---
title: "Moments, Couples and the Conditions for Equilibrium"
description: "A rigid body is in equilibrium when the resultant force is zero and the total moment about any point is also zero. A couple is the special case with no resultant force at all, only a turning effect."
canonical: https://lightmysky.com/learn/science/moments-couples-and-the-conditions-for-equilibrium-mt_EDsdTZ0BNO
source: https://lightmysky.com/learn/science/moments-couples-and-the-conditions-for-equilibrium-mt_EDsdTZ0BNO.md
retrieved: 2026-09-12
---

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# Moments, Couples and the Conditions for Equilibrium

A rigid body is in equilibrium when the resultant force is zero and the total moment about any point is also zero. A couple is the special case with no resultant force at all, only a turning effect.

Subject: Science · Area: Forces & Motion · Ages 16 to 17
Page: https://lightmysky.com/learn/science/moments-couples-and-the-conditions-for-equilibrium-mt_EDsdTZ0BNO

## Ready when they can

- Takes moments about a chosen point to find an unknown support force on a loaded beam
- Shows the answer is the same whichever point is chosen, and picks the point that removes an unknown
- Separates a couple from a single force and gives its moment as one force times the separation

## Lesson: Turning forces and staying balanced

A moment measures how hard a force turns something. Multiply the force by the perpendicular distance from the pivot. The unit is the newton metre.

**Example.** A plank rests on a support at each end while a person stands off centre. Take moments about the left support so its force drops out, then set clockwise moments equal to anticlockwise moments to find the right support force.

You get the same answer whichever point you choose as the pivot. Choose the point where an unknown force acts, because its distance is zero and it vanishes from the maths.

**Tip.** A couple is two equal and opposite parallel forces with a gap between them. Its moment is one force times the gap, and it turns with no overall push. A body balances only when the resultant force is zero and the total moment is zero too.

**Recap.** Zero push plus zero turning means balance, and each moment comes from force times distance.

## Practice

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

## Needs first

- [Moments, Pressure & Hooke's Law](https://lightmysky.com/learn/science/moments-pressure-and-hookes-law-mt_vuNjYx3qOy)

## Opens up

- [Rotational Dynamics and Rolling Without Slipping](https://lightmysky.com/learn/science/rotational-dynamics-and-rolling-without-slipping-mt_1mV6ukwDxK)
- [Work Done by a Force at an Angle](https://lightmysky.com/learn/science/work-done-by-a-force-at-an-angle-mt_OvBtur6dW5)