A body is in static equilibrium when it remains at rest while all applied forces and moments balance.

For a rigid body in the plane, equilibrium requires

$$\sum F_x=0,$$

$$\sum F_y=0,$$

$$\sum M=0.$$

Translational equilibrium

If the vector sum of the forces is not zero, the body accelerates translationally. A body at rest can therefore remain at rest only when the horizontal and vertical force components cancel.

Rotational equilibrium

Balanced forces alone are not enough. Two equal and opposite forces can still create a net turning effect. The sum of moments about any point must also vanish.

Solving equilibrium problems

A typical analysis begins by isolating the body, drawing every external force on a free-body diagram, choosing convenient axes and then applying the equilibrium equations.

Unknown forces can often be found by taking moments about a point through which some unknown forces pass, causing those forces to contribute zero moment.

Static equilibrium is the foundation for analysing supports, trusses, beams and many simple machines.