A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see$$ $$fig) . A massless string is wrapped over its rim and two blocks of masses $$m1$$ and $$m2m1$$$$m2$$ are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when $$m1$$ descents by a distance h is

Question

A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see$$ $$fig) . A massless string is wrapped over its rim and two blocks of masses  $$m1$$ and $$m2m1$$>$$m2$$ are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when $$m1$$ descents by a distance h is

Infinity Learn · Accepted Answer

According to work energy $$theoremWTotal=$$Δ$$KEm1gh$$−$$m2gh=12m1+m2v2+12I$$ω$$2$$          ​⇒$$m1$$−$$m2gh=12m1+m2R2$$ω$$2+12I$$ω$$2$$      ∵$$v=R$$ω​⇒$$m1$$−$$m2gh=$$ω$$2m1+m2R2+I2$$         ​⇒ω$$=2m1$$−$$m2ghm1+m2R2+I1/2$$

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