equilibrant

In physics, the equilibrant of a system of forces is the force that would balance the system and bring it into equilibrium. It is defined as a force equal in magnitude to the resultant of all external forces acting on a body but opposite in direction.

The resultant is the vector sum of all forces. If the forces acting on a body have resultant vector R, then the equilibrant is the force F_eq = -R. When the equilibrant is applied at the same point, the net force becomes zero and translational equilibrium is achieved (the body does not accelerate).

To determine the equilibrant, calculate the components of all forces, find the resultant’s magnitude and direction, and then take the opposite direction with the same magnitude. For example, a 3-N force to the right and a 4-N force upward give a resultant of 5 N at a 53.13-degree angle above the +x axis; the equilibrant would be a 5-N force directed opposite (down-left).

Notes: The term is primarily used in statics. It emphasizes that any set of forces producing a nonzero resultant has a unique balancing force that can restore equilibrium. The concept is closely related to, but distinct from, the resultant; the equilibrant is not an independent physical quantity but the balancing counterpart to the resultant.