# A particle is moving in a circle

1. Sep 20, 2013

### mrknowknow

A particle is moving in a circle of radius R in the xy plane. During the motion, neither the x- nor y-component of the particle's velocity exceeds v. Find the minimum possible time for the particle to complete one circle. (I.e., find the minimum possible period of revolution.)

Hint 1: I don't think it can be solved without Calculus.
Hint 2: Answer is in the form of an equation without any rounding of any numbers involved.

Considering I haven't taken Calculus yet I don't know the right way to approach this problem.

2. Sep 20, 2013

### HallsofIvy

Staff Emeritus
Since the problem says "minimum time" you can get at least an estimate without Calculus. The particle has maximum speed $\sqrt{2} v$ so cannot go a distance $2\pi R$ is less than
$$\dfrac{2\pi R}{\sqrt{2} v}= \sqrt{2}\pi \dfrac{R}{v}$$.

3. Sep 20, 2013

### BruceW

I think it means that the max possible x-component of velocity is v. But it is worded a bit vaguely.

edit: and a similar statement for y, separately.

edit again: never mind, I am being stupid. I thought there was a problem, but there is not.

edit number 3: yeah, my mistake was thinking the question gave the max values of components of velocity. But it does not. It gives upper bounds.

Last edited: Sep 20, 2013
4. Sep 20, 2013

### Staff: Mentor

5. Sep 20, 2013

### BruceW

hehe, yeah, I thought the same thing initially.

6. Sep 20, 2013

### mrknowknow

Well how would I solve the problem with Calculus?

7. Sep 20, 2013

### Saitama

Not sure but if you consider the uniform circular motion, the conditions mentioned in the problem are satisfied.

Is it possible for you to post the answer?

8. Sep 20, 2013

### BruceW

well calculus doesn't really help to get a better answer in this case. If they told you the velocity as a function of time, then you could use calculus. But they don't tell you that.

9. Sep 20, 2013

### BruceW

even without assuming uniform motion, we can still get a 'minimum time'.

edit: (as Hallsofivy has done)

10. Sep 20, 2013

### mrknowknow

Well My professor stated as a hint he doesn't think it could be solved without Calculus. Could he be wrong?

11. Sep 20, 2013

### BruceW

the way you have described the problem, I don't think you need calculus. But you should make up your own mind. (Although I guess that might be tricky if you haven't been taught what calculus is).