Torque

Torque is a force applied at an axis. The magnitude of torque about a given axis is defined as:

Alternatively:

Meaning:

We can also reason that:

The quantity represents the Rotational Inertia or Moment of Inertia, .

We can see the similarity:

Using Angular Momentum, know that:

To define the direction of our torque, use the Right-hand Rule for Rotation.

In terms of the Cross Product:

Torque due to Gravity

Combined Rotational and Translational Motion

Torque due to Angular Momentum