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.

Mechanics · Quantities & units

Modelling assumptions & SI units

Why it works

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.

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 $= 0$
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

Notice these are independent ideas, and mixing them up is a classic error: light is about mass, smooth is about friction, inextensible is about length. A string can be light and inextensible (the usual case) — those say two different things. "Light + inextensible" is precisely what makes [[forces.connected-particles]] and [[forces.pulleys]] work: light gives one tension, inextensible gives one acceleration.

SI units — the language the numbers are in. Mechanics is built on three base units: mass in kilograms (kg), length in metres (m), time in seconds (s). Everything else is derived from them:

velocity in $\text{m s}^{-1}$ , acceleration in $\text{m s}^{-2}$ ;
force in newtons (N), where $1\,\text{N}$ is the force that accelerates

1\,\text{kg}

1\ \text{m s}^{-2}

— so

1\,\text{N} = 1\,\text{kg}\,\text{m}\,\text{s}^{-2}

, straight from

F = ma

.

Keep units consistent: never mix grams with metres, or centimetres with seconds. If a mass is given in grams, convert to kilograms before using

F = ma

. The standard value of gravitational acceleration is

g = 9.8\ \text{m s}^{-2}

unless a question says otherwise.

Mass is not weight. Mass (kg) is how much matter there is and never changes; weight (N) is the gravitational force

mg

on it and depends on

g

. A

5\,\text{kg}

bag has a weight of

5 \times 9.8 = 49\,\text{N}

on Earth. Answering "what is its weight?" with "

5\,\text{kg}

" is a unit-level mistake, not a slip.

Answering "state a limitation / assumption." These marks go to naming a real simplification the model makes and (often) its effect — not to vague worries like "the rope might break." Good answers point at the assumptions above: *air resistance has been ignored, the string is modelled as light so its mass is neglected, the car is modelled as a particle so its length is ignored, the road is assumed smooth*. Refining the model means switching one assumption back on — and you should be able to say which way the answer then moves. Include air resistance, for instance, and it opposes motion, so a predicted acceleration would be smaller and a predicted top speed lower.