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. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. This article is about the moment of inertia of a rotating object. In Physics and Mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation but gains an In Physics, a force is whatever can cause an object with Mass to Accelerate. 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. A pulley (also called a sheave or block) is a Wheel with a groove between two Flanges around its Circumference This is the page for mechanical Gears For other uses see Gear (disambiguation For the gear-like device used to drive a roller chain see Sprocket In Physics and Engineering, mechanical advantage (MA is the factor by which a mechanism multiplies the force put into it The SI unit for moment is the newton meter (Nm). Newton metre is the unit of moment ( Torque) in the SI system

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

## Overview

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

$\mathbf{M_A} = \mathbf{r} \times \mathbf{B} \,$

where

r is the position where quantity B is applied.
× represents the cross product of the vectors. In Mathematics, the cross product is a Binary operation on two vectors in a three-dimensional Euclidean space that results in another vector which

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. In Mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference

## Parallel axis theorem

Main article: Parallel axis theorem

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

$\mathbf{M_B} = \mathbf{R} \times \mathbf{B} + \sum_{i=0}{\mathbf{r_i} \times \mathbf{b_i}} \,$

where

$\mathbf{B} = \sum_{i=0}{\mathbf{b_i}} \,$

or alternatively,

$\mathbf{M_B} = \mathbf{R} \times \mathbf{B} + \mathbf{M_A} \,$

## 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. In Physics, the parallel axis theorem can be used to determine the Moment of inertia of a Rigid body about any axis given the moment of inertia of the 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 (L = Iω ), the rotational analog of momentum. In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product
• Moment of inertia ($I = \sum m r^2$), which is analogous to mass in discussions of rotational motion. This article is about the moment of inertia of a rotating object. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object
• Magnetic moment ($\mathbf{\mu}=I\mathbf{A}$), a dipole moment measuring the strength and direction of a magnetic source. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a

## History

The principle of moments is derived from Archimedes' discovery of the operating principle of the lever. Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer 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.