Center of Percussion

It is the point where the perpendicular impact does not produce showk at the pivot.

This point is calculated by considering the equalibrium of torque about the center of mass and force at the pivot.

\begin{align*} \ddot{x}_\text{cm} = \frac{F}{M}\\ \dot{\omega} = \frac{Fb}{I}\\ \end{align*}

The acceleration at the pivot is required to be zero: \[ 0 = \ddot{x}_\text{cm} - p\dot{\omega} = \left(\frac{1}{M} - \frac{pb}{I}\right)F \implies b = \frac{I}{pM} \] which means that \( b \) is the inversion of \( p \) with respect to the radius of gyration \( k \).

• Center of percussion - Wikipedia