Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 63

63 In Fig. 11-51, a 30 kg child stands on the edge of a stationary merry-go-round of radius 2.0 m. The rotational inertia of the merry-go-round about its rotation axis is 150 kg·m². The child catches a ball of mass 1.0 kg thrown by a friend. Just before the ball is caught, it has a horizontal velocity \(\vec{v}\) of magnitude 12 m/s, at angle \(\phi = 37^\circ\) with a line tangent to the outer edge of the merry-go-round, as shown. What is the angular speed of the merry-go-round just after the ball is caught?