Answer:
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:

![\dot n_{f} = \left(15.3\,\frac{rev}{min} \right)\cdot \left[\frac{\frac{1}{2}\cdot (182\,kg) + 17.4\,kg +28.5\,kg + 32.8\,kg }{\frac{1}{2}\cdot (182\,kg) + 17.4\,kg + 32.8\,kg } \right]](https://tex.z-dn.net/?f=%5Cdot%20n_%7Bf%7D%20%3D%20%5Cleft%2815.3%5C%2C%5Cfrac%7Brev%7D%7Bmin%7D%20%5Cright%29%5Ccdot%20%5Cleft%5B%5Cfrac%7B%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%28182%5C%2Ckg%29%20%2B%2017.4%5C%2Ckg%20%2B28.5%5C%2Ckg%20%2B%2032.8%5C%2Ckg%20%7D%7B%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%28182%5C%2Ckg%29%20%2B%2017.4%5C%2Ckg%20%2B%2032.8%5C%2Ckg%20%7D%20%5Cright%5D)

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