Question

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 200 kg and a radius of 1.6 m. A 34- kg child rides at the center of the merry-go-round while a playmate sets it turning at 0.15rpm. If the child then walks along a radius to the outer edge of the disk, how fast will the disk be turning? (in rpm - but enter no unit)

Answer 1

Mass of the merry-go-round = M = 200 kg

Radius of the merry-go-round = R = 1.6 m

Moment of inertia of the merry-go-round = I

I = MR²/2

I = (200)(1.6)²/2

I = 256 kg.m²

Mass of the child = m = 34 kg

Initial angular speed of the merry-go-round = ₁ = 0.15 rpm = 0.15 x (2/60) rad/s = 1.571 x 10^-2 rad/s

Angular speed of the merry-go-round after the child walks to the outer edge = ₂

The child walks from the center to the outer edge of the merry-go-round therefore the child will be at a distance equal to the radius of the merry-go-round from the center.

By conservation of angular momentum,

I₁ = (I + mR²)₂

(256)(1.571x10^-2) = [256 + (34)(1.6)²]₂

₂ = 1.172 x 10^-2 rad/s

Converting from rad/s to rpm,

₂ = 0.112 rpm

Angular speed of the merry-go-round after the child walks to the outer edge = 0.112 rpm