 Lever arm

The lever arm of a nonzero force about an origin is the shortest distance from that origin to the line through the application point parallel to the force. Its length is $\ell =|\mathbf{r}\times \hat{\mathbf{F}}|$, with unit vector $\hat{\mathbf{F}}=\mathbf{F}/|\mathbf{F}|$. Thus torque magnitude is $F\ell$, maximal at a right angle for fixed $r$ and $F$, and zero if the line passes through the origin. Sliding the application point along that line leaves torque unchanged, since $(\mathbf{r}+s\hat{\mathbf{F}})\times \mathbf{F}=\mathbf{r}\times \mathbf{F}$. The same perpendicular-distance construction gives angular momentum magnitude $p\ell$ for a line parallel to nonzero momentum through the particle.