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A small child of mass mc is sitting on the edge of a large merry-go-round which...

A small child of mass mc is sitting on the edge of a large merry-go-round which is initially at rest. For simplicity, assume the merry-go-round is a uniform disk of mass mm and radius R. An ice-cream truck drives by and in a moment of benevolence, the driver hurls a huge scoop of vanilla ice cream at the child. The scoop has mass ms and is traveling parallel to the ground and tangent to the merry-go-round at a speed of vs i just before the child catches it in its mouth. This incident causes the child and merry-go-round to rotate (you can assume that the child is "fixed" to the merry-go-round). A time tf  after the child catches the ice-cream everything has slowly come back to rest due to friction between the axle and the merry-go-round. Express your final answers to the questions below in terms of any of mc mm R ms vs i and tf .

1. Find an expression for the angular speed of the child just after he catches the ice-cream in his mouth.

2. Find an expression for the magnitude of the average torque from the friction between the axle and the merry-go-round from just after the child catches the ice cream until everything has just come back to rest.

3. Taking your system to be the child+merry-go-round+ice-cream, did the linear momentum of the system change during the "collision" of the ice-cream with the child's mouth? If so, explain why.

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