Equilibrium: (b) couple; torque of a couple; torque = Fd

The idea

A couple is a pair of equal and opposite parallel forces whose lines of action do not coincide. A couple produces rotation without any resultant translational force. The torque of a couple is the product of one of the forces and the perpendicular distance between the lines of action of the two forces: torque = Fd, where F is the magnitude of one force and d is the perpendicular separation. The unit is the newton metre (N m). Because the two forces are equal and opposite, they cancel translationally but their moments add to give a pure turning effect. A steering wheel turned by two hands is a common example.

What earns the marks

• A couple consists of two equal and opposite parallel forces whose lines of action do not coincide.
• A couple produces rotation with no resultant translational force.
• Torque = Fd, where F is one force and d is the perpendicular distance between the lines of action.
• The unit of torque is the newton metre (N m).
• The moments of the two forces add because they act in the same rotational sense.

Common mistakes and how to put them right

• Confusing a couple with two forces that act along the same line.

  Put it right: A couple requires separated, parallel lines of action.

• Using the distance between the points of application rather than the perpendicular distance between the lines of action.

• Thinking the forces cancel completely.

  Put it right: They cancel translationally but produce a net turning effect.

• Forgetting that torque has the same unit as moment, the newton metre.

Exam tips

• State that the two forces are equal in magnitude and opposite in direction.
• Identify the perpendicular distance between the lines of action, not between the points of application.
• Use torque = Fd and give the unit N m.
• Check whether the question asks for a moment or a torque and use the correct term.