Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 55

55 Figure 11-46 is an overhead view of semicircular ring of mass m and radius R that lies on a frictionless surface. The ring is connected by elevated spokes (not shown) to a pivot at the center of the semicircle. The ring can rotate around that pivot but is initially stationary. A bead of mass m and speed v is shot into the ring, entering under the spokes and tangentially to the ring and then sliding along the ring. The ring and bead then rotate together around the pivot. Find their angular speed.