- #1
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Consider a merry-go-round (carousel) with a tube fixed radially on it. I use a pole to push a bowling ball slowly through the tube towards the center. (Slowly, so that the kinetic energy is negligible when the ball reaches the center. Also assume zero friction).
What happens to the work that I do in this process? Since I can think of no other possibility, my first guess would be that it somehow goes to increase the angular velocity of the system (via coriolis force acting against the tube's wall).
But then, on the other hand --- my force is normal to the direction of the instantaneous tangential acceleration, so it's not very convincing that I could be doing work to spin up the carousel. Considered this way, the carousel spins up only because the ball slows down as its orbit shrinks and it is forced to give up its velocity in order to conserve angular momentum, and coriolis is the force that mediates this exchange.
So then, where does my work end up?
What happens to the work that I do in this process? Since I can think of no other possibility, my first guess would be that it somehow goes to increase the angular velocity of the system (via coriolis force acting against the tube's wall).
But then, on the other hand --- my force is normal to the direction of the instantaneous tangential acceleration, so it's not very convincing that I could be doing work to spin up the carousel. Considered this way, the carousel spins up only because the ball slows down as its orbit shrinks and it is forced to give up its velocity in order to conserve angular momentum, and coriolis is the force that mediates this exchange.
So then, where does my work end up?