Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 57

57 A uniform disk of mass $10m$ and radius $3.0r$ can rotate freely about its fixed center like a merry-go-round. A smaller uniform disk of mass $m$ and radius $r$ lies on top of the larger disk, concentric with it. Initially the two disks rotate together with an angular velocity of $20\text{ rad/s}$. Then a slight disturbance causes the smaller disk to slide outward across the larger disk, until the outer edge of the smaller disk catches on the outer edge of the larger disk. Afterward, the two disks again rotate together (without further sliding). (a) What then is their angular velocity about the center of the larger disk? (b) What is the ratio $K/K_0$ of the new kinetic energy of the two-disk system to the system’s initial kinetic energy?