Please help me and show me a detailed solution This problem describes one experi

Question

Please help me and show me a detailed solution

This problem describes one experimental method for determining the moment of inertia of an irregularly shaped object such as the payload for a satellite. Figure P10.47 shows a counterweight of mass m suspended by a cord wound around a spool of radius r, forming part of a turntable supporting the object. The turntable can rotate without friction. When the counterweight is released from rest, it descends through a distance h, acquiring a speed v. Show that the moment of Inertia I of the rotating apparatus (including the turntable) is mr2(2gh/v2 - 1).

Explanation / Answer

PE = KE
m*g*h = 1/2*m*v**2 + 1/2*I*?**2

Recall that v = r*? so that ?**2 = v**2/r**2
m*g*h = 1/2*m*v**2 + 1/2*I*v**2/r**2

Now solve for I to get
I = mr^2(2gh/(v^2) - 1)

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