Opening a door

To open a door you need to apply torque to the door with respect to its hinging axis. The following observations are all consistent with the torque equation:

• Pushing further from the hinge axis produces larger angular acceleration, .
• Pushing perpendicular to the surface of the door produces larger
• The heavier a door the larger its moment of inertia and the larger a torque is required to induce a given angular acceleration.

For a numerical example consider a normal wooden door with mass m=20 kg and width w=1.5 m. Its moment of inertia (treet it as a rod of length w and use table 9-1) is

How long will it take to open the door by applying a force, F=10 N, which is normal to the door at a distance r=1.2 m from the hinge axis.

From kinematics we have

Inserting the expression for the angular acceleration from Newton's second law in rotational form:

we get

Putting in numbers we get

which is quite a reasonable value.