--- title: "Motion on a Rough Inclined Plane" description: "Resolve weight along and perpendicular to a slope, include friction in the correct direction, and find the acceleration or the angle at which sliding starts." canonical: https://lightmysky.com/learn/mathematics/motion-on-a-rough-inclined-plane-mt_0rBy66HFNO source: https://lightmysky.com/learn/mathematics/motion-on-a-rough-inclined-plane-mt_0rBy66HFNO.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`. # Motion on a Rough Inclined Plane Resolve weight along and perpendicular to a slope, include friction in the correct direction, and find the acceleration or the angle at which sliding starts. Subject: Mathematics · Area: Mechanics · Ages 17 to 18 Page: https://lightmysky.com/learn/mathematics/motion-on-a-rough-inclined-plane-mt_0rBy66HFNO ## Ready when they can - Resolve the weight into components along and perpendicular to the slope and mark friction's direction - Find the acceleration of a body sliding down a rough slope - Derive the angle of friction at which a body is on the point of slipping ## Lesson: Splitting weight on a slope A slope splits weight into two useful pieces: mg sin theta pulling down the surface and mg cos theta pressing into it. The normal reaction answers that press and sets the friction limit as mu times normal. Friction always fights the slide, so for a block sliding down it points up the slope, and it flips if something drags the block upward. **Example.** A 2 kg block slides with sin 0.6, cos 0.8, mu 0.25 and g 10. The down slope pull per mass is 6 and friction per mass is 2, so acceleration is 4 metres per second squared. A 5 kg block with cos 0.8 has normal reaction 5 times 10 times 0.8, which is 40 N. A 50 N weight with sin 0.6 pulls down the slope with 30 N. The slip angle is the tilt at which a resting block just starts to slide. Balancing along and across the slope at that point gives mu equals tan of the angle, so a 45 degree slip angle means mu equals 1. Tilt your axes along and across the slope, and motion along the surface becomes a single line equation. **Tip.** Draw a free body diagram before any algebra: one arrow per force, all starting at the block. Choose friction direction only after naming the motion or impending motion, never before. **Recap.** Split weight with sin and cos, oppose friction to the motion, and read mu off the slip angle. ## Practice 14 questions on this page, each with its working shown. ## Needs first - [Solving Trigonometric Equations in a Given Interval](https://lightmysky.com/learn/mathematics/solving-trigonometric-equations-in-a-given-interval-mt_74_jiK2xXA) - [Friction and the Coefficient of Friction](https://lightmysky.com/learn/mathematics/friction-and-the-coefficient-of-friction-mt_EwFUd9N24W) - [Newton's Second Law in Two Dimensions](https://lightmysky.com/learn/mathematics/newtons-second-law-in-two-dimensions-mt_yNUFF3lxlj)