# Moment (physics)

This article needs attention from an expert in Physics. (December 2007) |

In physics, the **moment of force** (often just **moment**, though there are other quantities of that name such as moment of inertia) is a pseudovector quantity that represents the magnitude of force applied to a rotational system at a distance from the axis of rotation. The concept of the **moment arm**, this characteristic distance, is key modelling the operation of the lever, pulley, gear, and most other simple machines involving a mechanical advantage. The SI unit for moment is the newton meter (Nm).

Moment = Magnitude of Force × Force arm [the perpendicular distance to the pivot (Fd)]

## Contents

## Overview

In general, the (first) moment **M** of a vector **B** is

where

**r**is the position where quantity**B**is applied.- × represents the cross product of the vectors.

If **r** is a vector relative to point *A*, then the moment is the "moment **M** with respect to the axis that goes through the point *A*", or simply "moment **M** around *A*". If *A* is the origin, one often omits *A* and says simply *moment*.

## Parallel axis theorem

Since the moment is dependent on the given axis, the moment expression possess a common y,

where

or alternatively,

## Principle of Moments

The Principle of Moments, also known as Varignon's Theorem states that the moment of a force is equal to the sum of the components of that force. This allows resolution of a moment into its component moments to solve more complex problems.

## Related quantities

Some notable physical quantities arise from the application of moments:

- Angular momentum ( ), the rotational analog of momentum.
- Moment of inertia (), which is analogous to mass in discussions of rotational motion.
- Magnetic moment (), a dipole moment measuring the strength and direction of a magnetic source.

## History

The principle of moments is derived from Archimedes' discovery of the operating principle of the lever^{[citation needed]}. In the lever one applies a force (in his day most often human muscle), to an *arm* beam of some sort. Archimedes noted that the amount of force applied to the object, the *moment of force*, is defined as *M = rF*, where *F* is the applied force, and *r* is the distance from the applied force to object.

## See also

bg:Момент на сила ca:Moment de força cs:Moment síly de:Moment (Physik) el:Ροπή eo:momanto (fiziko) nl:moment (mechanica) no:Moment (fysikk) sl:Navor fi:Momentti sv:Moment th:โมเมนต์

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