Main Question or Discussion Point
I'm afraid I need some help on this one. We are studying rotational dynamics and I read in my textbook, the explanation of a common classroom deonstration. A person sits on a rotating stool and holds heavy weights in their outstretched hands. Someone sets the individual into rotational motion and when they pull their hands in, the speed of rotation increases. This is easily understood with the conservation of angular momentum. We are asked to imagine that we actually perform this demonstration and that pulling our arms in results in halving our total moment of inertia. This obviously doubles our angular speed according to the law of conservation of angular momentum. If we consider the rotational kinetic energy, we quickly see that we have doubled the energy associated with that rotation. Again, not a difficult concept because we have done work on the weights (The source of energy being food that we ate earlier that day, or perhaps even days ago.) But here's the problem I have. Suppose we do a DIFFERENT experiment. Suppose we tether a volleyball on a pole. Now we strike the volleyball perpendicularly to the string that holds it on the pole. We have given the ball a certain amount of energy and it begins to rotate at a given angular speed. The string wraps around the pole and in a period of time, the radius will have decreased just enough to make the moment of inertia half of its orignal value just as in the previous demonstration. When that happens, again the angular speed will double and the kinetic energy will also double. But this time, NO ADDITIONAL ENERGY WAS ADDED AND THE POLE DIDN'T HAVE LUNCH TODAY... OR YESTERDAY EITHER! How do we reconcile the fact that the ball seems to have gained energy with no additional energy input here? I really need help here. Thanks, in advance, for whatever you can supply.