= Effective contact mass
{title2=$m_{\rm contact}^{-1}=M^{-1}+b^2/I$}
A normal <impulse> $j$ on a free planar <rigid body> of <mass> $M$ and <moment of inertia> $I$, at perpendicular lever arm $b$, changes the contact point's normal <velocity> by $j(1/M+b^2/I)$. Its effective mass in that direction is therefore $(1/M+b^2/I)^{-1}$. This follows by adding the translational change $j/M$ to the rotational contribution $b(jb/I)$.
For an incoming <point mass> $m$, the inverse reduced contact mass is $1/m+1/M+b^2/I$. A smooth <elastic collision> with initial relative approach speed $u$ has impulse $2u/(1/m+1/M+b^2/I)$, since the relative normal velocity reverses. This separates effective inertia at a contact from the body's total mass and explains the lever-arm dependence in an <equal-speed elastic impact on a free rod>.
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