Budding engineers going into university are wildly ecstatic about fields such as dynamics, thermodynamics, electromagnetism and quantum mechanics. But when they come out they appreciate something quite different, sitting quietly in an unassuming corner of the engineering syllabus - statics.
Statics is about stationery objects. Not very as exciting, huh? But it turns out to be the most relevant and useful part of the engineer's repertoire. And the cornerstone of statics is the principle of moments.
When you set a top spinning, your fingers apply a twitching force at the edges. In this way you apply a torque to it. Torque is something like force, but while proper force makes the object move as a whole, torque is something that makes it spin, or rotate. In the simplest case scenario, imagine a rod fixed at some point along its length, which is labeled O. If a force of magnitude F is applied at right angles to the rod at a point d distance away from O, then we say that the body experiences a torque given as follows:
τ = F x d
The above also describes a moment of force. Torque is a more general concept, used throughout physics to determine how bodies spin and rotate. The moment of force, on the other hand, is only used in statics, but for all intents and purposes they are the same thing.
When a body does not spin or rotate, it can either mean that there are no moments of force, or that the moments of force cancel each other out. Either case may be summed up by saying that the sum of the moments is zero. (Yes, moments of force may be shortened to "moments"). This is the principle of moments.
Moments may be considered as vectors, which will cover the general case, and also be able to deal with dynamic motion. But in statics, when motion is not involved, it is more useful to consider the moments as scalars. They are calculated in the exact same way as torque above.
When the applied force is not at right angles to the rod, the component of the force at right angles is taken. You also need to consider whether the force is anticlockwise or clockwise. If the former, then the moment is positive, otherwise negative. In statics there are always both positive and negative moments (excluding the case with no moments at all), otherwise there would be a net torque and the body would not be stationary. Sometimes the convention is to do away with negative moments. In other words, all the anticlockwise moments are considered, followed by the clockwise moments, and then the two are equated.
The principle of moments is the sine cua non of architecture and engineering. In buildings, bridges, roads, these are all stationary constructs, and need to remain so. In other words, a building must not totter, a bridge crack, or a road disfigure. Therefore, architects and engineers need to consider all the forces that their projected constructions will be subjected to. To make sure that every hinge in a bridge will sustain itself, all possible forces are considered and their moments calculated. It does not only concern the various vehicles that will cross that bridge, but also forces of the river, wind, snow, and many others.
It was due to its importance in architecture and engineering that statics quickly distinguished itself as a separate field from dynamics in the 19th century. People usually quote the slide rule as once the engineer's constant companion. It may be added that the principle of moments was the bread-and-butter of his daily routine, and continues to be so.