The rigid body (slab) has a mass $m$ and rotates with an angular velocity $\omega$ about an axis passing through the fixed point $O .$ Show that the momenta of all the particles composing the body can be represented by a single vector having a magnitude $m v_{G}$ and acting through point $P$, called the center of percussion, which lies at a distance $r_{P / G}=k_{G}^{2} / r_{G / O}$ from the mass center $G$. Here $k_{G}$ is the radius of gyration of the body, computed about an axis perpendicular to the plane of motion and passing through $G$.