A brave child decides to grab onto an already spinning merry‑go‑round. The child is initially at rest and has a mass of 36.5 kg. The child grabs and clings to a bar that is 1.65 m from the center of the merry‑go‑round, causing the angular velocity of the merry‑go‑round to abruptly drop from 47.0 rpm to 19.0 rpm. What is the moment of inertia of the merry‑go‑round with respect to its central axis?

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A brave child decides to grab onto an already spinning merry‑go‑round. The child is initially at rest and has a mass of 36.5 kg. The child grabs and clings to a bar that is 1.65 m from the center of the merry‑go‑round, causing the angular velocity of the merry‑go‑round to abruptly drop from 47.0 rpm to 19.0 rpm. What is the moment of inertia of the merry‑go‑round with respect to its central axis?

Expert Solution
GIVEN:

Mass of the child is given as, m = 36.5 kg

The distance between the bar and the centre of merry-go-round is given as, R = 1.65 m

The initial angular velocity is given as, ωi = 47.0 rpm (or) ωi = 47.0 rpm×1 m60 s (or) ωi = 0.78 rad/s

The final angular velocity is given as, ωf = 19.0 rpm (or) ωf = 19.0 rpm×1 m60 s (or) ωf = 0.32 rad/s

TO DETERMINE:

The moment of inertia of merry-go-round with respect to central axis, I

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