All Questions
8 questions
4
votes
2
answers
943
views
Mass travelling with constant speed in a circle
Imagine a 2D circle has a point mass traveling along its circumference with constant speed. The only force experienced is centripetal. However, if we take the 2D plane the circle sits on and rotate it ...
0
votes
1
answer
54
views
Coordinates-free, geometry-free, algebraic way to derive facts about circular motions
I would like to derive the following facts about non-uniform smooth circular motion in three dimensions.
The sole boundary conditions given are:
Three dimensions of Euclidean space, one dimension of ...
3
votes
3
answers
653
views
Confusion about successive derivatives of position in circular motion
Suppose we define a unit vector $\vec r$ along radial direction for a particle in uniform circular motion at an angular frequency $\omega$. Then we can write:
$$\vec r = \cos(\omega t)\hat i + \sin(\...
- 326
3
votes
1
answer
139
views
Is there an equation that relates angular acceleration to centripetal acceleration? Tangential to centripetal?
Is there an equation that relates tangential and centripetal acceleration? I ask this question because it's been on my mind ever since I solved a problem involving the giant swing ride commonly seen ...
- 169
0
votes
1
answer
2k
views
Derivation of centripetal acceleration
While reading HC Verma chapter 7 circular motion I came across a derivation which I couldnt understand. I have marked my doubt with red. I don't understand from where +dw/dt [- i sine +j cos0] came ...
- 997
2
votes
1
answer
859
views
Angular and linear displacement of a turning car
My illustration is supposed to show a simplified car (with just two wheels, where the front wheel has been rotated $-90 \text{ degrees}$). Let the car travel at constant speed. This means that the ...
- 141
2
votes
4
answers
2k
views
Does circular motion cause centripetal force OR does centripetal force cause circular motion?
Does circular motion cause centripetal force, or does centripetal force cause circular motion, or are they both occurring hand in hand together instantaneously?
One more question: If I project a body ...
- 923
8
votes
4
answers
20k
views
Proof of centripetal acceleration formula ($a_c = v^2/r$) for non-uniform circular motion
The formula for centripetal (radial) acceleration is well known, and there exist many proofs for it: $$||a_c|| = \frac{||v||^2}{r}$$
However, all the proofs I've seen rely on the fact that it is ...
- 1,605