--- title: "Mechanics" description: "14 topics in Mathematics, in the order they build on each other." canonical: https://lightmysky.com/learn/mathematics/areas/mechanics source: https://lightmysky.com/learn/mathematics/areas/mechanics.md retrieved: 2026-09-02 --- > **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`. # Mechanics 14 topics in Mathematics, in the order they build on each other. Page: https://lightmysky.com/learn/mathematics/areas/mechanics - [Modelling Motion in a Straight Line](https://lightmysky.com/learn/mathematics/modelling-motion-in-a-straight-line-mt_no78_6w1rS): Set up a motion problem before calculating anything: choose which direction counts as positive, treat the object as a particle, and keep displacement, velocity and acceleration apart from distance, speed and everyday words like slowing down. - [Motion Graphs: Gradients and Areas](https://lightmysky.com/learn/mathematics/motion-graphs-gradients-and-areas-mt_KhJeCMYBSL): Read the gradient of a displacement-time graph as velocity and the area under a velocity-time graph as displacement, and describe a whole journey from the shape of the graph alone. - [The Constant-Acceleration Equations](https://lightmysky.com/learn/mathematics/the-constant-acceleration-equations-mt_Nyc3BcikQ9): Derive the five constant-acceleration equations from a straight-line velocity-time graph, then choose the one that uses the three quantities you know and gives the one you want. - [Vertical Motion Under Gravity](https://lightmysky.com/learn/mathematics/vertical-motion-under-gravity-mt_IgNj9bn14O): Apply the constant-acceleration equations to an object thrown or dropped, taking the acceleration as g downwards and keeping one sign convention for the whole solution. - [Kinematics with Calculus](https://lightmysky.com/learn/mathematics/kinematics-with-calculus-mt_2kNspOOoDw): When the acceleration is not constant, differentiate displacement to get velocity and velocity to get acceleration, and integrate back the other way, using an initial condition to fix each constant. - [Forces as Vectors: Resolving and Resultants](https://lightmysky.com/learn/mathematics/forces-as-vectors-resolving-and-resultants-mt_-qDRgd2g8v): Draw every force acting on a body as an arrow, add them as vectors to get the resultant, and split any force into components along two perpendicular directions of your choosing. - [Equilibrium and Newton's First Law](https://lightmysky.com/learn/mathematics/equilibrium-and-newtons-first-law-mt_e6RFRQkRPo): A body with no resultant force stays still or keeps a constant velocity. Setting the components in two perpendicular directions to zero turns that into equations that find unknown forces. - [Moments and the Equilibrium of a Rigid Body](https://lightmysky.com/learn/mathematics/moments-and-the-equilibrium-of-a-rigid-body-mt_FX5egGL4LI): Measure the turning effect of a force as force times perpendicular distance from a point, and solve a beam problem by setting both the total force and the total moment to zero. - [Newton's Second Law: Force, Mass and Acceleration](https://lightmysky.com/learn/mathematics/newtons-second-law-force-mass-and-acceleration-mt_SKO85AcKdb): A resultant force gives an acceleration in its own direction, with F = ma. Weight is mass times g, which is why objects of different mass fall together. - [Friction and the Coefficient of Friction](https://lightmysky.com/learn/mathematics/friction-and-the-coefficient-of-friction-mt_EwFUd9N24W): Model friction as a force bounded by the coefficient times the normal reaction, and decide whether a body stays put or slides. - [Newton's Second Law in Two Dimensions](https://lightmysky.com/learn/mathematics/newtons-second-law-in-two-dimensions-mt_yNUFF3lxlj): Resolve the forces along the direction of motion and perpendicular to it, then apply F = ma along that direction while the perpendicular components balance. This is what makes a slope problem solvable. - [Connected Particles and Pulleys](https://lightmysky.com/learn/mathematics/connected-particles-and-pulleys-mt_pZ6zV0RFdC): Two bodies joined by a string share one acceleration and pull on each other equally and oppositely. Write F = ma for each body, then solve the two equations together for the acceleration and the tension. - [Motion on a Rough Inclined Plane](https://lightmysky.com/learn/mathematics/motion-on-a-rough-inclined-plane-mt_0rBy66HFNO): 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. - [Projectile Motion](https://lightmysky.com/learn/mathematics/projectile-motion-mt_O1C-QxCSJN): Split the launch velocity into horizontal and vertical parts, then run constant velocity across and constant acceleration downwards, with time as the only quantity the two share. Range, greatest height and flight time follow.