Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 75

In a playground, there is a small merry-go-round of radius \(1.20\text{ m}\) and mass \(180\text{ kg}\). Its radius of gyration (see Problem 79 of Chapter 10) is \(91.0\text{ cm}\). A child of mass \(44.0\text{ kg}\) runs at a speed of \(3.00\text{ m/s}\) along a path that is tangent to the rim of the initially stationary merry-go-round and then jumps on. Neglect friction between the bearings and the shaft of the merry-go-round. Calculate (a) the rotational inertia of the merry-go-round about its axis of rotation, (b) the magnitude of the angular momentum of the running child about the axis of rotation of the merry-go-round, and (c) the angular speed of the merry-go-round and child after the child has jumped onto the merry-go-round.