Cambridge Syllabus Notes

Turning Effects of Forces

What is a Couple?

A couple is a pair of equal‑magnitude forces that act in opposite directions, are parallel, and are separated by a distance. Because the forces are parallel and opposite, they produce no net translation but create a pure rotation about a point.

Think of a door handle – you push one side of the handle up and the other side down. The forces are equal, opposite, and separated, so the door swings without sliding.

How Couples Produce Rotation

The turning effect of a couple is measured by its torque (or moment), defined as the product of the force magnitude and the perpendicular distance between the lines of action:

$$\tau = F \times d$$

Because the forces are equal and opposite, the net force is zero, but the torque is non‑zero, causing rotation.

Examples & Analogies

🔧 Wrench – turning a bolt: the handle exerts a couple on the bolt head.
✂️ Scissors – the two blades apply a couple to cut material.
🚪 Door handle – pushes and pulls on opposite sides of the hinge.
🛠️ Hammer on a nail – the hammer’s head and the nail’s head form a couple that rotates the nail.

Key Equations

Quantity	Symbol	Formula
Torque of a couple	$\tau$	$F \times d$
Resultant force of a couple	$F_{\text{net}}$	$0$ (no translation)

Exam Tips

Remember: A couple always produces pure rotation – no net force. If you see a question about a pair of forces that cause rotation but no translation, identify it as a couple.

When calculating torque, always use the perpendicular distance between the lines of action. If the problem gives an angle, use the sine of that angle: $d = r \sin\theta$.

Check units: torque is in N·m. If you get a result in N·m, you’ve likely used the correct formula.

Important Note

⚠️ A couple can be formed by any two forces that satisfy the conditions, not just by a wrench or scissors. Even a simple push on a door and a pull on the opposite side can be a couple.

understand that a couple is a pair of forces that acts to produce rotation only