Consider a body in Equilibrium.
I. For a rigid body to be in mechanical equilibrium, the net external force must be zero.
II. For a rigid body to be in mechanical equilibrium, the net external torque must be zero.
III. A body can be in translational equilibrium but not rotational equilibrium.
IV. A body can be in rotational equilibrium but not translational equilibrium.
V. The Center of Gravity is the point where the total gravitational torque is zero.