# Why is the moment of forces on a rigid body in static equilibrium must be zero about any point, even if the position of that point is not on the body

Why is it necessary for the moment of the forces on a rigid body in static equilibrium to be zero about any point, even if the position of that point is not on the body itself.

• Because what do you think would happen if there were a point at which the net force is not zero? Commented Dec 7, 2016 at 13:46
• Succinctly put, of the body is in equilibrium then any point of reference can be used for calculating that equilibrium including being on the surface of the sun due to laws of motion #1... that body will remain at rest until its equilibrium its upset by another force acting upon it. Commented Jan 7, 2019 at 18:59

Consider a body to be in equilibrium under the action of forces $F_i$, $i=1,\ldots,n$ which act at locations $r_i$, $i=1,\ldots,n$.
Equilibrium of the body implies $$\sum _{i=1}^n r_i \times F_i=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \sum _{i=1}^n F_i=0$$
$$\sum _{i=1}^n (r_i-p) \times F_i = \sum _{i=1}^n r_i \times F_i-p\times\sum _{i=1}^n F_i = 0-p\times 0 = 0$$