A Level Maths: Resolving Non-Perpendicular Forces 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.
- Resolving Non-Perpendicular Forces at a Point (OCR)
- Statics and Dynamics in 2d Without Friction (OCR)
- Statics and Dynamics in 2d With Friction (OCR)
- Statics and Dynamics in 2d With Friction (Edexcel)
- Connected Particles With Friction (Edexcel)
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:
- Resolving Forces and Newton's Second Law (F = ma) — foundational
- Trigonometry — needed for resolving
- Vectors — vector decomposition is central
A Level Maths resolving non-perpendicular forces is the Year 2 mechanics topic that handles forces acting in directions not aligned with each other. This Year 2 mechanics topic is essential for the statics and dynamics in 2D problems that appear in the Mechanics strand — inclined planes, ladders, suspended objects, and more.
You extend the resolution techniques from Resolving Forces and Newton's Second Law (F = ma) to handle problems where multiple forces act in arbitrary directions. The strategy is to choose two perpendicular axes (often horizontal/vertical, or parallel/perpendicular to a surface) and resolve every force into components along these axes. You then apply $F = ma$ in each direction independently. Lami's theorem and the triangle of forces give alternative geometric approaches when three forces are in equilibrium. You handle problems involving particles on rough inclined planes (with friction along the slope), suspended particles with two or more strings at different angles, and ladders leaning against walls. You also analyse situations where the direction of friction is unknown and must be determined.
Resolving non-perpendicular forces 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: choose your axes BEFORE resolving — on inclined planes, parallel and perpendicular to the slope is usually much easier than horizontal and vertical; remember that weight always acts vertically, so on a slope it must be resolved into BOTH directions; the normal reaction is NOT always equal to the weight — it depends on what other vertical forces are present; and for problems involving friction, the friction force opposes motion (or attempted motion) — get the direction right before resolving.