Actually, I don't have to have an infinitely thin pole. All I need is that the length of the string >> the diameter of the pole. So I could have the string at 2 m in length, while a pole that's 1 cm in diamter. With such geometry, it is very hard for me to be convinced that there's any significant angular component to the tension in the string.krab said:I think Doc Al is right. If you put the assembly of ball, rope, pole on an air table, (actually you'll need 2 balls, one on either side, to avoid wobble), then as the balls wind up, the assembly will begin to turn as well. The string does no work. In a tether-ball situation, the ball does not speed up; it has 1/2mv^2 energy at the start and has the same 1/2mv^2 at the end just before it is all wound up and crashes into the pole. It seems to go faster at the end, but in fact is only going a faster angular speed, not a faster linear speed.
ZZ and lee are arguing in the limit of zero pole thickness. In that limit, there is no torque of the ball on the pole, but OTOH, neither does the string wind up.
It is also puzzling to me that no work is thought of being done, especially when the mass is moving in radially. A centripetal force alone will simply cause a uniform circular motion. It requires an additional force to pull the ball in. This additional force translates to an additional tension in the string beyond just having it move in a circular motion. Again, relating this to a similar observation, this is what most science museum has where a ball rolls on the outer edged of a "funnel" and people see it moving faster and faster it it reaches the center of the funnel. Here, instead of a string pulling the ball in, it is the side of the funnel that is pushing the ball in with the help of gravity. Here, it should be even more complicated than the ball+string+pole, since the contact point here is not on the vertical side of the ball, but rather at an angle below the horizontal. Yet, all of these demonstrations claim to show conservation of angular momentum.