-Lagrange
equations for L in the rotating coordinates:
L = m/2(r˙ + ω× r )^2 − V .!
Indeed, I've been meaning to do a video on this for a while!
@@DrBenYelverton looking forward to it!
Lovely❤
Thanks!
no matter how many video, i dont get it. it confuse me
It is certainly not an easy thing to understand at first! Ultimately the key idea is that in a rotating frame, the rate of change of a vector quantity is different from what we might expect, because the basis vectors themselves are changing over time. See this video for the details: ruclips.net/video/Vautr1lDJ78/видео.html
Coming back to this video, your frame notation on the derivative seems to be a bit confusing.... A time derivative operator will always be the same no matter what frame (leaving special relativity out of this).
Yes, according to the formal definition the d/dt (S) operator is the "true" time derivative. Personally I do find the d/dt (S') notation to be helpful for conceptual understanding because it's the operator that gives the rate of change that would be observed in S'. But looking at it from a strictly mathematical point of view I can see how it might cause confusion.