An object at rest is in equilibrium or in static equilibrium. An object at rest is described by Newton's First Law of Motion. An object in static equilibrium has zero net force (Resultant Force) acting upon it.
The condition for Equilibrium is that the vector sum of all the forces acting on a body vanishes. ie. All forces acting balance, and destroy eachother, leading to no resultant force.
Alternatively you can break this down into two seperate conditions for easier processing:
- Sum of all forces (in 2 perpendicular directions) must equal zero.
- Sum of all the moments about any point is zero.