The side view of a foot-pedal sewing machine mechanism is shown below. The mechanism is intended to amplify the foot motion on the treadle (the name for the foot pedal) into fast movement of the needle, which is driven by pulley F on the sewing machine head Link BD causes rotation of the wheel mounted at E, which is attached by a belt to stationary pulley At this moment, the treadle has WAB = 0.5 rad/s counterclockwise and theta= 30°. Find the angular velocity of pulley F. Assume that the belt does not slip.