Mechanics is the mathematics of how things move and why. It is one third of the applied content of every A-Level Maths specification — Edexcel, AQA, OCR and OCR MEI all examine it — and it is the section students most often neglect, because it arrives early in Year 12 feeling unfamiliar and gets mentally filed under 'physics'. It is not physics. It is applied mathematics, it follows rules as precise as any in pure maths, and the opening topics are some of the most learnable marks on the whole course.
This guide is for the Year 12 student meeting mechanics for the first time, or the Year 13 student who avoided it and now needs to fix that. It covers what the subject actually is, how to draw the diagrams everything depends on, and where the early, reliable marks are.
What mechanics actually is
Mechanics splits into two halves. Kinematics is the description of motion: displacement, velocity, acceleration, and the constant-acceleration equations (often called the suvat equations). Dynamics is the explanation of motion: forces, Newton's laws, and why things accelerate or stay still. In the second year you add moments, friction in more depth, and projectile motion.
The unifying idea is modelling. Real objects are complicated, so mechanics simplifies them: a car becomes a 'particle' with mass but no size, a rope becomes a 'light inextensible string' with no weight, a surface becomes 'smooth' with no friction. Every exam question states its modelling assumptions, and every 'comment on your model' mark at the end is earned by understanding what was assumed away.
Kinematics first: the suvat equations
The earliest mechanics topic is usually motion in a straight line with constant acceleration, and it is more approachable than it looks. There are five quantities — displacement s, initial velocity u, final velocity v, acceleration a and time t — and a small set of equations connecting them. Every question gives you three of the five and asks for a fourth.
The skill is not algebraic; it is organisational. Write down, every single time, a list of s, u, v, a, t with the values you know and a question mark against the one you want. Then choose the equation that contains exactly those four. Students who skip the list pick the wrong equation; students who write it rarely do. This habit alone is worth several marks per paper.
- Decide a positive direction before you start, and write it down. Velocity and acceleration can be negative, and sign errors are the most common kinematics mistake.
- Check units: if time is in seconds, speeds should be in metres per second, not kilometres per hour. Convert first.
- A calculator is allowed, but show the substituted equation before the answer — the method marks sit there.
Forces and the diagram that runs the subject
Dynamics begins with a question: what forces act on this object? The answer is always a picture — a force diagram, sometimes called a free-body diagram — and the single biggest difference between students who find mechanics manageable and students who find it impossible is whether they draw that picture, every time, before writing any equations.
The diagram is simple in principle. Draw the object as a small dot or box. Then draw every force acting on it as an arrow, labelled, pointing the right way. For the early topics, the forces you will meet are few:
- Weight — always present (unless the object is modelled as light), acting vertically downwards, with magnitude mg, where g is taken as 9.8 metres per second squared unless told otherwise.
- Normal reaction — the push back from a surface the object rests on, always perpendicular to that surface.
- Tension — the pull along a string or rope, acting away from the object along the line of the string.
- Friction — present only if the surface is not smooth, acting parallel to the surface, opposing motion or impending motion.
- Applied forces — pushes, pulls, driving forces, resistances such as air resistance, as described in the question.
The discipline that matters: forces the object exerts on other things do not go on the diagram. Only forces acting on the object. A book on a table feels its weight and the table's normal reaction — the force the book exerts on the table belongs on the table's diagram, not the book's. Mixing these up is the beginner error that breaks everything downstream.
Newton's laws: from diagram to equation
Once the diagram exists, the mathematics is one sentence long: the resultant force equals mass times acceleration, F = ma. If the object is in equilibrium — stationary or moving at constant velocity — the resultant force is zero, so all the forces balance. If it is accelerating, the resultant force points in the direction of the acceleration, and its magnitude is ma.
In practice you resolve the forces in chosen directions — usually 'along' and 'perpendicular to' a surface, or 'horizontal' and 'vertical' — and write F = ma in each direction. Resolving means splitting a force at an angle into components using sine and cosine, which is why a solid grasp of GCSE trigonometry is the true prerequisite for mechanics. The force along a slope of angle θ is mg sin θ; the force into the slope is mg cos θ. These two appear constantly.
- Draw the object and every force acting on it, labelled.
- Choose your directions and mark the positive sense.
- Resolve any angled forces into your chosen directions.
- Write F = ma (or 'forces balance' if in equilibrium) in each direction.
- Solve the resulting equations — often simultaneous, which is why simultaneous equations matter here.
- Sanity-check: is the acceleration's direction and size physically sensible?
Connected particles: the pulley questions
The classic early dynamics question is two particles joined by a string over a pulley, or a car towing a trailer. The method extends naturally: draw a separate force diagram for each object, apply F = ma to each, and solve the equations together. The connecting force — tension in the string, thrust in the tow bar — appears in both diagrams with equal magnitude and opposite effect, because the string is modelled as light and inextensible.
Students lose marks here in three repeatable ways: putting both objects on one diagram, assuming the tensions differ across the pulley, and forgetting that both objects share the same acceleration magnitude. All three are fixed by the same habit — one diagram per object, labelled assumptions, then equations.
Where the first ten marks hide
On every board, the mechanics section opens with questions that reward the basics done carefully. These are the marks a well-drilled beginner should treat as non-negotiable:
- A suvat question with three values given — write the list, pick the equation, substitute, solve. Two to four marks.
- A force diagram sketch, or a 'state the forces acting' prompt — one or two marks for a labelled, correct picture.
- A vertical motion under gravity question — the same suvat list with a = ±9.8 and the sign convention stated.
- A one-mark modelling comment — 'we assumed no air resistance', 'the string has no mass' — free if you learned the assumptions.
- A straightforward F = ma application for a single object moving horizontally or vertically.
Ten marks of a mechanics paper is a large slice of a grade boundary. Students who claim they 'can't do mechanics' almost always can do all of the above; what they cannot yet do are the multi-part questions at the end of the paper, and they let that contaminate the marks they could already secure.
How to practise mechanics effectively
Mechanics responds to practice faster than most A-Level topics, because the repertoire of question types is genuinely small. A focused fortnight looks like this.
- Spend two sessions only on force diagrams: take ten scenarios and draw the diagram with no calculation at all. Check against a mark scheme or textbook.
- Do suvat questions in sets of five, writing the s-u-v-a-t list every time until it becomes automatic.
- Move to single-object F = ma questions: horizontal, then vertical, then on a slope.
- Then connected particles, always with one diagram per object.
- Finish with a timed mixed set from your board's past papers, marking strictly and classifying every lost mark: diagram, resolving, equation, or arithmetic.
If the diagram step still feels shaky after the first two sessions, that is the point to get help — not after a month of practising on top of a broken foundation. Mechanics punishes guessing more than any other part of the course, and rewards structure more too.