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 m 1 and m 2 m 1

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 $m_{1}$ and $m_{2} (m_{1} > m_{2})$ are attached to the ends of the string. The system Is released from rest. The angular speed of the wheel when $m_{1}$ descends by a distance $h$ is:

TestHub · Accepted Answer

T E i = T E f K i + U i = K l i n e a r + K r o t a t i o n a l + U f i n a l 0 + 0 = 1 2 m 2 v 2 + 1 2 m 1 v 2 + 1 2 I ω 2 - m 1 g h + m 2 g h 2 m 1 - m 2 g h m 1 + m 2 + I R 2 R 2 = ω 1 R 2 m 1 - m 2 g h m 1 + m 2 + I R 2

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