Varignon's principle of moments | Varignon's Theorem

Varignon's theorem also called the principle of moments. 

Varignon's Principle:

Varignon's principle states that if a number of concurrent forces acting on a particle are in equilibrium, then the algebraic sum the moments that each force creates about a single point will be equal to the moment of their resultant force about the same point.  

Varignon's Theorem

From the above figure, F1 and F2 are two concurrent forces and their resultant is R. The moment produced by R with respect to a moment center O is R × d. The moment produced by the force F1 and F2 is respectively F1 × d1 and F2 × d2. 

As per varignon's therorem R d = F1 d1 + F2 d2

Notes:

This theorem initially stated for two concurrent forces, but, it is true for any system of forces and any number of concurrent or coplanar forces. 

One of the practical applications of this theorem is to find the unknown reactions when a system is known to be in equilibrium under the action of a number of forces. Since the resultant is zero for a system in equilibrium we can equate the moment summation of all forces to zero leading to the solution of unknown reactions.