# Equilibrium

A body which is in equilibrium is either moving at constant velocity in a straight line, or it is not moving. If it is not moving, it said to be in static equilibrium. The reason why the body does not move is because the forces acting on it cancel each other out. In this simple phrase we are expressing the two conditions necessary in order for a body to be in equilibrium:

- The sum of rotational forces or moments must add to zero.
- The vector sum of all external forces, is zero.

In mathematical terms, Σ**F**_{rot} = 0 and Σ**F** = 0

## Proving Equilibrium

To prove that a body is in equilibrium, we can follow a set proceedure.

- Draw the free-body diagram, which shows the forces acting on the object.
- Resolve the forces in any two conveinient directions, for example, ΣF
_{x}= 0 and ΣF_{y}= 0, which will result in two equations from which the two unknowns can be found.

## Theorems on Equilibrium

If three forces are in equilibrium, then the lines of force pass through a single point.

### Equilibrium in three Dimensions

So far we have discussed equilibrium where the forces are coplanar. In three dimensions we need to ensure that the sum of the moments in the three independent directions are zero the sum of the vector forces also must be zero.

Σ *F*_{x,y,z} = 0

Σ*τ*_{x,y,z} = 0