Couples
- A couple is a pair of equal and opposite coplanar forces that acts to produce rotation only
- A couple consists of a pair of forces that are:
- Equal in magnitude
- Opposite in direction
- Perpendicular to the distance between them
A couple must consist of two equal and opposite forces separated by a perpendicular distance
- Couples produce a resultant force of zero, so, due to Newton’s Second law (F = ma), the object does not accelerate
- Unlike moments of a single force, the moment of a couple doesn’t depend on a pivot
- The moment of a couple is equal to:
Force × Perpendicular distance between the lines of action of the forces
Worked example
Which pair of forces act as a couple on the circular object?
ANSWER: A
- In diagram A, the forces are:
- Equal in size
- In opposite directions
- Perpendicular to the distance between them
- B is incorrect as the forces are in the same direction
- C is incorrect as the forces are different in size
- D is incorrect as the distance between the forces is not perpendicular
Examiner Tip
The forces that make up a couple cannot share the same line of action which is the line through the point at which the force is applied. An example of this is shown in the diagram below:
