The moment of a force: turning effect, coordinates and Varignon

A force can push a body along, and it can also turn it. Try closing a classroom door by pushing near the hinge, then far from it: the same push turns the door much more easily at the far point. The turning effect of a force F about a point O is called the moment of F about O. It depends on two things: the size of the force, and how far its line of action is from O, measured at right angles. That distance is the arm L. So |M| = F × L. Why the perpendicular distance? A force that points straight at O (or straight away from it) only pushes on the hinge and cannot turn anything: its arm is zero. Only the part of the force at right angles to OA turns, and F sin θ × OA is the same number as F × (OA sin θ). Sliding the force along its line of action changes nothing, because the arm stays the same. Sign convention used in every lesson: an anticlockwise moment is positive and a clockwise moment is negative. The unit is a force unit times a length unit: N·m (or N·cm, where 100 N·cm = 1 N·m). If the line of action passes through O, the arm is 0 and the moment about O is 0.