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what is the new angular velocity in rpm?

what is the new angular velocity in rpm?

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**Problem:** Three children are riding on the edge of a merry-go-round that is 162 kg, has a 1.60 m radius, and is spinning at 15.3 rpm. The children have masses of 22.4, 29.0, and 40.8 kg. If the child who has a mass of 40.8 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm? *Answer:* _____ rpm
Transcribed Image Text:**Problem:** Three children are riding on the edge of a merry-go-round that is 162 kg, has a 1.60 m radius, and is spinning at 15.3 rpm. The children have masses of 22.4, 29.0, and 40.8 kg. If the child who has a mass of 40.8 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm? *Answer:* _____ rpm
Expert Solution
Step 1

Angular momentum of the merry go round will be conserved in rotation motion.

initial angular momentum = final angular momentum

angular momentum is given as 

L = Iω

where I is moment of inertia and ω is angular velocity

Iiωi = Ifωf

Ii = Moment of inertia of merry go round + moment of inertia of three children

Ii = Im + (m1+m2+m3)r2

IF= Im + (m1+m2)r2 + m3x0 ( m3 is at center)

 

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