The rigid body (slab) has a mass m and rotates with an angular velocity about an axis passing through the fixed point O. Show

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 ² _G/rG/O from the mass center G. Here is the kG radius of gyration of the body, computed about an axis perpendicular to the plane of motion and passing through G.

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