Torque

Torque is an important quantity for describing the dynamics of a rotating rigid body. We see the application of torque in many ways in the world, such as when pressing the accelerator in a car, which causes the engine to apply additional torque on the drivetrain. Here, we define torque and provide a framework to create an equation to calculate torque for a rigid body with fixed-axis rotation.

Torque can be considered as the rotational counterpart to force. Since forces change the translational motion of objects, the rotational counterpart must be related to changing the rotational motion of an object about an axis. We call this rotational counterpart torque.

In everyday life, we rotate objects about an axis all the time, so intuitively we already know much about torque. Consider, for example, how we rotate a door to open it. 

1. When we push a door very close to its hinges, the door opens slowly. The most efficient way to open a door is to push the door far from the hinges. Hence, the effectiveness of the force depends on how far it is applied from the axis of rotation.
2. It also depends on the direction from which it is applied. For example, if we push parallel to the plane of the door, we are not able to rotate it.
3. The larger the force, the more effective it is in opening the door; the harder you push, the quicker the door opens. 

The first point implies that the farther the force is applied from the axis of rotation, the greater the angular acceleration; the second implies that the effectiveness depends on the angle at which the force is applied; the third implies that the magnitude of the force must also be part of the equation. Note that for rotation in a plane, torque has two possible directions; torque is positive when the rotation is counterclockwise and negative when the rotation is clockwise. 

This text is adapted from Openstax, University Physics Volume 1, Section 10.6: Torque.