Moments and Torques

Moment of a force — the turning effect of a force about a point:

moment = F × perpendicular distance from the pivot to the line of action

Measured in newton metres (N m). Note that this is not a joule, even though a joule is also a newton metre — a moment and an energy are different quantities.

The word "perpendicular" is doing the work — it is the perpendicular distance from the pivot to the line of action of the force, not the distance to where the force is applied. A force pointing straight at the pivot has zero perpendicular distance and therefore no turning effect at all, however large it is.

Example: pushing a door at the handle, at right angles to the door, gives the largest moment. Pushing the same handle towards the hinges does nothing, because the line of action passes through the pivot.

Force at an angle — either resolve the force to find the component perpendicular to the lever arm, or find the perpendicular distance from the pivot to the line of action. Both give the same answer, so use whichever the geometry makes easier.

Couple — a pair of equal, opposite, parallel forces whose lines of action do not coincide. A couple produces a turning effect with no resultant force, so it rotates a body without accelerating its centre of mass.

Torque of a couple —

torque = one force × perpendicular separation of the forces

Use one of the two forces, not their sum. Turning a steering wheel with both hands, or a tap with finger and thumb, applies a couple.

Stability and centre of mass — a body topples when the vertical line through its centre of mass falls outside its base. A low centre of mass and a wide base therefore make an object stable, because it must be tilted much further before that line escapes the base. This is why a racing car is low and wide and a double-decker bus carries ballast low down.