Question

Prove that

Moment of couple = Force x Couple arm.

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Answer 1

At A and B two forces each of magnitude F are applied, which are equal and opposite forces. The two forces rotate the bar in anticlockwise direction. AB is the perpendicular distance between two forces which is called the couple arm.

Moment of force F at the end A

= F × OA (anticlockwise)

Moment of force F at the end B

= F × OB (anticlockwise)

Total moment of couple = F × OA + F × OB

= F × (OA + OB)

= F × AB

= F × d (anticlockwise)

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

Hence, Moment of couple = Force × Couple arm.