What is angular velocity of the cockroach-disk, Ask an Expert

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A cockroach of mass m lies on the rim of a uniform disk of mass 5 m that can rotate freely about its center like a merry-go-round. Firstly the cockroach and disk rotate together with an angular velocity of 0.285 rad/s. Then the cockroach walks halfway to the center of the disk.

(a) What after that is angular velocity of the cockroach-disk system?

(b) What is ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?

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