The uniform window shade AB has a total weight of 0.4 lb. When it is released, it winds up...

The uniform window shade AB has a total weight of 0.4 lb. When it is released, it winds up around the spring-loaded core O. Motion is caused by a spring within the core, which is coiled so that it exerts a torque M = 0.3(10−3) lb•ft, where θ is in radians, on the core. If the shade is released from rest, determine the angular velocity of the core at the instant the shade is completely rolled up, i.e., after 12 revolutions. When this occurs, the spring becomes uncoiled and the radius of gyration of the shade about the axle at O is kO = 0.9 in. Note: The elastic potential energy of the torsional spring is , where M = kθ and k = 0.3(10−3) lb•ft/rad.