Physics

A brave child decides to grab onto an already spinning merry‑go‑round. The child is initially at rest and has a mass of 24.5 kg. The child grabs and clings to a bar that is 1.60 m from the center of the merry‑go‑round, causing the angular velocity of the merry‑go‑round to abruptly drop from 55.0 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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1. initial angular momentum of system = I wi
where I is out unknown and wi is omega i, the initial angular velocity
wi= = 55 * 2pi radians/min * 1 min/60 s = 5.76 rad/s
so initial ang momentum = 5.76 I

final angular velocity = wf = 19 * 2 pi /60 = 1.99 If
If = I + m r^2 = I + 24.5 (1.6)^2 = I + 62.7

BUT, final angular momentum = initial angular momentum
so
1.99 ( I + 62.7) = 5.76 I
solve for I

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Damon

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