The double pulley consists of two parts that are attached to one another. It has a weight of 50 lb and a centroidal radius of gyration of k_O = 0.6 ft and is turning with an angular velocity of 20 rad s clockwise. Determine the angular velocity of the pulley at the instant the 20-lb weight moves 2 ft downward.

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w = 20 rad/s 0.5 ft 1 ft B 30 lb A 20 lb