Moment
Category : JEE Main & Advanced
The moment of a force about a point O is given in magnitude by the product of the forces and the perpendicular distance of O from the line of action of the force.
If F be a force acting at point A of a rigid body along the line AB and \[OM(=p)\] be the perpendicular distance of the fixed point O from AB, then the moment of force about O
\[=F.p=AB\times OM=2\left[ \frac{1}{2}(AB\times OM) \right]\]\[=2\text{ }(\text{Area of }\Delta AOB)\]
The S.I. unit of moment is Newton-meter \[(N-m)\].
(1) Sign of the moment : The moment of a force about a point measures the tendency of the force to cause rotation about that point. The tendency of the force \[{{F}_{1}}\] is to turn the lamina in the clockwise direction and of the force \[{{F}_{2}}\] is in the anticlockwise direction.
The usual convention is to regard the moment which is anticlockwise direction as positive and that in the clockwise direction as negative.
(2) Varignon's theorem : The algebraic sum of the moments of any two coplanar forces about any point in their plane is equal to the moment of their resultant about the same point.
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