--- title: "The Centre of Mass and the Motion of a System" description: "The centre of mass of any system moves as if all the mass sat there and every external force acted on it, whatever the internal forces do. Internal forces cancel in pairs, which is why an exploding sh" canonical: https://lightmysky.com/learn/science/the-centre-of-mass-and-the-motion-of-a-system-mt_fHO_KrMNKo source: https://lightmysky.com/learn/science/the-centre-of-mass-and-the-motion-of-a-system-mt_fHO_KrMNKo.md retrieved: 2026-09-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # The Centre of Mass and the Motion of a System The centre of mass of any system moves as if all the mass sat there and every external force acted on it, whatever the internal forces do. Internal forces cancel in pairs, which is why an exploding shell keeps its parabola. Subject: Science · Area: Forces & Motion · Ages 19 to 21 Page: https://lightmysky.com/learn/science/the-centre-of-mass-and-the-motion-of-a-system-mt_fHO_KrMNKo ## Ready when they can - Locates the centre of mass of a set of particles and of a simple continuous body by integration - Shows that internal forces cancel and so cannot move the centre of mass - Predicts the path of the centre of mass of a body that breaks apart in flight ## Lesson: The point that moves for the whole crowd The centre of mass is the mass weighted average of every position in the system. For separate lumps you add each mass times its position and divide by the total mass. For smooth bodies that sum becomes an integral over the shape. Symmetry hands out free answers: uniform rods balance at the middle and rings at the empty centre. Total momentum is simply total mass times the velocity of this point. **Example.** Park 2 kg at x = 0 and 4 kg at x = 3: add 0 + 12 and divide by 6 to get x = 2. Inside pushes always cancel in pairs: when two parts shove each other, equal and opposite forces sum to zero. So internal drama leaves total momentum untouched. A trio with 1 kg at 1 and 3 kg at 5 gives (1 + 15) over 4 = 4. Only outside forces can move the centre of mass. With none acting, it cruises at constant velocity. A shell bursts mid flight: shards spray everywhere, but the centre of mass keeps the original parabola. The breakup is internal, so the average path never notices. Explosions, collisions, and separating stages all obey this quiet rule. **Tip.** Take the chaos shortcut: find the special point and track one clean trajectory instead of every fragment. For a bursting firework, draw the smooth arc first, then spray shards around it. Always ask which forces are outside before anything else. **Recap.** Average the mass positions, cancel the inside forces, and let outside forces steer the point. ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Integration as the Reverse of Differentiation](https://lightmysky.com/learn/mathematics/integration-as-the-reverse-of-differentiation-mt_edtk3ArxRk) ## Opens up - [Variable Mass and the Rocket Equation](https://lightmysky.com/learn/science/variable-mass-and-the-rocket-equation-mt_4IugclcEVi) - [The Two-Body Problem, Orbital Energy and Kepler's First Two Laws](https://lightmysky.com/learn/science/the-two-body-problem-orbital-energy-and-keplers-first-two-laws-mt_CjHFftkB6M) - [Coupled Oscillators and Normal Modes](https://lightmysky.com/learn/science/coupled-oscillators-and-normal-modes-mt_vnTGOIqZzP)