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