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)
I_child = mr²
I_disk = 0.5MR²

The Attempt at a Solution

1)
I_child = mr²
I_disk = 0.5MR²

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

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

2)
I_f = 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 I_f is now equal to only the moment of inertia of the merry-go-round, 0.5MR²?

 

[kuruman]

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.

 

[haruspex]

800pi kgm²

Check the units.