Real objects have size, shape and imperfections that would make every problem intractable. Mechanics works by deliberately stripping these away — and knowing exactly which assumption you are making, and what it changes, is half of doing the subject well.
7 min read3 worked examples
Why mechanics needs a model
A real football spins, deforms slightly on impact, and feels air resistance that depends on its speed, its surface and the wind. None of that is solvable with the tools of this course. So mechanics replaces the real object with a deliberately simplified model: a small set of stated assumptions that strip away the complications you are not being asked to deal with, leaving a problem that algebra and calculus can actually solve. Every assumption is a choice, and you should be able to name it and say what it does.
The standard modelling assumptions
Particle — the object is treated as a single point with mass but no size or shape, so it cannot spin and every force on it acts at the same point.
Rod — a rigid, one-dimensional object with length but no thickness.
Lamina — a flat, two-dimensional shape with no thickness.
Uniform (rod, lamina or body) — mass is distributed evenly, so the weight acts at the geometric centre.
Light (string, rod or pulley) — the mass is so small it is taken as exactly zero, so it has no weight and does not itself need accelerating.
Inextensible (string) — the string does not stretch, so two particles joined by it have the same speed and the same magnitude of acceleration at every instant.
Smooth (surface or pulley) — there is no friction; a smooth pulley also has the same tension in the string on both sides.
Rough (surface) — friction acts, opposing relative sliding or the tendency to slide.
Rigid body — the object does not bend, twist or deform, so distances between points on it stay fixed.
Negligible air resistance — drag from the air is ignored, so gravity (and any other stated forces) act alone.
Modelling assumptions are marks in the exam
Questions often ask you to state the modelling assumptions used, or to explain how the answer would change if one were dropped. Learn the precise wording above — "light" means zero mass, not "not very heavy"; "smooth" means zero friction, not "fairly slippery". Mark schemes reward the exact technical meaning, not an approximate paraphrase.
What changes if you don't assume it?
Every assumption exists because dropping it makes the problem harder in a specific, predictable way. If a string is not light, its own weight contributes to the forces in the system and its tension is no longer uniform along its length. If a surface is rough rather than smooth, a friction force appears that opposes motion, and you can no longer assume the object accelerates freely. If air resistance is not negligible, an object falling under gravity decelerates as it speeds up rather than accelerating at a constant $g$, and the SUVAT formulae from the kinematics lessons stop applying exactly. If a body cannot be modelled as a particle, forces acting at different points can make it turn as well as move — which is exactly the situation the moments lessons later in this course are built to handle.
Worked example 1
Identifying assumptions in a scenario
A crate is pulled across a warehouse floor by a rope. The rope is modelled as light and inextensible, the floor as rough, and the crate as a particle. State what each of these three assumptions means for the resulting equations of motion.
MethodTranslate each named assumption into its effect on the model
1
"Light" rope: the rope has no mass, so no force is needed to accelerate the rope itself — the tension is transmitted directly and unchanged along its length.
Zero mass, zero weight.
2
"Inextensible" rope: the rope does not stretch, so the crate's acceleration equals whatever is applied to the other end of the rope — there is no lag or elastic give.
Fixed length.
3
"Rough" floor: a friction force acts on the crate, opposing its motion, and must be included in the equation of motion alongside the pulling force.
Not smooth, so friction is present.
4
"Particle" crate: every force on the crate is treated as acting at a single point, so the crate cannot topple or rotate in this model — only its motion in a straight line matters.
No size, so no turning effect.
▪ solved
Worked example 2
Removing an assumption
Two particles are connected by a string over a pulley that is modelled as smooth and light. Explain how the calculation of the acceleration and tension would change if the pulley were rough instead of smooth.
MethodIdentify exactly what "smooth" was doing in the original model
1
"Smooth" guarantees the tension in the string is the same on both sides of the pulley, because there is no friction between the string and the pulley to reduce it.
This is the key simplification "smooth" provides.
2
If the pulley were rough, friction between the string and the pulley surface would act, and the tension on the side of the string moving into the rotation would be greater than on the side moving out of it.
Friction resists relative sliding of the string over the pulley.
3
The two particles could no longer be analysed with a single tension $T$ — you would need two different tensions, $T_1$ and $T_2$, related by a further equation describing the friction at the pulley.
One equation becomes two, plus an extra relationship.
▪ solved
Worked example 3
Particle vs no particleChallenge
A sheet of paper and a coin of similar mass are dropped from the same height at the same time. In practice the coin lands first by a noticeable margin, but a first model of "an object falling under gravity" (from the vertical motion lessons) predicts they land together. Explain which modelling assumptions break down for the paper but not for the coin, and why.
MethodCompare the two objects against each assumption in turn
1
The vertical-motion model assumes the object is a particle falling under gravity alone, with air resistance negligible.
Recall the assumptions behind $a = g$.
2
The coin is small, dense and compact: the air resistance it experiences is tiny compared with its weight, so "negligible air resistance" is an excellent approximation and it falls very close to $a = g$.
High weight-to-surface-area ratio.
3
The paper has a large surface area for its weight, so air resistance on it is not negligible — the assumption fails, and the paper's actual acceleration is far less than $g$ for most of the fall.
Low weight-to-surface-area ratio.
4
The paper also tumbles and flutters, so it cannot really be modelled as a non-rotating particle either — a second assumption breaks down at the same time.
Shape allows rotation and instability.
▪ explained
A model is only ever as good as its assumptions
This is the point of stating assumptions explicitly: a model's predictions are only reliable within the range where its assumptions roughly hold. The vertical motion equations are not "wrong" — they answer the question "how would this fall if air resistance really were negligible?" precisely. Whether that question is a good approximation to reality depends entirely on the object.
Common mistake
Writing "light" to mean "not very heavy", or "smooth" to mean "fairly slippery", loses the mark even when the reasoning is otherwise correct. These words have exact technical meanings in mechanics — zero mass, and zero friction, respectively — and mark schemes are strict about the precise wording expected.
Check yourself
A ladder problem states that the ladder is "uniform" and the ground is "rough" but the wall is "smooth". Explain what each of these three words tells you about the forces in the problem.
Uniform: the ladder's weight acts at its midpoint, since its mass is evenly spread along its length.
Rough ground: a friction force acts where the ladder meets the ground, opposing the tendency of the base to slide.
Smooth wall: no friction acts where the ladder meets the wall — only a normal reaction, perpendicular to the wall.