= Relative speed retention in an oblique collision
{title2=$q=|\mathbf w_{\rm rel}'|/|\mathbf w_{\rm rel}|$}
For a two-particle <collision> conserving total <momentum>, the outgoing <speeds> in the <centre-of-momentum frame> are multiplied by the same $q$. The relative <kinetic energy> is multiplied by $q^2$. For a smooth <oblique collision> with normal <coefficient of restitution> $e_n$ and incident relative <velocity> inclined by $\chi$ to the contact normal, unchanged tangential relative motion gives $q^2=e_n^2\cos^2\chi+\sin^2\chi$. Thus $q=e_n$ is not a general oblique-impact identity: $e_n=1/2$ and $\chi=\pi/4$ give $q=\sqrt{5/8}$. Sticking requires all relative motion to vanish, not merely its normal component.
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