# Child on a Merry-Go-Around

## Homework Statement

In the figure below, a 30 kg child stands on the edge of a stationary merry-go-round of mass 100 kg and radius 2.0 m. The rotational inertia of the merry-go-round about its rotation axis is 150 kg·m2. The child catches a ball of mass 1.1 kg thrown by a friend. Just before the ball is caught, it has a horizontal velocity v of magnitude 11 m/s, at angle ϕ = 37° with a line tangent to the outer edge of the merry-go-round, as shown. What is the angular speed of the merry-go-round just after the ball is caught? p = mv
L = Iw

## The Attempt at a Solution

So I'm assuming that angular momentum is conserved. Thus,

mv = Iw
I found the total I.
I_merrygoaround = 150
I_child = MR^2 = 120
I_ball = MR^2 = 1.1(rsin(phi))^2 = 1.44
I_total = 271.44

$$\omega$$ = (mv) / (I_total) = 12.1/271.44 = 0.0445 rad/s

But this is incorrect.
What did I do wrong?

## Answers and Replies

tiny-tim
Science Advisor
Homework Helper
hi bewger! you seem to be mixing up the angular momentum of the ball before with the angular momentum of the ball after Hi tiny-tim

I'm trying to figure out my mistake with your advice, but I'm a little stumped by what you mean by that.

Can you elaborate on that?

tiny-tim
Science Advisor
Homework Helper
hi bewger! I'm finding it a little difficult to read what you posted (try using the X2 tag just above the Reply box ), but I don't think you've included both the angular momentum of the ball before and the different angular momentum of the ball after 