Couples and Torque: A Detailed Explanation

Couples are pairs of forces that are equal in magnitude but opposite in direction and act along different lines of action. They create a turning effect or torque on an object.

Example: Turning a Steering Wheel

When a driver turns a steering wheel, they apply forces to opposite sides of the wheel. These forces are equal in magnitude but opposite in direction, forming a couple. This couple produces a torque that causes the steering wheel to rotate.

Characteristics of a Couple

  • Equal magnitude: The two forces in a couple must be of the same size.

  • Opposite direction: The two forces must act in opposite directions.

  • Different lines of action: The two forces must not act along the same line.

Torque Produced by a Couple

The torque produced by a couple is given by the product of one of the forces and the perpendicular distance between them. Mathematically, this can be expressed as:

Torque = Force × Perpendicular Distance

In the case of a double-arm spanner, the two forces applied at points A and B form a couple. The torque produced by this couple causes the spanner to rotate about point O.

Key Points

  • Couples are pairs of forces that produce a turning effect.

  • The torque produced by a couple is equal to the product of one of the forces and the perpendicular distance between them.

  • Couples are used in various applications, such as turning steering wheels, opening nuts, and operating machinery.

Understanding couples and torque is essential for understanding rotational motion and the principles of mechanics.