Torque

For any force applied at an axis, there is an axial component and a tangential component. The tangential part induces rotation, and a force that acts further out on the axis induces more rotation. We call this tangential portion the Torque, .

Here we use the Cross Product.

Or just the magnitude:

Using the

The quantity represents the 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