Walker, Halliday & Resnick — Rolling, Torque, and Angular Momentum: Problem 48

48 A Texas cockroach walks from the center of a circular disk (that rotates like a merry-go-round without external torques) out to the edge at radius \(R\). The angular speed of the cockroach–disk system for the walk is given in Fig. 11-43 (\(\omega_a = 5.0 \text{ rad/s}\) and \(\omega_b = 6.0 \text{ rad/s}\)). After reaching \(R\), what fraction of the rotational inertia of the disk does the cockroach have?