An automobile is started from rest with one of its doors initially at right angles. If the hinges of the door are toward the front of the car, the door will slam shut as the automobile picks up speed. Obtain a formula for the time needed for the door to close if the acceleration f is constant, the radius of gyration of the door about the axis of rotation is r0, and the center of mass is at a distance a from the hinges. Show that if f is 0.3 m/s2 and the door is a uniform rectangle 1.2 m wide, the lime will be approximately 3.04 s.
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