Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 79

Change in angular speed. In Fig. 11.8.6, a cockroach with mass \(m\) rides on a uniform disk of mass \(M = 8.00m\) and radius \(R = 0.0800 \text{ m}\). The disk rotates like a merry-go-round around its central axis. Initially, the cockroach is at radius \(r = 0\) and the angular speed of the disk is \(\omega_i = 1.50 \text{ rad/s}\). Treat the cockroach as a particle. The cockroach crawls out to the rim of the disk. When the cockroach passes \(r = 0.800R\), at what rate \(d\omega/dr\) does the angular speed change as it moves outward?