Moments about A

However, a better approach is to define the moment of the force F, acting at a point B, about the point A as the vector (rB−rA) × F, where × denotes the vector product and rA, rB are the position vectors of A and B. 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. The moment of the couple about A is equal to

which is independent of the position of A.