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## Homework Statement

a. A merry go round is rotating in the counter-clockwise direction. Initially, a 50 kg child is sitting on the edge of the merry-go-around, which rotates at 0.5 radians per second. The moment of inertia of the merry-go-round is 2150 kg-m2. The radius is 2.50 meters. The child can be treated as a point mass. What is the total angular momentum?

b. If the child crawls to the center of the merry-go-round, will the speed at which it rotates change? If so, what is the new rotation speed?

## Homework Equations

[tex]\vec{L}[/tex] = I[tex]\vec{w}[/tex]

I = m

_{1}r

_{1}

^{2}+ m

_{2}r

_{2}

^{2}

## The Attempt at a Solution

The moment of inertia of the merry-go-round is 2150 kg-m

^{2}. We need to add to that value the moment of inertia of the child.

I

_{child}= (2.50 m) * (50 kg) = 125 kg-m

^{2}

I

_{total}= 2150 + 125 = 2275 kg-m

^{2}

[tex]\vec{L}[/tex] = I[tex]\vec{w}[/tex] = (2275)(0.5) = 1137.5