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**

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