Mechanics · Quantities & units
Chapter 1 · 4
The idea
Modelling assumptions & SI units
What each standard modelling word actually lets you ignore — particle, light, inextensible, smooth, rigid, uniform — so you can read an assumption off a question and know its consequence, the SI units mechanics is built on, and how to answer "state a limitation" by naming what the model leaves out.
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Mechanics · Quantities & units
Modelling assumptions & SI units
What each standard modelling word actually lets you ignore — particle, light, inextensible, smooth, rigid, uniform — so you can read an assumption off a question and know its consequence, the SI units mechanics is built on, and how to answer "state a limitation" by naming what the model leaves out.
Why it works
One word switches off one complication
Real objects are messy — they have size, bend, stretch, rub and spin. Modelling is the deliberate act of ignoring the parts that don't matter so the maths stays doable. Every mechanics question is built on a few standard assumptions, each a single word that switches off one complication. Knowing exactly what each word buys you is half the subject.The dictionary of assumptions
| Assumption | What it lets you ignore | Consequence you use |
|---|---|---|
| Particle | the object's size and shape | all its weight acts at one point; no rotation |
| Light (string, rod, pulley) | its mass | tension is the same all along it; weight |
| Inextensible (string) | any stretching | connected bodies share one acceleration |
| Smooth (surface, pulley) | friction | no friction force; a smooth pulley doesn't change the tension |
| Rough (surface) | — (friction is present) | a friction force acts along the surface |
| Rigid (rod) | bending | the rod keeps its shape; it can push (thrust) as well as pull |
| Uniform (body) | uneven mass distribution | the weight acts at the geometric centre |
| Thin / lamina | thickness / 3-D shape | treat it as a line or a flat sheet |
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