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. The moment of inertia I of the rotating apparatus is

Question

Infinity Learn · Accepted Answer

Each point on the cord moves at a linear speed of v $$=$$ ωr where r is the radius of the spool. The energy conservation equation for the counter weight turn $$table-Earth$$ system is:(K1+K2+Ug)i+Wother$$ $$=$$ $$(K1+K2+Ug)fSpecializing$$, we $$have0+0+$$$$mgh$$$$+0$$ $$=$$ $$12mv2+12I$$ω$$2+0mgh$$ $$=$$ $$12mv2+12Iv2r22mgh$$ $$-mv2$$ $$=$$ $$Iv2r2$$ and finally, I $$=$$ $$mr2(2ghv2-1)

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