= Lever arm
{title2=$\ell=r\sin\phi$}
= Moment arm
{synonym}
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 $\ell=|\mathbf r\times\widehat{\mathbf F}|$, with <unit vector> $\widehat{\mathbf F}=\mathbf F/|\mathbf F|$. 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 $(\mathbf r+s\widehat{\mathbf F})\times\mathbf F=\mathbf r\times\mathbf F$. The same perpendicular-distance construction gives <angular momentum> magnitude $p\ell$ for a line parallel to nonzero <momentum> through the particle.
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