Physics Inertia : Merry-go-round

A playground merry-go-round of radius 1.96 m has a moment of inertia 335 kg m2 and is rotating at 12.3 rev/min. A child with mass 43.1 kg jumps on the edge of the merry-go-round. What is the new moment of inertia of the merry-go-round and child, together? Answer in units of kg m2.

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  1. add them: Inew=335 kg m^2+43.5*1.96^2 kg m^2

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    bobpursley
  2. Thank you, but what equation do you use? I cant seem to get the correct answer.What happens to the rev/min? Is it: inertia+child mass*radius^2

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  3. The rev/min is not needed.

    here is the equation:

    momentofINertiatotal=momentinertiaMerryGoRound + momentinertiaKid.

    Then you add them.

    That is it. Now, if the problem goes on, you may need to find what the new angular speed is, but that is a different problem, you didn't ask that.

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  4. if you want to find the final angular speed, wf, you take:

    momentinertiaMerryGoRound(initial angular speed) = (momentinertiaMerryGoRound + momentinertiaKid)(wf)

    then solve for wf

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  5. Correct

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  6. What is the moment of inertia of the kid?

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  7. The moment of inertia of a point mass (i.e. the kid in this case) is MR^2 (we use radius R of the merry-go-round because the kid's on the edge). So the complete expression of the final angular momentum is: L_f = (335 + 43.1 * 1.96^2) (w_f)

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