Chapter 19.2, Problem 1P

The rigid body (slab) has a mass m and rotates with an angular velocity ω 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 mv_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 at gyration of the body, computed about an axis perpendicular to the plane of motion and passing through G.