The Turning Effect of Forces (Moments)

A moment is the turning effect of a force about a pivot, equal to force times perpendicular distance from the pivot. A spanner, a seesaw and a wheelbarrow all work this way. Moments questions appear in almost every 0625 series, and they reward students who measure distances from the right point, the pivot, and punish everyone else.

What is the moment of a force?

The moment of a force is its turning effect about a pivot. In words: moment equals force multiplied by perpendicular distance from the pivot. In symbols: $\text{moment} = Fd$.

Quantity	Symbol	Unit
Moment	(none)	newton metre (N m)
Force	$F$	newton (N)
Perpendicular distance from pivot	$d$	metre (m)

The distance must be perpendicular, at right angles to the line of the force. That word carries a mark in definitions, so never drop it. Moments act clockwise or anticlockwise, and you must state the direction when asked.

What is the principle of moments?

When an object is in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point. Equilibrium needs two conditions: zero resultant force and zero resultant moment. Extended candidates must state both conditions and apply the principle to beams carrying more than one load on each side. Core candidates apply it to a simple two-force balance.

The classic experiment: balance a metre rule at its centre, hang known weights either side, and show that $F_1 d_1 = F_2 d_2$ within experimental error. Repeating with several weight positions demonstrates the principle rather than one lucky balance.

Worked Exam Question

A uniform seesaw is pivoted at its centre. A child of weight 300 N sits 2.0 m from the pivot. An adult sits on the other side, 1.2 m from the pivot. The seesaw balances. (a) Calculate the weight of the adult. [3] (b) State why the weight of the seesaw itself can be ignored. [1]

Solution (a). Principle of moments: clockwise moment = anticlockwise moment. Substitute: $300 \times 2.0 = W \times 1.2$. Rearrange: $W = 600 \div 1.2$. Answer: $W = 500\ \text{N}$.

Solution (b). The seesaw is uniform and pivoted at its centre, so its weight acts at the pivot and has zero distance, and therefore zero moment.

Mark scheme

• M1: clockwise moments = anticlockwise moments stated or used.
• M1: $300 \times 2.0 = W \times 1.2$ (correct substitution).
• A1: 500 N with unit.
• B1 (b): weight acts at/through the pivot, so its moment is zero.

Common Mistakes

• Measuring distance from the end of the beam. All distances go from the pivot. Fix: mark the pivot on the diagram and measure every distance from it.
• Dropping “perpendicular” from the definition. Fix: learn the full sentence, force × perpendicular distance from the pivot.
• Writing the unit as N/m or J. Fix: the moment unit is N m (newton metre), and it is not a joule.
• Adding moments from the same side. Two weights on the left both turn anticlockwise; they add together, not cancel. Fix: label every moment CW or ACW before summing.
• Forgetting the beam’s own weight when the pivot is off-centre. Fix: a non-central pivot means the beam’s weight acts at its centre and creates a moment.

Exam Technique Tip

Start every moments answer with the sentence “Taking moments about the pivot: clockwise = anticlockwise.” Then build each side as force × distance with the numbers labelled. That opening sentence is usually the M1 mark by itself, and it forces you to sort the directions before any arithmetic happens.

How This Is Examined

Moments span Core and Extended. Papers 1 and 2 ask single-balance MCQs and unit checks. Papers 3 and 4 set beam calculations; Paper 4 (Extended) adds off-centre pivots, multiple loads and the two equilibrium conditions, often for 4-5 marks. Paper 6 features the balanced metre rule experiment: expect to tabulate $F$ and $d$, compute $Fd$ both sides and comment on the comparison. Describe the experiment as numbered steps with “repeat for different distances” included, because that repetition line is a standing B1 mark.