Walker, Halliday & Resnick — Rolling, Torque, and Angular Momentum: Problem 44

44 A Texas cockroach of mass 0.20 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has radius 18 cm, rotational inertia $5.0 \times 10^{-3} \text{ kg} \cdot \text{m}^2$, and frictionless bearings. The cockroach’s speed (relative to the ground) is 2.0 m/s, and the lazy Susan turns clockwise with angular speed $\omega_0 = 2.8 \text{ rad/s}$. The cockroach finds a bread crumb on the rim and, of course, stops. (a) What is the angular speed of the lazy Susan after the cockroach stops? (b) Is mechanical energy conserved as it stops?