define and apply the torque of a couple

Objective

Define and apply the torque of a couple in real‑world situations.

A couple consists of two equal and opposite forces that do not act along the same line. The forces are separated by a distance (the lever arm), so the system produces a turning effect.

Because the forces are equal and opposite, the net force on the system is zero, but the net torque is not.

The magnitude of the torque produced by a couple is simply the product of the force magnitude and the separation distance:

$$\tau = F \times d$$

where F is the magnitude of each force and d is the perpendicular distance between the lines of action of the forces.

Direction is given by the right‑hand rule: point your fingers along the first force, curl towards the second, and your thumb points in the direction of the torque.

When you push on a door handle, you apply a force F = 15 N at a distance d = 0.3 m from the hinge.

Because the hinge provides an equal and opposite reaction force, the two forces form a couple.

Torque produced:

$$\tau = 15\,\text{N} \times 0.3\,\text{m} = 4.5\,\text{N·m}$$

This torque turns the door clockwise (right‑hand rule).

• Always check that the two forces are equal and opposite before treating them as a couple.
• Remember that the torque of a couple is independent of the point of application; only the separation matters.
• Use the right‑hand rule to state the direction of rotation clearly in your answer.
• When given a diagram, identify the lever arm as the perpendicular distance between the force lines.
• Show all units and keep them consistent (N, m, N·m).