Question

A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. what is its angular velocity (in rev/s) after a 22.0 kg child gets onto it by grabbing its outer edge? the child is initially at rest.

Answer 1

To answer this problem, we must remember that momentum is conserved. Therefore,

Initial momentum = Final momentum

In this case we use angular momentum which it is defined as:

Momentum =0.5 m ω^2

So finding for final angular velocity, ωf:

mi * ωi^2 = mf * ωf^2

120 kg * (0.5 rev / s)^2 = (120 kg + 22 kg) * ωf^2

ωf^2 = 0.2113

ωf = 0.46 rev/s