# Three children are riding on the edge of a merry-go-round

## Problem 40PE Chapter 10

Physics: Principles with Applications | 6th Edition

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Physics: Principles with Applications | 6th Edition

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Problem 40PE

Three children are riding on the edge of a merry-go-round that is 100 kg, has a 1.60-m radius, and is spinning at 20.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm?

Step-by-Step Solution:

Step-by-step solution Step 1 of 4 The external torque is not present, so according to the conservation of angular momentum. Here, is the initial moment of inertia of the system, is the moment of inertia of the system after a kid moves towards center, is the initial angular velocity of the merry-go-round and is the final angular velocity. Step 2 of 4 The moment of inertia of the system when all the three kids were at the edge is, Here, is the mass of the merry-go-round, is the radius of the merry-go-round (disc), , and are the mass of the children a, b and c respectively. Substitute for , 1.6 m for R, 22 kg for , 28 kg for and 33 kg for .

Step 3 of 4

Step 4 of 4

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