4 This problem describes one experimental method for determining the moment of i

Question

4 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 P10.15 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

Explanation / Answer

KR + K = Ugrav

½ Iw2 +  ½ mv2 = mgh

½ Iw2 = mgh - ½ mv2

I = 2(mgh - ½ mv2) / w2

I = (2mgh        - mv2) / (v/r)2

I = mr2 (2gh    - v2) / v2

I = mr2 (2gh/v2  - 1)

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