JEE Main & Advanced Mathematics Statistics Moment

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.

• The algebraic sum of the moments of any two forces about any point on the line of action of their resultant is zero.

• Conversely, if the algebraic sum of the moments of any two coplanar forces, which are not in equilibrium, about any point in their plane is zero, their resultant passes through the point.

• If a body, having one point fixed, is acted upon by two forces and is at rest. Then the moments of the two forces about the fixed point are equal and opposite.