Calculating Torque

There are two other ways we can write this equation, if the two vectors are not perpendicular. First, we can write $$\mathrm{\tau }=r{F}_{\perp }$$ where $F_{\perp }$ is the component of the force which is perpendicular to the lever arm. A little trig will show us that $F_{\perp }=F\sin \theta$, which is where this equation comes from.

We can also write $$\mathrm{\tau }=r_{\perp }F$$ where $r_{\perp }$ is the component of the lever arm that is perpendicular to the force. (This quantity $r_{\perp }$ is sometimes called the moment arm, but we will avoid this term to avoid confusion with the lever arm $\overrightarrow{r}$.)