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A particle is moving in a circle

  • Thread starter mrknowknow
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  • #1
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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.
 

Answers and Replies

  • #2
HallsofIvy
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Since the problem says "minimum time" you can get at least an estimate without Calculus. The particle has maximum speed [itex]\sqrt{2} v[/itex] so cannot go a distance [itex]2\pi R[/itex] is less than
[tex]\dfrac{2\pi R}{\sqrt{2} v}= \sqrt{2}\pi \dfrac{R}{v}[/tex].
 
  • #3
BruceW
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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:
  • #4
DrClaude
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The particle has maximum speed [itex]\sqrt{2} v[/itex]
Could you please explain your reasoning here?
 
  • #5
BruceW
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hehe, yeah, I thought the same thing initially.
 
  • #6
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Well how would I solve the problem with Calculus?
 
  • #7
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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
BruceW
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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
BruceW
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even without assuming uniform motion, we can still get a 'minimum time'.

edit: (as Hallsofivy has done)
 
  • #10
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Well My professor stated as a hint he doesn't think it could be solved without Calculus. Could he be wrong?
 
  • #11
BruceW
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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).
 

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