Question

A 1.80 m radius playground merry-go-round has a mass of 120 kg and is rotating with an angular velocity of 0.330 rev/s. what is its angular velocity, in rev/s, after a 27.5 kg child gets onto it by grabbing its outer edge? the child is initially at rest.

Answer 1

 Solution.
Initial angular  velocity ωi = 0.330 × 2π rad/sec
                                         = 2.0737 rad/sec
The initial moment of inertia li = 0.5×M×r²
                                                = 0.5 × 120 × 1.8²
                                                = 194.4 kgm²
But the angular momentum is given by the product of moment of inertia and the angular velocity.
  = li × ωi
  = 2.0737 × 194.4
  = 403.13 kg.m²/s which is constant 
Child moment of inertia (point mass) = m × r² 
                                                          = 27.5 × 1.8²
                                                         =  27.5 × 3.24
                                                         =  89.1 kgm²
Thus, the final moment of inertia if = 194.4 + 89.1 =  283.5 kgm²
Therefore; the final speed: =403.13/ 283.5 
                                            = 1.422 rad/sec
This is equivalent to;
 1.422/2π = 0.2263 rev/s