A cockroach of mass m lies on the rim of a uniform disk of mass 4m 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. 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? State your answer in terms of the given variables.