A cockroach of mass m lies on the rim of a uniform disk of mass 4.00 m that can rotate freely about its center like a merry-goround. Initially the cockroach and disk rotate together with an angular velocity of 0.320 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//K_(0)` of the new kinetic energy of the system to its initial kinetic energy? ( c) What accounts for the change in the kinetic energy?

Explanation

(a) 0.427 rad/s, (b) 1.33, ( c) The cockroach does positive work while walking toward the center of the disk, increasing the total kinetic energy of the system.