Introduction

Let's now learn how to find the moment about an axis. We can do so by following these steps:

• Determine the moment of $ \vec{F} $ about any point O on a line AB. $ \vec{M_o} = \vec{r} \times \vec{F} $.
• Take the dot product of $ \vec{M_o} $ with a unit vector along line AB. $ | \vec{M_{AB}} | = \vec{M_o} \cdot \hat{u}_{AB} = (\hat{r} \times \hat{F}) \cdot \hat{u}_{AB} $

A Visual Aid

Let's take a look at a visual of this to better understand what is going on.

Example image of a moment about an axis.

In the example image, we have a vector $ \vec{r} $ spanning from the line axis AB going to the vector $ \vec{F} $. What we can do is take a unit vector in the direction of axis AB, $ \hat{u}_{AB} $, and we can multiply the cross product of $ \vec{r} $ and $ \vec{F} $ with this unit vector to find out "how much" of that force is in the direction of axis AB to produce a moment.