A Level Maths: Newton's Third Law (Objects in Contact and Connected Particles) 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.
No exam questions yet for this topic.
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) — applying F = ma is the foundation
- Vectors — needed for direction of forces and motion
- Kinematics — Constant Acceleration (SUVAT)}}: needed for follow-up motion analysis
A Level Maths Newton's third law and connected particles extends force analysis to systems of two or more objects interacting. Newton's third law (every action has an equal and opposite reaction) lets you analyse internal forces — tensions, normal reactions between bodies, contact forces — and solve problems with pulleys, lifts, and trains of particles.
You meet the connected particle setup: two objects joined by a light inextensible string passing over a smooth pulley, or two objects in direct contact. Because the string is inextensible, both objects have the SAME acceleration (in magnitude); because the pulley is smooth, the tension is the SAME throughout the string. You analyse each object separately using $F = ma$, getting one equation per object. The two equations together let you solve for both the system's acceleration and the unknown tension. You handle horizontal connected particles, particles on smooth or rough surfaces, and particles connected over a pulley with one hanging and one on a horizontal surface or slope.
Newton's third law and connected particles 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: for connected particles, both have the same acceleration MAGNITUDE but possibly different directions (one might move up while the other moves down) — choose a consistent sign convention; the tension is the same throughout a single string over a smooth pulley, but different strings have different tensions; when the string is about to become taut or slack, the system behaves differently — check these transitions; and weight always points straight down, regardless of the direction of motion.