Question

Three children are riding on the edge of a merry-go-round that is a solid disk with a mass of 95.8 kg and a radius of 1.72 m. The merry-go-round is initially spinning at 5.84 revolutions/minute. The children have masses of 29.0 kg, 28.2 kg and 33.6 kg. If the child who has a mass of 28.2 kg moves to the center of the merry-go-round, what is the new angular velocity in revolutions/minute?

Answer 1

let

M = 95.8 kg

m1 = 29 kg

m2 = 28.2 kg

m3 = 33.6 kg

R = 1.72 m

Wi = 5.84 rev/minute

wf = ?

initial moment of inertia of the system, Ii = 0.5*M*R^2 + (m1 + m2 + m3)*R^2

final moment of inertia of the system, Ii = 0.5*M*R^2 + (m1 + m3)*R^2

Apply conservation of momentum,

Lf = Li

If*wf = Ii*wi

wf = Ii*wi/If

= (0.5*M*R^2 + (m1 + m2 + m3)*R^2)*wi/(0.5*M*R^2 + (m1 + m3)*R^2 )

= ( 0.5*95.8*1.72^2 + (29 + 28.2 + 33.6)*1.72^2)*5.84/( 0.5*95.8*1.72^2 + (29 + 33.6)*1.72^2 )

= 7.33 revolutions/minute <<<<<<<------Answer