Physics 9702 · Paper 2

Couples & Torque

A single force pushes and turns. There is one arrangement of forces that turns without pushing.
Two hands on a steering wheel: one pushes up, one pushes down. The wheel turns, but it does not move away.

What a couple is

Two hands gripping opposite edges of a car steering wheel, seen face-on. — A couple is two equal, opposite, parallel forces whose lines of action do not meet. They give a turning effect with no resultant force, so the wheel turns but does not move from its axle. Torque of a couple = one force × the distance between the two forces.

A is a pair of forces that are equal in magnitude, opposite in direction, parallel, and not along the same line.
The two forces cancel as a push (resultant force = 0), so the object does not accelerate away. They do not cancel as a turn. A couple produces rotation only (9702/13/O/N/24 Q13).
The turning effect of a couple is called its .

\text{torque} = F \times s

Symbols

$F$ = one of the two forces (N)
$s$ = perpendicular distance between the two forces (m)

A couple: two equal forces, opposite in direction, not along the same line. Torque = one force × the perpendicular distance between them = 15 × 0.40 = 6.0 N m.

Worked example

Smallest case: a couple on a tap

Two forces of 8.0 N act as a couple on a tap handle, 0.30 m apart. Find the torque.

$\text{torque} = F \times s = 8.0 \times 0.30 = 2.4 \text{ N m}$ .

Answer

\text{torque} = 2.4 \text{ N m}

Common mistake

Torque of a couple = one force × the distance between the forces. The wrong options in the multiple-choice paper multiply by both forces, by half the distance, or by twice the force (9702/12/M/J/25 Q17).

Your turn— tap to reveal the worked answer (9702/13/M/J/24 Q10)

Water leaves the two ends of a garden sprinkler as jets, each pushing with 3.0 N in opposite directions at the ends of a tube 0.15 m long. Find the torque on the sprinkler. (9702/13/M/J/24 Q10)

$\text{torque} = F \times s = 3.0 \times 0.15 = 0.45 \text{ N m}$ .

Answer: 0.45 N m.

Deciding whether two forces form a couple

The exam shows two forces and asks: do they form a couple? Check all the parts of the definition, one by one.
Equal in magnitude? Opposite in direction? Parallel? Not along the same line? All four must hold.
A real 2025 case: a 60 N force and a 220 N force at right angles to each other. Not a couple, because the resultant force is not zero and the forces are not parallel (9702/22/O/N/25 Q2(a)(ii)).

The torque is the same about any point

Take moments about the centre of the wheel in the figure: each 15 N force acts 0.20 m away, both turning the same way, so the total is $15 \times 0.20 + 15 \times 0.20 = 6.0$ N m.

Now take moments about the point where one force acts: that force contributes zero, and the other acts 0.40 m away, giving $15 \times 0.40 = 6.0$ N m again.

A couple's torque does not depend on the chosen point. That is why a single number, $F \times s$ , is enough to describe it (9702/11/O/N/25 Q14).

One force turning about a pivot: moment = F × perpendicular distance from the pivot. Two equal opposite forces: torque = one force × distance between them, about any point.

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