---
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: 2026-09-12
---

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# 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

Some quantities carry only a size. Distance, speed and mass belong in that group, called scalars. Others carry a direction too: displacement, velocity, force and weight. Those are vectors, and sorting each new quantity into its group is your first job.

A force is a push or pull with size and direction that changes motion. Contact forces like friction and tension act through touch, while weight pulls without contact. Forces add as vectors, not plain numbers: two equal opposite pulls cancel to zero.

**Example.** A free-body diagram strips a situation to one dot with arrows. Isolate the object, draw one arrow per force to scale from the same dot, and label each with its source. Practise on a hanging lamp first, where the upward pull balances the weight, then try a towed sledge and a falling ball.

**Tip.** The resultant is the single arrow left after every force has had its say. Along one line, add them allowing for direction, with balanced forces cancelling. For two forces at right angles, set up a scale drawing and read the diagonal, or use Pythagoras with the two forces.

**Recap.** Sort scalars from vectors, draw every force as a scaled arrow, then read the resultant.

## 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)