---
title: "Moments and the Equilibrium of a Rigid Body"
description: "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."
canonical: https://lightmysky.com/learn/mathematics/moments-and-the-equilibrium-of-a-rigid-body-mt_FX5egGL4LI
source: https://lightmysky.com/learn/mathematics/moments-and-the-equilibrium-of-a-rigid-body-mt_FX5egGL4LI.md
retrieved: 2026-09-12
---

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# Moments and the Equilibrium of a Rigid Body

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.

Subject: Mathematics · Area: Mechanics · Ages 17 to 18
Page: https://lightmysky.com/learn/mathematics/moments-and-the-equilibrium-of-a-rigid-body-mt_FX5egGL4LI

## Ready when they can

- Find the moment of a force about a point using the perpendicular distance
- Find both support reactions on a loaded uniform beam
- Work out how far a load can move along a plank before it tips

## Lesson: Turns must balance too

The turning effect of a force is its moment: force times perpendicular distance from the pivot. A 10 N push at right angles 2 m out gives 10 times 2 = 20 N m. With the force fixed, doubling the distance doubles the moment.

**Example.** A uniform beam 4 m long weighs 40 N and rests on supports at its ends, with a 60 N load at its middle. Total downward load is 40 + 60 = 100 N. Both loads sit centred, so symmetry gives each support 50 N.

A rigid body at rest needs no overall push and no overall twist: resultant force zero and total moment about any point zero. Free body diagrams grow up here to include where each force acts, since the same push twists more from further out.

**Tip.** A uniform 6 m plank weighing 60 N sticks 2 m past a wall edge, so its centre sits 1 m inside with a restoring moment of 60 N m. A 40 N child walking out tips the plank when 40 times d = 60, at d = 1.5 m. At the tipping point the moments match exactly.

**Recap.** Balance every push and every twist, since distance matters as much as force.

## Practice

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

## Needs first

- [Equilibrium and Newton's First Law](https://lightmysky.com/learn/mathematics/equilibrium-and-newtons-first-law-mt_e6RFRQkRPo)
- [Trigonometry basics](https://lightmysky.com/learn/mathematics/trigonometry-basics-mt_KB_Czd7RQH)

## Opens up

- [Triple Integrals and Coordinates for Solids](https://lightmysky.com/learn/mathematics/triple-integrals-and-coordinates-for-solids-mt_RFeK8LD_jT)