Question

A playground merry–go–round has a mass of 118 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.470 rev/s. What is its angular velocity after a 20.0–kg child gets onto it by grabbing its outer edge? The child is initially at rest.

Answer 1

I omega = constant

before
I suppose we could model the device as a flat disk
I = .5 M r^2 = .5(118)(1.8)^2

I omega = I (.47*2 pi)

now after
Inew = I + 20(1.8)^2
so

I omega = Inew Omeganew
.5(118)(1.8)^2(.47*2 pi)=Inew* Omeganew

that will give omega new in radians/sec
divide by 2 pi to get revs/s