Conservation of energy and tether ball

[gg4bella]

Homework Statement

When a tether ball wraps around a pole, the speed of the ball does not change. I need to explain why using conservation of energy but am struggling in this class and need to see if I'm on the right track. The second part of the problem states that if the length of the tether is decreased the velocity of the ball doesn't change but the rotational speed of the ball changes how?

Homework Equations

The Attempt at a Solution

I think because the ball has kinetic energy while wrapping, when there is no more rope to wrap around the pole, the ball has potential energy to unwrap. Once this happens the ball has kinetic energy again. The second part I think, would have the rotational speed of the ball decrease but I'm not sure why. Any help would be appreciated.

 

[PeterO]

Homework Statement

When a tether ball wraps around a pole, the speed of the ball does not change. I need to explain why using conservation of energy but am struggling in this class and need to see if I'm on the right track. The second part of the problem states that if the length of the tether is decreased the velocity of the ball doesn't change but the rotational speed of the ball changes how?

Homework Equations

The Attempt at a Solution

I think because the ball has kinetic energy while wrapping, when there is no more rope to wrap around the pole, the ball has potential energy to unwrap. Once this happens the ball has kinetic energy again. The second part I think, would have the rotational speed of the ball decrease but I'm not sure why. Any help would be appreciated.

For part (b): If we assume part (a) is correct, and the kinetic energy of the ball isn't changing, the speed of the ball isn't changing. When the rope is half wrapped, the ball will be traveling in circle of half the original radius, and thus half the circumference. SInce it is traveling at the same speed it will take less time to complete a turn, so the angular speed is higher.