Moments and equilibrium

The moment of a force quantifies its turning effect about a chosen pivot and is calculated using:

M = Fx

where x is the perpendicular distance from the pivot to the line of action of the force. When the force acts at an angle to the body, the perpendicular distance must be found by extending the line of action and dropping a perpendicular from the pivot onto that line.

The moment is directly proportional to both the force and the perpendicular distance, so increasing either produces a greater turning effect. The unit of moment is the newton metre (N m).

Key Definition The centre of gravity is the single point through which the entire weight of an extended body acts, and for uniform regular bodies it lies at the geometric centre.

Key Definition The principle of moments states that, for a body in rotational equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that same point.

Combined with the condition of zero resultant force, this provides the full requirement for the equilibrium of an extended body: both the resultant force and the resultant moment about any point must be zero.

Choosing a pivot at the point of action of an unknown force eliminates that force from the moment equation, simplifying calculations involving beams supported at two points.