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. Initially 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 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?