Force, couple and moment with sketch

Force

A force is the action of one body on another that changes, or tends to change, the state of rest or motion of the body. It is a vector with magnitude, direction and point of application. Unit: newton (N).

Moment of a force

The moment of a force about a point (or axis) is the turning effect of the force about that point. M = F × d, where d is the perpendicular distance from the point to the line of action of the force (the moment arm). In vector form, M_O = r × F. Unit: N·m. By convention, anticlockwise moments are taken as positive.

                 | F
                 v
  O o------------+
     <--- d --->
  (moment centre)        M_O = F × d  (clockwise here)

Couple

A couple is a pair of equal, opposite and parallel forces whose lines of action are different. It has no resultant force, only a turning effect, M = F × d, where d is the perpendicular distance between the forces.

     F  ^                 F at A and −F at B
        |    d            M = F × d  (clockwise here)
    A   o-----------o B
                    |
                    v F