Slide 7 of 12
Notes:
An object hanging in static equilibrium from some support point arranges itself so that the center of gravity is directly below the support point. This guarantees that the line of action of the upward force on the object exerted at the support point will be the same as the line of action of the gravity force, which is, by definition, downward and effectively applied at the center of mass. The coincidence of the lines of action and the fact (from Newton’s 1st Law) that the two forces are equal and opposite, guarantees that the torques due to the two forces are equal and opposite no matter what axis is chosen.