This problem describes one experimental method for determining the moment of ine

Question

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 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 = m*r**2(2*g*h/(v**2) - 1)

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