Force and Moments

A force does not always make a body move in a straight line. When a body is pivoted (free to rotate about a fixed point or axis), a force can make it turn instead. This turning effect is called the moment of the force, or torque. You feel it every day: a door turns about its hinges, a spanner turns a nut, a see-saw turns about its central support. The further the force acts from the pivot, the greater the turning effect, which is why door handles are placed far from the hinge and why a long spanner loosens a tight bolt that a short one cannot.

The moment of a force about an axis equals the force multiplied by the perpendicular distance of the line of action of the force from the axis of rotation. In symbols, moment = F × d, where d is measured at right angles to the force. Its SI unit is the newton metre (N m). It is a vector. Two forces can be equal in size yet have very different moments if one acts close to the pivot and the other acts far away. To get the largest moment for a given force, apply it as far from the axis as possible and at right angles to the arm.

A moment can turn a body either clockwise or anticlockwise. By convention an anticlockwise moment is taken as positive and a clockwise moment as negative. When a body is in equilibrium under several forces, the principle of moments states that the total anticlockwise moment about any point equals the total clockwise moment about that point. A balanced see-saw and a physical (beam) balance both work on this principle: the child or weight that is lighter must sit further from the pivot so that the two moments match.

A couple is a pair of equal, opposite, parallel forces whose lines of action are different; it produces only rotation, no straight-line motion. Turning a steering wheel or a tap with two fingers is a couple, and its moment equals one force times the couple arm (the perpendicular distance between the two forces). The centre of gravity is the single point through which the whole weight of a body seems to act, whatever the body's position. A body is in equilibrium when the resultant force on it is zero and the resultant moment is zero. Equilibrium can be static (body at rest) or dynamic (body moving uniformly), and a body at rest is stable, unstable or neutral depending on how its centre of gravity moves when it is slightly tilted.