Equilibrium of concurrent forces

A body that is at rest, or is moving with constant velocity, is in a state of equilibrium. The acceleration of a body in equilibrium is zero in any direction. Therefore the resultant force in any direction is also zero.

The converse of this statement is not necessarily true because, although forces with zero resultant cannot make and object move in a line they can cause an object to turn .

However a set of concurrent forces ( i.e. all passing through one point ) can never cause turning so, as at present we will deal only with concurrent forces, the problem of turning will not arise yet. If the resultant is zero, the collected components in each direction must individually be zero i.e. X = 0 and Y = 0.

Applying this fact to a concurrent system in equilibrium, in which some forces are unknown, provides a method for finding the unknown quantities. By condition of equilibrium of a system of forces is meant a relation which they must fulfill in order that they may be in equilibrium or a relation which they fulfill when they are in equilibrium.

In order that any system may be in equilibrium, or be balanced, their equilibrant, and hence their resultant, must be zero, and this is a condition of equilibrium. If a system is known to be in equilibrium, then, since the forces balance among themselves, their equilibrant and hence their resultant also equals zero. This (the necessity of a zero resultant) is known as the general condition of equilibrium for it pertains to all kinds of force systems. The "graphical condition of equilibrium" for a system of concurrent forces is that the polygon for the forces must close. For if the polygon closes, then the resultant equals zero