Couples and their moments

Push the rim of a tap with one finger and it turns, but it also tries to slide sideways. Push with two fingers on opposite sides, with equal pushes in opposite directions, and it only turns. Two forces of equal size, opposite directions and different lines of action are called a couple. Their resultant is zero (F + (−F) = 0), so there is no push in any direction, yet the body is not in equilibrium: this is why Week 8 needed the moment condition as well as the force condition. The arm L of the couple is the perpendicular distance between the two lines of action. Its moment is M = F × L, written with the sign of the turning: anticlockwise positive, clockwise negative. Why F × L? Take moments about a point on the line of action of one force: that force has no moment, and the other force F, with arm L, gives F × L. (Next lesson shows that every point gives the same answer.) If the force doubles and the arm halves, M does not change, so the same turning effect can be made with a small force and a long arm. The unit is N·m (or N·cm).