A 27.5 kg child stands on the edge of a stationary merry-go-round of mass 165, k

Question

A 27.5 kg child stands on the edge of a stationary merry-go-round of mass 165, kg and radius 2.11 m. The rotational inertia of the merry-go-round about its axis of rotation is 139. kg*m^2. The child catches a ball of mass 1.83 kg thrown by a friend. Just before the ball is caught, it has a horizontal velocity of 12.0 m/s that makes an angle of 37.0 degree with a line tangent to the outer edge of the merry-go-round, as shown in the overhead view of figure 12-44. What is the angular speed of the merry-go-round just after that ball is caught? rad/s

Explanation / Answer

Conserving angular momentum

initial momentum=final momentum

mvrsin(thteta)=I*w +(M+m)r^2*w

theta=90-37=53 degrees

r=2.11 m

I=139

M=27.5 kg

m=1.83 kg

we got

w=0.137 rad/s

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