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 0.550 rev/s. What is its angular velocity (in rev/s) after a 18.0 kg child gets onto it by grabbing its outer edge? The child is initially at rest.

Answer 1

Treat the merry-go-round as a uniform disk (I_disk = 1/2 M R^2) and the child as a point mass at the rim (I_child = m R^2). Angular momentum is conserved: I_i ω_i = I_f ω_f.

I_disk = 1/2 (120 kg)(1.80 m)^2 = 194.4 kg·m^2
I_child = (18.0 kg)(1.80 m)^2 = 58.32 kg·m^2
I_f = 194.4 + 58.32 = 252.72 kg·m^2

ω_f = (I_i / I_f) ω_i = (194.4 / 252.72)(0.550 rev/s) ≈ 0.423 rev/s

So the final angular velocity is about 0.423 rev/s.