Moment of a Force

The moment of a force is the turning effect of that force about a pivot (also called a fulcrum).

The equation

$\text{moment} = F \times d$

Symbol	Quantity	Unit
moment	Moment of the force	N m
$F$	Force	N
$d$	Perpendicular distance from the pivot to the line of action of the force	m

The distance must be measured perpendicular (at right angles) to the line of action of the force, not along the beam or lever.

Direction of moments

A moment can be clockwise or anticlockwise about the pivot. The direction depends on which way the force would rotate the object.

Increasing the moment

A moment increases when:

• the force increases
• the perpendicular distance from the pivot increases

This is why a long spanner makes it easier to undo a tight bolt, and why a door handle is placed far from the hinge.

Worked example

A force of 20 N acts at a perpendicular distance of 0.30 m from a pivot. Calculate the moment.

$\text{moment} = 20 \times 0.30 = 6.0\text{ N m}$

Common errors and how to correct them

Using the distance along the beam instead of the perpendicular distance. If the force acts at an angle, the perpendicular distance to the pivot is shorter than the beam length. Always check which distance is perpendicular to the force.

Forgetting to state the direction (clockwise or anticlockwise). The moment is not complete without its direction.

How to apply this in an exam

State the equation, substitute with the perpendicular distance, calculate the value, and give the unit (N m). If the question involves equilibrium, you will need to compare clockwise and anticlockwise moments.