Calculating Torque

There are two other ways we can write this equation, if the two vectors are not perpendicular. First, we can write $$\tau=rF_\perp$$ 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 $$\tau=r_\perp F$$ 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 \(\vec r\).)