In a playground, there is a small merry-go-round of radius 1.20 m and mass 180 kg. Its radius of gyration is 91.0 cm. A child of mass 44.0 kg runs at a speed of 3.00 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.