# Homework Help: Conservation of momentum on merry-go-round

1. Jan 13, 2004

### tandoorichicken

A playground merry-go-round has a disk-shaped platform that rotates with negligible friction about a vertical axis. The disk has a mass of 200kg and a radius of 1.8 m. A 36-kg child rides at the center of the merry-g-round while a playmate sets it turning at 0.25 rev/sec. If the child then walks along a radius to the outer edge of the disk, how fast will the disk be turning.

Work:
$$\omega_0 = 0.5\pi$$ rad/sec.
$$I_0 = \frac{1}{2} m r^2$$ (MOI for disk).
$$L = I_0\omega_0 = \frac{1}{2} m r^2 \omega_0$$
So, if angular momentum is conserved, $$L = I_f\omega_f$$
My only problem is figuring out the MOI for a disk with an object spinning around the outer edge. Anyone know?

2. Jan 21, 2004

### Staff: Mentor

Treat the child as a point mass. Its moment of inertia is $mr^2$. The total MOI is that of the disk plus that of the child.