Moment of couple defined as force × perpendicular distance between the…

The idea

A couple is a pair of equal forces acting in opposite directions along different lines of action, so their resultant force is zero but they still rotate an object. The moment of a couple is defined as force × perpendicular distance between the lines of action of the forces. The distance is measured perpendicular to the force direction, between the two parallel lines along which the forces act, not between their points of application. For example, two 12 N forces act in opposite directions on a steering wheel, with lines of action 0.25 m apart, giving a moment of 12 × 0.25 = 3.0 N m. Because the two forces are equal and opposite, the object does not accelerate linearly; the couple produces only rotation.

What earns the marks

• A couple consists of two forces that are equal in magnitude, opposite in direction and act along different parallel lines of action.
• The resultant force of a couple is zero, so a couple produces rotation without translational acceleration.
• The moment of a couple is calculated as force × perpendicular distance between the lines of action of the two forces.
• The perpendicular distance is measured at right angles to the direction of the forces, between the two lines of action, not between the points where the forces are applied.
• The unit of the moment of a couple is the newton metre (N m), and the moment is a vector quantity whose direction indicates the sense of rotation.
• For a couple, the moment is the same about any point, because the two forces are equal and opposite and their lines of action are separated by a fixed perpendicular distance.

Common mistakes and how to put them right

• Measuring the distance between the points of application of the two forces instead of the perpendicular distance between their lines of action.

  Put it right: Draw the lines of action and measure the perpendicular separation.

• Using the sum of the two forces rather than one force in the calculation.

  Put it right: Use the magnitude of one of the equal forces, because the couple is defined by a single force value.

• Assuming a couple produces a resultant linear force.

  Put it right: Recognise that the two forces cancel as vectors, leaving only a turning effect.

Exam tips

• Sketch the two forces and extend their lines of action, then mark the perpendicular distance between those lines before substituting into the equation.
• Check that the distance is perpendicular to the force direction; if the separation is given at an angle, resolve to find the perpendicular component.
• State the direction of the moment (clockwise or anticlockwise) when the question asks for the sense of rotation, and give the unit N m.