Condition for Equilibrium

An object acted on by several forces is in equilibrium only if two conditions for equilibrium are both met. There must be no resultant force, and there must be no resultant moment about any point.No resultant force means the forces balance in every direction. Resolving horizontally and vertically, the upward forces equal the downward forces and the forces to the left equal the forces to the right. Without this the object would accelerate.No resultant moment means the object has no tendency to start rotating. This is the principle of moments: the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point. The moment of a force is the force multiplied by the perpendicular distance from the pivot to its line of action.When solving problems, take moments about a point where an unknown force acts. That force then has no moment about the point, so it drops out of the equation, and the remaining unknown can be found. The force condition can then be used to find the last unknown.A pair of equal and opposite forces that do not act along the same line is called a couple. It has no resultant force but does have a resultant moment, so an object acted on by a couple is not in equilibrium and will start to rotate.