(Solution) - A cockroach of mass m lies on the rim of -(2025 Original AI-Free Solution)

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A cockroach of mass m lies on the rim of a uniform disk of mass 4.00m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.260 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?
(c) What accounts for the kinetic energy?