A means of measuring the turning effect of a force about a point. For a system of coplanar forces, the moment of one of the forces F about any point A in the plane can be defined as the product of the magnitude of F and the distance from A to the line of action of F, and is considered to be acting either clockwise or anticlockwise. For example, suppose that forces with magnitudes F1 and F2 act at B and C, as shown in the figure. The moment of the first force about A is F1d1 clockwise, and the moment of the second force about A is F2d2 anticlockwise. The principle of moments considers when a system of coplanar forces produces a state of equilibrium.
However, a better approach to measuring the turning effect is to define the moment of a force about a point as a vector, as follows. The moment of the force F, acting at a point B, about the point A is the vector (rB−rA)×F, where this involves a vector product. The use of vectors not only eliminates the need to distinguish between clockwise and anticlockwise directions, but facilitates the measuring of the turning effects of non-coplanar forces acting on a 3-dimensional body.
Similarly, for a particle P with position vector r and linear momentum p, the moment of the linear momentum of P about the point A is the vector (r−rA)×p. This is the angular momentum of the particle P about the point A.
Suppose that a couple consists of a force F acting at B and a force −F acting at C. Let rB and rC be the position vectors of B and C, and let rA be the position vector of the point A. The moment of the couple about A is equal to (rB−rA)×F+(rC−rA)×(−F)=(rB−rC)×F, which is independent of the position of A.