# Angular momentum changing as mass moves to center

jybe

## Homework Statement

A 25kg child is spinning on a merry-go-round of mass 150kg and radius 2m at a constant angular velocity of 1rev/s. The child slowly walks to the center of the merry-go-round. Treat the child as a point mass and the merry-go-round as a uniform solid disk, and neglect friction of the merry-go-round's axle.

1) What is the total initial moment of inertia (Ii) and angular momentum (Li)?

2) What is the total final moment of inertia (If) and angular momentum (Lf)?

## Homework Equations

L = IW (W for angular velocity)
Ichild = mr2
Idisk = 0.5MR2

## The Attempt at a Solution

1)
Ichild = mr2
Idisk = 0.5MR2

Itotal = R2(m + 0.5M)
Itotal = 22(25 + 0.5*150)
Itotal = 400 kgm2 (total initial moment of inertia)

Linitial = Ii*W
Linitial = 400*(1 rev/s)*(2 pi)
Linitial = 800pi kgm2 (total initial angular momentum)

2)
If = mr2 + 0.5MR2

But this is where I get confused. Is it correct that once the child has moved to the center of the merry-go-round, the radius is now zero? So If is now equal to only the moment of inertia of the merry-go-round, 0.5MR2?

Homework Helper
Gold Member
But this is where I get confused. Is it correct that once the child has moved to the center of the merry-go-round, the radius is now zero? So If is now equal to only the moment of inertia of the merry-go-round, 0.5MR2?
That is correct for a point child. Unfortunately, most children are not point children. 