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A cockroach of mass m lies on the rim of a uniform disk of mass 3.00...

A cockroach of mass m lies on the rim of a uniform disk of mass 3.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.466 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then is the angular velocity of the cockroach-disk system? (b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?

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