Rotational kinetic energy explaination

[Michael C]

hmm it's just that when you see the ball for the point of contact between string and pole it makes a uniform circular motion. So can't you say that the angular momentum is conserved in this frame for the ball? And why does that not qualify to the ball's angular momentum being conserved like if the rotation was around the center of mass? :)

The point of contact is changing all the time: it's turning in a circle around the pole, so (as Philip pointed out) it's constantly accelerating. If we fix one point on the surface of the pole and measure the angular momentum around this point, we'll see that the momentum of the ball must be changing, since there is only one instant when the ball exerts no torque in this frame: the instant when the centre of rotation is at the point we have fixed. For the rest of the time, the centre of rotation is not at the point we have fixed, so there is torque around this point.

 

[aaaa202]

yes okay, I should have realized that. But doesn't there exist conservation laws in non inertial reference frames?

 

[Philip Wood]

I expect so. Indeed I expect we could easily find such a frame in which angular momentum is conserved for the ball. But that would not be anything to be especially pleased about. The ball's angular momentum would be conserved simply because we've chosen a special frame in which it is conserved. In this frame, things whose angular momentum we'd normally expect to be conserved won't have it conserved... The laws of Physics are usually easier in inertial frames.