Three children are riding on the edge of a merry-go-round that is 182 kg, has a 1.60 m radius, and is spinning at 15.3 rpm. The children have masses of 17.4, 28.5, and 32.8 kg. If the child who has a mass of 28.5 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm

The new angular velocity of the merry-go-round is 18.388 revolutions per minute.

Explanation:

The merry-go-round can be represented by a solid disk, whereas the three children can be considered as particles. Since there is no external force acting on the system, we can apply the principle of angular momentum conservation:

(1)

Where:

- Mass of the merry-go-round, in kilograms.

, , - Masses of the three children, in kilograms.

- Radius of the merry-go-round/Distance of the children with respect to the center of the merry-go-round, in meters.

, - Initial and final angular speed, in revolutions per minute.

If we know that , , , , and , then the final angular speed of the system is:

The new angular velocity of the merry-go-round is 18.388 revolutions per minute.

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