A cockroach of mass m lies on the rim of a uniform disk of mass 5.00…

A cockroach of mass m lies on the rim of a uniform disk
of mass 5.00 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 0.410 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?