- #1

opticaltempest

- 135

- 0

Hello,

I am trying to analyze the following situation:

A tetherball is kicked with velocity of [tex]v[/tex] meters per second at time [tex]t=0[/tex] seconds. The length of the string attaching the tetherball to the pole is [tex]l[/tex] meters. The radius of the pole is [tex]r[/tex]. Assume no gravity and no air resistance so that the ball wraps around the pole in the plane in which it is initially kicked. In other words, when the ball makes one complete revolution around the pole the length of the string is reduced by [tex]2\pi r[/tex].

1. I would like to set up a differential equation that describes the length of the string at any time [tex]t[/tex].

2. My ultimate goal is to analyze the angular velocity and linear velocity at any time when the ball is wrapping inward towards the pole without using the conservation of angular momentum.

This isn't a homework problem so I might have left out information needed to complete the problem.

I am having trouble on all approaches. Any help will be greatly appreciated.

I am trying to analyze the following situation:

A tetherball is kicked with velocity of [tex]v[/tex] meters per second at time [tex]t=0[/tex] seconds. The length of the string attaching the tetherball to the pole is [tex]l[/tex] meters. The radius of the pole is [tex]r[/tex]. Assume no gravity and no air resistance so that the ball wraps around the pole in the plane in which it is initially kicked. In other words, when the ball makes one complete revolution around the pole the length of the string is reduced by [tex]2\pi r[/tex].

1. I would like to set up a differential equation that describes the length of the string at any time [tex]t[/tex].

2. My ultimate goal is to analyze the angular velocity and linear velocity at any time when the ball is wrapping inward towards the pole without using the conservation of angular momentum.

This isn't a homework problem so I might have left out information needed to complete the problem.

I am having trouble on all approaches. Any help will be greatly appreciated.

Last edited: