---
title: "Equilibrium and Newton's First Law"
description: "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."
canonical: https://lightmysky.com/learn/mathematics/equilibrium-and-newtons-first-law-mt_e6RFRQkRPo
source: https://lightmysky.com/learn/mathematics/equilibrium-and-newtons-first-law-mt_e6RFRQkRPo.md
retrieved: 2026-09-12
---

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# Equilibrium and Newton's First Law

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.

Subject: Mathematics · Area: Mechanics · Ages 17 to 18
Page: https://lightmysky.com/learn/mathematics/equilibrium-and-newtons-first-law-mt_e6RFRQkRPo

## Ready when they can

- Show three given forces are in equilibrium by resolving in two directions
- Find the tension in each of two strings holding a hanging mass
- Name every force on a book resting on a table and say what exerts it

## Lesson: Still means balanced

A body with no resultant force keeps doing what it is doing: rest stays rest and steady motion stays steady. Equilibrium means the vector sum of the forces is zero. Test it by resolving in two perpendicular directions: both totals must be zero, so 5 N east cancels 5 N west and leaves any northward push unbalanced.

**Example.** A 6 kg mass hangs at rest from two vertical strings sharing the load equally, with g = 10 N/kg. Its weight is 6 times 10 = 60 N downward. The two tensions add to 60 N upward, so each string pulls 30 N.

Name every force and what exerts it: on a book resting on a table, gravity pulls down from Earth and a normal force pushes up from the table. A puck gliding in a straight line at steady speed has balanced horizontal forces, since steady velocity means zero net force by the first law.

**Tip.** Two forces combine tip to tail: 6 N east and 8 N north give a 10 N resultant, since root (36 + 64) = 10. The balancing third force is 10 N pointing exactly opposite. Equal size, opposite direction, total zero.

**Recap.** Zero resultant means rest or steady motion, so resolve both directions and balance every push.

## Practice

14 questions on this page, each with its working shown.

## Needs first

- [Forces as Vectors: Resolving and Resultants](https://lightmysky.com/learn/mathematics/forces-as-vectors-resolving-and-resultants-mt_-qDRgd2g8v)
- [Proving Geometry Facts with Vectors](https://lightmysky.com/learn/mathematics/proving-geometry-facts-with-vectors-mt_A00MA7Ecgf)

## Opens up

- [Friction and the Coefficient of Friction](https://lightmysky.com/learn/mathematics/friction-and-the-coefficient-of-friction-mt_EwFUd9N24W)
- [Moments and the Equilibrium of a Rigid Body](https://lightmysky.com/learn/mathematics/moments-and-the-equilibrium-of-a-rigid-body-mt_FX5egGL4LI)