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.