We know that,

Thus.

However O is fixed, thus ;

For the common case of rotation of a rigid body about a fixed axis through its mass center G, clearly a = 0, and therefore . The resultant of the applied forces then is the couple .

CENTER OF PERCUSSION:

We have seen that if a body is rotating about fixed point not passing through its mass center, then the force system on the body may be reprsented by two forces passing through its center of mass in the normal and tangential direction, together with a moment . The moment may be eliminated if the line of action of tangential force is shifted to pass from the point Q instead of G, as shown in the figure below. This point Q is then called center of percussion.