a. What is the moment of inertia of the door in Problem 21?

b. If you let go of the open door, what is its angular acceleration immediately afterward?

Problem 21

A professor's office door is \(0.91 \mathrm{~m}\) wide, \(2.0 \mathrm{~m}\) high, and \(4.0 \mathrm{~cm}\) thick; has a mass of \(25 \mathrm{~kg}\); and pivots on frictionless hinges. A "door closer" is attached to the door and the top of the door frame. When the door is open and at rest, the door closer exerts a torque of \(5.2 \mathrm{~N} \cdot \mathrm{m}\). What is the least force that you need to apply to the door to hold it open?