The revolving door consists of four doors which are attached to an axle AB. Each door can be assumed to be a 50-lb thin plate. Friction at the axle contributes a moment of 2 lb · ft which resists the rotation of the doors. If a women passes through one door by always pushing with a force P = 15 lb perpendicular to the plane of the door as shown, determine the door’s angular velocity after it has rotated 90°. The doors are originally at rest. 

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7 ft 3 ft A 2.5 ft B AL P = 15 lb