One of the basement doors is left open in the vertical position when it is given a nudge a...

One of the basement doors is left open in the vertical position when it is given a nudge and allowed to freely fall to the closed position. Given that the door has mass m and that it is modeled as a uniform thin plate of width w and length d, determine its angular velocity when it reaches the closed position. Hint: Treat the problem as symmetric with respect to a plane of motion in which the acceleration due to gravity is g cos θ rather than g.

Figure P8.17