Moment of a force

• The moment (torque) of a force F about a point O is M = F × d, where d is the perpendicular distance from O to the line of action of the force. Unit: N·m.
• Only the perpendicular component contributes: if F makes an angle θ with the arm of length r, then M = F·r·sin θ.
• Moment is a turning effect; the sign convention is anticlockwise positive.
• A force has zero moment about any point on its own line of action.

Varignon's theorem

The moment of the resultant of a system of coplanar forces about any point equals the algebraic sum of the moments of its components about the same point.

Worked example

A force of 20 N acts at the end of a 0.5 m arm making 30° with the arm: M = 20 × 0.5 × sin 30° = 5 N·m. If instead the force is perpendicular to the arm, M = 20 × 0.5 = 10 N·m.