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Home » Prove that Moment of couple = Force x Couple arm.
Prove that Moment of couple = Force x Couple arm.
Class 10 | Force | ICSE | Physics | Selina
Prove that Moment of couple = Force x Couple arm.

Two equal and opposite forces, each of magnitude F, are applied at points A and B. The bar is rotated in an anticlockwise manner by the two forces. The coupling arm, or AB, is the perpendicular distance between two forces.

Moment of force F at the end A

=\text{ }F\text{ }\times \text{ }OA (anticlockwise)

Moment of force F at the end B

=\text{ }F\text{ }\times \text{ }OB (anticlockwise)

Total moment of couple =F\text{ }\times \text{ }OA\text{ }+\text{ }F\text{ }\times \text{ }OB

= F\text{ }\times \text{ }\left( OA\text{ }+\text{ }OB \right)

=\text{ }F\text{ }\times \text{ }AB

=\text{ }F\text{ }\times \text{ }d (anticlockwise)

= Either force × perpendicular distance between the two forces or couple arm

Hence, Moment of couple = Force × Couple arm.

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