Question

A 39.5 kg child stands at the center of a 125 kg playground merry-go-round which rotates at 3.10 rad/s. If the child moves to the edge of the merry-go-round, what is the new angular velocity of the system? Model the merry-go-round as a solid disk

Answer 1

Using the law of conservation of angular momentum, we have 

I1 w1 = I2 w2 

ie., m1r^2/2 x w1 = ( m1r^2/2 + m2r^2 ) w2 

ie., new angular velocity w2 = m1 w1 / ( m1+ 2m2) = 125 x 3.1 / ( 125 + 2 x39.5 ) 

= 1.8995 = 1.9 rad /sec ( nearly )