Couples:

A system of 2 equal and unlike parallel forces, the lines of which action are not the same, is called as couple or a torque.

• Moment of Couple: The moment of couple is the product of one of the forces forming couple and the arm of the couple. The perpendicular distance between forces is called as arm of couple.
• The moment of couple is regarded as positive or negative according as it has a tendency to turn body in anti clockwise of clockwise direction.
• The algebraic sum of moments of the 2 forces forming a couple about any point in their plane is constant, and equal to the moment of the couple.
• The 2 couples, acting in 1 plane upon a rigid body, whose moments are equal and opposite balance one another.
• Any number of couples in same plane acting on the rigid body is equivalent to a single couple, whose moment is equal to algebraic sum of moments of the couples.
• If 3 forces, acting upon the rigid body, are represented in direction, magnitude, and line of action by the sides of triangle taken in order, they are equivalent to a couple whose moment can be represented by twice the area of triangle.

Example: The two unlike parallel forces each having magnitude of 20 √3 units acting on the rigid body form an anticlock couple. If these forces lie in xy plane and act at the points
A (-1, 0), B (3, 0) and are inclined at 60⁰ to x axis, find the moment of couple.

Solution: From B, draw BM perpendicular to line of action of force passing through A.                         As, AB = 4 units and ÐMAB = 600                         From right angled triangle AMB                         MB = AB sin 600 = 2√3 units                         Therefore, the moment of the couple                         = 20√3 x MB = 20√3 x 2√3 units                         = 120 units

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