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[This question is meant to be entirely conceptual∗ . Probably the best thing to do is to close your eyes and imagine the situation in detail once you've read the problem description.]
You and a friend decide to play a game on an ideal merry-go-round (with frictionless axle), as follows:
1. You stand facing inward on the edge of the merry-go-round while your friend spins it up to some speed. The game starts when you reach the southernmost point of your circular trajectory (marked start in the figure);
2. You ride the merry-go-round all the way around (arc 1) until you reach the starting point, then jump due north (2) to a smaller radius;
3. You ride the smaller radius arc (3) around a full circuit, then jump due north (4) to yet a smaller radius;
4. Repeat the cycle of riding the merry-go-round all the way around to the southernmost point at a given radius, and then jump due north to a smaller radius, until you reach the very middle of the merry-go-round.
By the time you've reached the middle of the merry-go-round, it is spinning faster than when you started. I'd like to know why the merry-go-round is spinning faster than it was. The axle has no friction, and any friction or air resistance would slow the merry-go-round, not speed it up.
You can answer this in terms of Lfinal = Linitial , but that's not really what I'm getting at. What I really want you to think about (and answer) is: Did you exert a torque with all of your jumping around? If so, where and how? If not, then what's going on?