A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child gets onto it by grabbing its outer edge? The child is initially at rest.
Step-by-step solution Step 1 of 3 The conservation of angular momentum can be applied, as no external torque is acted upon the merry-go-round. So, initial angular momentum is equal to final angular momentum of the system. Here, is the moment of inertia of the merry-go-round, is the angular velocity of the merry-go-round, is the moment of inertia of the system with the kid at the edge of the merry-go-round and is the required angular velocity. Step 2 of 3 Convert initial angular speed in rad/s. The moment of inertia of merry-go-round is, The moment of inertia of the system is calculated as, Here, is the moment of inertia of the merry-go-round considered as a uniform disc and is the moment of inertia of the kid, at the edge, considered as a point load. Here, is the mass of the merry-go-round, is the radius of the disc and is the mass of the kid.