For a body to be completely motionless (i.e. neither moving nor rotating), it must be in both translational and rotational equilibrium. In other words, the net force and net moment acting on the body must both be zero.
In general, should be evaluated using the centre of mass (CM) of the body as the pivot point. However, it turns out that if , then evaluates to be the same value about any point.
Since is always true for a body in static equilibrium, it follows that must evaluate to be zero using any point as the pivot point.
Consider a plank weighing 60 N and 7.0 m long is at rest, supported by the contact force N of the floor, and the tension force T from a rope. Determine N and T.
Take moments about X:
Horizontally, ΣFx = 0:
Vertically, ΣFy = 0:
Beyond the Syllabus