The solid wood door of a gymnasium is 1.00 m wide and 2.00 m high, has total mass 35.0 kg, and is hinged along one side. The door is open and at rest when a stray basketball hits the center of the door head-on, applying an average force of 1500 N to the door for 8.00 ms. Find the angular speed of the door after the impact. [Hint: Integrating Eq. (10.29) yields ΔLz = f (Σ Tz)dt = (Σ Tz).At. The quantity f(Σ Tz) dt is called the angular impulse.]