General Condition of Equilibrium Theorem

The necessary and sufficient condition that a system of coplanar forces acting on a rigid body, be in equilibrium, is that algebraic sum of resolved parts of all the forces along two mutually perpendicular straight lines be separately zero and the moment of all the forces about a point in the plane is zero.

A number of forces acting at a point will be in equilibrium if the sum of resolved parts in any two perpendicular directions are both zero.

Principle of resolution of forces:

• The algebraic sum of the resolved parts of a number of forces in a given direction is equal to the resolved part of their resultant in the same direction.

Method for the resolution for the resultant force:

• Resolve all the forces horizontally and find the algebraic sum of the horizontal components.
• Resolve all the forces vertically and find the algebraic sum of the vertical components.

The resultant of the above both can be given below as,

\(R = \sqrt {{{\left( {\sum H} \right)}^2} + {{\left( {\sum V} \right)}^2}}\)