--- title: "Vectors, Scalars and Free-Body Diagrams" description: "Sorting quantities into scalars, which carry only a size, and vectors, which carry a direction too. Every force on one object is then drawn as an arrow whose length is its size, and the resultant is r" canonical: https://lightmysky.com/learn/science/vectors-scalars-and-free-body-diagrams-mt_erzORFj2-1 source: https://lightmysky.com/learn/science/vectors-scalars-and-free-body-diagrams-mt_erzORFj2-1.md retrieved: 2026-11-12 --- > **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`. # Vectors, Scalars and Free-Body Diagrams Sorting quantities into scalars, which carry only a size, and vectors, which carry a direction too. Every force on one object is then drawn as an arrow whose length is its size, and the resultant is read off the diagram. Subject: Science · Area: Forces & Motion · Ages 14 to 15 Page: https://lightmysky.com/learn/science/vectors-scalars-and-free-body-diagrams-mt_erzORFj2-1 ## Ready when they can - Sorts distance, speed and mass from displacement, velocity, force and weight, saying which need a direction - Draws a free-body diagram for a hanging lamp, a towed sledge and a falling ball, with arrows to scale - Finds the resultant of two forces along one line, and of two forces at right angles by scale drawing ## Lesson: Arrows that push and pull Scalars have a size but no direction. Distance, speed and mass are scalars. Vectors have size and direction: displacement, velocity, force and weight. Distance counts the whole path. Displacement describes the change from start to finish, including direction. Velocity gives speed and direction. A force is a push or pull with size and direction. Friction and tension act through contact; weight is the force of gravity. Only the combined force, called the resultant, determines the change in motion. Equal opposite forces cancel, leaving motion unchanged. **Example.** For a point-model free-body diagram, draw one dot for the chosen object. Draw each external force from it at one scale and label its source. Keep the resultant separate. A still lamp has tension up and weight down. A horizontally towed sledge has weight down, ground support up, tow force forward and friction backward when present. A falling ball has weight down and air resistance up when relevant. Along one line, choose a positive direction. Add same-direction forces and subtract opposing forces. A pull of 11 N forward opposed by 6 N leaves 5 N forward. The number line shows these signed force additions, not distances travelled. Equal opposite forces give zero. **Example.** For perpendicular forces, draw them head to tail using a ruler, at a right angle and one scale. At 1 cm for 2 N, draw 6 N east as 3 cm, then 8 N north as 4 cm from its tip. The resultant joins the first tail to the last tip: 5 cm represents 10 N. The arrows and resultant form a right triangle. Squaring means multiplying a number by itself; a square root undoes this. For perpendicular forces only, R = square root of (6² + 8²) = square root of 100 = 10 N. **Recap.** Sort scalars from vectors, draw every force as a scaled arrow, then read the resultant. *Lesson, questions and flashcards written for this dataset.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Resultant Forces](https://lightmysky.com/learn/science/resultant-forces-mt_AiWlJfvC3O) - [Investigating Forces](https://lightmysky.com/learn/science/investigating-forces-mt_xkn2sf93WJ) ## Opens up - [Acceleration from Velocity-Time Graphs](https://lightmysky.com/learn/science/acceleration-from-velocity-time-graphs-mt_nmvfbSgnOn) - [Resolving Vectors into Components](https://lightmysky.com/learn/science/resolving-vectors-into-components-mt_tc698unGJG)