- #1

jybe

- 41

- 1

## 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)

I

_{child}= mr

^{2}

I

_{disk}= 0.5MR

^{2}

## The Attempt at a Solution

1)

I

_{child}= mr

^{2}

I

_{disk}= 0.5MR

^{2}

I

_{total}= R

^{2}(m + 0.5M)

I

_{total}= 2

^{2}(25 + 0.5*150)

I

_{total}= 400 kgm

^{2}(total initial moment of inertia)

L

_{initial}= I

_{i}*W

L

_{initial}= 400*(1 rev/s)*(2 pi)

L

_{initial}= 800pi kgm

^{2}(total initial angular momentum)

2)

I

_{f}= mr

^{2}+ 0.5MR

^{2}

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 I

_{f}is now equal to only the moment of inertia of the merry-go-round, 0.5MR

^{2}?