A 20-kg child starts at the center of a playground merry-go-round that has a radius of 1.5 mm and rotational inertia of 500kg⋅m2 and walks o

Question

A 20-kg child starts at the center of a playground merry-go-round that has a radius of 1.5 mm and rotational inertia of 500kg⋅m2 and walks out to the edge. The merry-go-round has a rotational speed of 0.20 s−1 when she is at the center.

What is its rotational speed when she gets to the edge?

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King 4 years 2021-08-22T09:44:05+00:00 1 Answers 8 views 0

Answers ( )

  1. Philomena
    0
    2021-08-22T09:45:09+00:00
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    Answer:

    w = 0.189 rad/ s

    Explanation:

    This exercise we work with the conservation of the moment, the system is made up of the merry-go-round and the child, for which we write the moment of two instants

    Initial

             L₀ = I₀ w₀

    Final

              L_{f} = I w

             L₀ = L_{f}

             I₀ w₀ = I_{f} w

             .w = I₀/I_{f}   w₀

    The initial moment of inertia is

            I₀ = 500 kg. m2

    The final moment of inertia

             I_{f} = 500 + m r²

             I_{f} = 500 + 20 1.5

             I_{f} = 530 kg m²

    Initial angular velocity

             w₀ = 0.20 rad / s

    Let’s calculate

              w = 500/530 0.20

              w = 0.189 rad / s

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