Moments and Couples Revision Notes | A Level AQA Physics

1. Why Turning Effects Matter

Push a door near its hinges and it barely moves. Push it at the far edge and it swings open with ease. The force is the same — so what changes? The answer is the moment, and understanding it unlocks a huge section of AQA mechanics.

Moments appear everywhere in physics: from the design of bridges and cranes to the way a spanner tightens a bolt. At A Level, you need to be precise about both the definition and the calculation — examiners test the exact wording, not a rough idea.

2. The Moment of a Force

Picture a see-saw balanced on a pivot. A child pushes down on one end — that push creates a turning effect about the pivot. The size of that turning effect depends on two things: how hard they push, and how far from the pivot they are sitting.

Written as an equation: $M = F \times d_{\perp}$, where $F$ is the force in newtons and $d_{\perp}$ is the perpendicular distance in metres from the pivot to the line of action of the force.

The critical word here is perpendicular. The distance must be measured at right angles to the line of action of the force — not along the object, and not along some other convenient line. This is the most common source of errors in exam questions.

3. Calculating the Moment of a Force: Worked Example

Theory is straightforward — but exam questions often disguise the perpendicular distance. Here is a standard calculation to build the method before the questions get trickier.

Worked example: Calculating the Moment of a Force About a Pivot

A mechanic applies a force of 35 N to the end of a spanner. The perpendicular distance from the centre of the bolt (the pivot) to the line of action of the force is 0.25 m. Calculate the moment of the force about the bolt. [2 marks]

1. $M = F \times d_{\perp}$ — [M1] Correct formula scores the method mark.
2. $F = 35 \text{ N}, \quad d_{\perp} = 0.25 \text{ m}$ — Both values are given directly. Check that the distance is already perpendicular — the question states it is.
3. $M = 35 \times 0.25 = 8.75 \text{ N m}$ — [A1] Arithmetic check: 35 × 0.25 = 35 × (1/4) = 8.75. Units must be N m.
4. $M = 8.75 \text{ N m}$ — Always include units. An answer without units loses the accuracy mark at A Level.

Answer: M = 8.75 N m

Notice that doubling the perpendicular distance to 0.50 m would double the moment to 17.5 N m — without changing the force at all. This is exactly why a longer spanner makes it easier to undo a tight bolt.

4. Couples: A Special Pair of Forces

Now consider something different. When you turn a steering wheel, you push one side forward and pull the other side back simultaneously. There is no net force trying to move the car sideways — the wheel only rotates. This is the defining feature of a couple.

The word coplanar means both forces lie in the same plane — they are not acting in different directions in 3D space. At A Level, you will always be dealing with coplanar couples unless told otherwise.

Because the two forces are equal and opposite, they cancel out as a resultant force: $F_{net} = F - F = 0$. The object does not accelerate in any direction — it can only rotate. This is what distinguishes a couple from a single force or an unbalanced pair.

5. The Moment of a Couple

Earlier, the moment of a single force was measured from a specific pivot point. A couple is different: because the net force is zero, the moment of a couple is the same about any point in the plane. This is a key conceptual distinction at A Level.

Notice the formula looks similar to the moment of a single force, but $d$ here is the perpendicular distance between the two lines of action — not the distance from one force to a pivot. You use only one force value ($F$), not $2F$, because the formula already accounts for both forces through the full separation distance $d$.

6. Calculating the Moment of a Couple: Worked Example

The formula is concise, but exam questions test whether you can correctly identify $F$ and $d$ from a diagram or description. Work through this example carefully.

Worked example: Calculating the Moment of a Couple

A student turns a tap by applying two equal and opposite forces of 4.5 N to opposite sides of the tap handle. The perpendicular distance between the lines of action of the two forces is 0.12 m. Calculate the moment of the couple. [2 marks]

1. $M = F \times d$ — [M1] State the correct formula. Here F is the magnitude of one force and d is the perpendicular distance between the lines of action.
2. $F = 4.5 \text{ N}, \quad d = 0.12 \text{ m}$ — F is the magnitude of one of the two equal forces. d is the full perpendicular separation between the lines of action — not half of it.
3. $M = 4.5 \times 0.12 = 0.54 \text{ N m}$ — [A1] Arithmetic check: 4.5 × 0.12 = 4.5 × 12 ÷ 100 = 54 ÷ 100 = 0.54. Units are N m.
4. $M = 0.54 \text{ N m}$ — The moment of the couple is 0.54 N m. Note: this value is the same regardless of which point in the plane you choose as your reference — a unique property of couples.

Answer: M = 0.54 N m

Compare this with the single-force moment calculation from Section 3. The formula structure is the same, but the physical meaning of $d$ is different. Keeping that distinction clear is what separates a confident A Level answer from a muddled one.

7. Comparing Moments and Couples

Now that both concepts are established, it is worth placing them side by side. Examiners frequently ask students to compare or distinguish between the two — a command word that demands both similarities and differences.

The most important distinction for exam purposes is the last two rows. A single force produces a moment that depends on where you measure from. A couple produces the same moment about every point — this is a direct consequence of having zero net force.

8. Exam Technique and Mark-Winning Strategies

Moments questions are reliable mark-earners if you apply a consistent method. The errors that cost students marks are almost always the same ones — so recognising them in advance puts you ahead.

For 'calculate' questions, the mark scheme typically awards one method mark for the correct formula and one accuracy mark for the correct numerical answer with units. Showing your substitution step explicitly protects the method mark even if you make an arithmetic slip.

Moments and couples are the foundation for equilibrium problems at A Level — once you can calculate turning effects confidently, applying the principle that the sum of clockwise moments equals the sum of anticlockwise moments (for a body in equilibrium) becomes a natural next step.