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## Homework Statement

A child (m

_{c}= 36 kg) is playing on a merry-go-round (m

_{m}= 225 kg, R = 2.9m) that is initially at rest. The child then jumps off in a direction tangent to the edge of the merry-go-round. The child has a speed of 5.0 m/s just before she lands on the ground. What is the magnitude of the final angular velocity of the merry-go-round?

## Homework Equations

L = I*ω

L

_{i,c}+ L

_{i,m}= L

_{f,c}+ L

_{f,m}

I = (1/2)m

_{m}R

^{2}for the merry-go-round.

I = m

_{c}R

^{2}for the child.

## The Attempt at a Solution

The initial angular momentum of the system is 0 so L

_{i,c}+ L

_{i,m}= 0.

So L

_{f,c}+ L

_{f,m}= 0

(1/2)m

_{m}R

^{2}* ω

_{f}+ m

_{c}R

^{2}* ω

_{f}= 0

(1/2)m

_{m}R

^{2}* ω

_{f}= - m

_{c}R

^{2}* ω

_{f}

However when I plug the values for mass of the merry-go-round and the child as well as the radius for the merry-go-round I cannot seem to find a way to isolate ω

_{f}to one side of the equation, I just keep getting 0 rad/s.