Question

Three children are riding on the edge of a merry-go-round that is 142 kg, has a 1.60 m radius, and is spinning at 17.3 rpm. The children have masses of 22.4, 29.0, and 38.8 kg. If the child who has a mass of 38.8 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?

Answer 1

In this we'll use the conservation of angular momentum principle,

  

Moment of inertia of 1st child

Moment of inertia of 2nd child

Moment of inertia of 3rd child

Since the merry-go-round will spin about an axis that passes through it center, thus in the second case when the 3rd child will move to the center of mass of merry-go-round then it wil not contribute in the moment of inertia of system.

Thus, we can write moment of inertias of all as

  

Using given values in above,

  

(ANS)