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A playground merry-go-round has a radius of 3.0 m and a rotational inertia of 600 kg.m2. it is initially spinning at 0.80 rad/s when a 20-kg child crawls from the center to the rim. when the child reaches the rim the angular velocity of the merry-go-round is:

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shinmin

The solution for this problem is:

 

Compute first for the initial Inertia:

 

Initial inertia = 600 + (20 * (0 ^ 2)) = 600 kg m^2 since the radius of the child is 0 originally 

 

Then look for the final inertia:


Final Inertia = 600 + (20 * (3^2)) = 780 kg m^2 

Now use conservation of angular momentum:


(I final) (W final) = (I initial) (w initial) = 780w = 600(0.80)

w = (600*0.80)/780 


So, final angular velocity:

W = 0.6154 rad/s

~0.62 rad/s

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