Moments: Couple as a pair of equal and opposite coplanar forces.

The idea

A couple consists of two forces that are equal in magnitude, opposite in direction and coplanar, meaning they act in the same plane. The forces do not act along the same line, so they produce a resultant turning effect without a resultant translational force. The moment of a couple is the sum of the moments of the two forces about any point in the plane, and it equals the magnitude of one force multiplied by the perpendicular distance between the lines of action of the two forces. For example, two 15 N forces acting in opposite directions along parallel lines 0.20 m apart form a couple with moment 15 N × 0.20 m = 3.0 N m. Because the forces are equal and opposite, their vector sum is zero, so a couple tends to rotate a body without translating it.

What earns the marks

• State that a couple is a pair of forces that are equal in magnitude, opposite in direction and coplanar.
• Explain that the lines of action of the two forces are parallel but not the same, so the forces produce a turning effect.
• Show that the resultant force of a couple is zero because the two forces are equal and opposite.
• Calculate the moment of a couple as the magnitude of one force multiplied by the perpendicular distance between the lines of action of the two forces.
• Recognise that the moment of a couple is the same about any point in the plane of the couple.
• Distinguish a couple from a single force or from two forces that are not equal and opposite.

Common mistakes and how to put them right

• Describing a couple as two forces that act along the same line.

  Put it right by stating that the lines of action are parallel and separated, so a turning effect exists.

• Assuming a couple produces a resultant translational force.

  Put it right by noting the resultant force is zero because the forces are equal and opposite.

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

  Put it right by measuring the perpendicular separation of the two lines of action.

• Treating any two opposite forces as a couple even when they are not equal in magnitude or not coplanar.

  Put it right by checking all three conditions: equal magnitude, opposite direction and coplanar.

Exam tips

• Check the three conditions for a couple: equal magnitude, opposite direction and coplanar, with different lines of action.
• For the moment of a couple, use the perpendicular distance between the two lines of action, not the distance between the points of application.
• State that the resultant force is zero and that the couple produces only a turning effect.