 Effective impact mass of a pivoted body

A short transverse impulse $J$ at lever arm $b$ gives a pivoted rigid body angular velocity $\Omega =Jb/I$ and contact-point velocity $b\Omega =J/m_{\mathrm{eff}}$, where $I$ is its pivot moment of inertia. Thus $m_{\mathrm{eff}}=I/b^2$ plays the role of a translational mass in the impact direction. A point projectile elastically striking an initially stationary body stops immediately after impact precisely when its mass equals this effective value. The pivot can exchange linear momentum while doing no work.