The motion of the uniform 80-lb garage door is guided at its ends by the track. If it is r...

The motion of the uniform 80-lb garage door is guided at its ends by the track. If it is released from rest at θ = 0°, determine the door’s angular velocity at the instant θ = 30°. The spring is originally stretched 1 ft when the door is held open, θ = 0°. Assume the door can be treated as a thin plate, and there is a spring and pulley system on each of the two sides of the door.