Modelling, quantities and units

The art of leaving things out

A model trades realism for solvability. Calling a crate a particle means its size and shape stop mattering, so all its mass acts at one point, every force acts at that point, and rotation leaves the problem entirely. That one move turns most of this course into arrows meeting at a dot.

The rest of the vocabulary works the same way, each word deleting one complication. A light string has no mass, so the tension is the same all along it. A smooth surface or pulley has no friction. An inextensible string cannot stretch, so the objects it joins share one acceleration. A uniform beam carries its weight at its midpoint and a rigid one does not bend.

A few more turn up in question stems. A rod is rigid and has length but no thickness. A lamina is flat with no thickness at all. A bead is threaded on a wire and can slide along it. A peg is a fixed point that a string can pass over. Behind all of them sits the assumption nobody writes down, that air resistance and wind have been ignored, which is the first thing to name when a question asks you to criticise the model.

Units and quantities

Mechanics runs on SI units. Metres, seconds and kilograms, plus everything built from them, so newtons for force and m s⁻¹ and m s⁻² for motion. Convert before calculating. A speed left in km h⁻¹ and fed into a suvat equation poisons every number after it. Weight is a force, W = mg, with g = 9.8 m s⁻² unless a question says otherwise.

Quantities split into scalars, which have size only, and vectors, which have size and direction. Distance against displacement. Speed against velocity. In one dimension the direction is carried entirely by the sign, so choose a positive direction at the start of a question, write it down, and then believe the signs that come out. Doing that prevents more mechanics errors than any other single habit.