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A 36.0 kg child runs with a speed of 2.80 m/s tangential to the rim of...

A 36.0 kg child runs with a speed of 2.80 m/s tangential to the rim of a stationary merry-go-round. The merry-go-round has a moment of inertia of 512 kg⋅m2 and a radius of 2.48 m. When the child jumps onto the merry-go-round, the entire system begins to rotate. What initial speed does the child have if the angular speed of the system after the collision is 0.500 rad/s?

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Answer #1

Considering the axis of rotation of the merry-go-round, the Angular Momentum of the merry-go-round and the child will be conserved if the rotation of the merry-go-round is assumed frictionless.The situation befor the child jumps on the merry-go-round is shown:

Let the velocity of the child be v as shown, mass of child be m, moment of inertia be I and angular velocity of the entire system be w.

Using Conservation of Angular momentum, as the child is on the merry-go-round its tangential speed with respect to the ground is w*r

The child has an initial speed of 4.1074 m/s.

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