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?

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

          = 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

          = 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