A Level Maths: Resolving Forces and Newton's Second Law (F = ma) Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Vectors — vector decomposition is the foundation of resolving forces
- Trigonometry — needed for resolving forces into components
- Kinematics — Constant Acceleration (SUVAT)}}: F = ma connects force to motion
A Level Maths resolving forces and Newton's second law is the core of force analysis in mechanics. You learn to break forces into perpendicular components, apply $F = ma$ to find unknown forces or accelerations, and handle problems where forces act in directions other than along the motion. This is the foundation for Newton's Third Law (Objects in Contact and Connected Particles) and the Year 2 extensions.
You resolve forces into perpendicular components — usually horizontal and vertical, or parallel and perpendicular to a slope. A force $F$ at angle $\theta$ to the horizontal has horizontal component $F\cos(\theta)$ and vertical component $F\sin(\theta)$. You apply Newton's second law $F = ma$ in each direction independently, treating perpendicular components as separate one-dimensional problems. Common contexts include particles on smooth horizontal surfaces, objects sliding on smooth inclined planes, and forces given as 2D vectors using $\mathbf{i}$ and $\mathbf{j}$ notation. You also handle problems where the particle is in equilibrium (net force is zero), or where you need to find the resultant of multiple forces.
Resolving forces and Newton's second law is part of the Mechanics strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: a force at angle $\theta$ to the horizontal has horizontal component $\cos(\theta)$ (NOT $\sin(\theta)$) — the cosine goes with the angle you measure FROM; weight always acts vertically downwards, not along the slope, so for inclined plane problems you must resolve weight into components parallel and perpendicular to the slope; the normal reaction $R$ does NOT always equal the weight — on a slope or with vertical applied forces, it is smaller or larger; and $F = ma$ requires NET force, not just one of the forces acting.