The moment of inertia of the door about the hinges is .
Further Explanation:
Since the force is applied perpendicular to the door and the door is hinged at the other end, the force will produce a torque in the door.
The torque produced in the door due to the applied force is given by:
Here, is the force applied and is the distance of application of force from the axis of rotation.
Substitute for and for in above expression.
The torque acting on the door produces an angular acceleration in the door. The torque is represented in terms of angular acceleration of the door as:
Here, is the moment of inertia of the door and is the angular acceleration of the door.
Substitute the values of and in above expression.
Thus, the moment of inertia of the door about the hinge is .
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Moment of Inertia
Keywords:
Moment of inertia, door, hinges, 72 kg person, small doorknob, 5.00 N, frictionless hinges, torque, angular acceleration, 2.0 rad/s^2.