A Level Maths: Coefficient Of Friction Topic Summary and Resources
Video Lessons
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Revision Notes
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Exam Questions
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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 force analysis
- Resolving Non-Perpendicular Forces — needed for sloped problems
- Newton's Third Law (Objects in Contact and Connected Particles) — connected particle context
A Level Maths coefficient of friction introduces friction as a contact force opposing motion (or attempted motion) between two surfaces. This is one of the most realistic additions to the mechanics model — real surfaces are not smooth — and friction shows up across mechanics problems involving sliding, blocks on slopes, and connected particles on rough surfaces.
You learn the coefficient of friction $\mu$, a number characterising how rough a particular pair of surfaces is. The friction force has magnitude at most $\mu R$ where $R$ is the normal reaction — so $F \le \mu R$ as the inequality, with $F = \mu R$ at the threshold of slipping (the limiting friction). Below the threshold, friction takes whatever value is needed to maintain equilibrium. The direction of friction OPPOSES motion (when moving) or OPPOSES the tendency to move (when stationary). You apply these ideas to particles on rough horizontal surfaces (pulled by horizontal or angled forces), particles on rough inclined planes (where you find the angle of friction and the minimum angle for slipping to occur), and connected particles where one surface is rough and one is smooth.
Coefficient of friction 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: the friction inequality $F \le \mu R$ is an inequality, not an equation — $F = \mu R$ only at the point of slipping; the normal reaction $R$ is NOT always $mg$ — on a slope, $R = mg\cos(\theta)$, and with applied forces $R$ changes; once an object is moving, friction equals $\mu R$ (not less than) and always opposes motion; and for problems asking 'will it slip?', compute the friction required to maintain equilibrium and compare to $\mu R$ — if more friction is needed than is available, the object slips.