Static Equilibrium in a Uniform Gravitational Field

The physics of the state of equilibrium of a rigid body in a uniform gravitational field underlies two laws of equilibrium, namely, those of translational and rotational equilibrium as judged by an inertial observer in the reference frame of the body. Although the subject rests on firm ground, there exist two important geometrical features that are somehow being ignored by most authors; however, their implications for the understanding of the subject are quite indispensable. The first feature relates to the fact that if the body considered in equilibrium is acted upon by three external coplanar forces, then their lines of action should all meet in a single point. The second feature relates to finding the resultant of two parallel forces acting on a body. This paper provides a more extensive treatment of these geometric features by considering a somewhat simplified problem that examines their validity and illustrates their extreme importance.