MOMENT (PHYSICS)

:'''Principle of Moments' redirects here. For the Robert Plant album, see The Principle of Moments. See also Moment (mathematics) for a more abstract concept of moments that evolved from this concept of physics.''

In physics, the 'moment of force' (often just 'moment', though there are other quantities of that name such as moment of inertia) is a 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 to the operation of the lever, pulley, gear, and most other simple machines capable of generating mechanical advantage. The SI unit for moment is the newton meter (Nm).
Moment = Magnitude of Force x Perpendicular distance to the pivot (Fd)

Contents

Overview

Related quantities

History

Overview

In general, the (first) moment 'M' of a vector 'B' is
: $mathbf\{M\_A\}\; =\; mathbf\{r\}\; imes\; mathbf\{B\}\; ,$
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,
: $mathbf\{M\_B\}\; =\; mathbf\{R\}\; imes\; mathbf\{B\}\; +\; sum\_\{i=0\}\{mathbf\{r\_i\}\; imes\; mathbf\{b\_i\}\}\; ,$
where
: $mathbf\{B\}\; =\; sum\_\{i=0\}\{mathbf\{b\_i\}\}\; ,$
or alternatively,
: $mathbf\{M\_B\}\; =\; mathbf\{R\}\; imes\; mathbf\{B\}\; +\; mathbf\{M\_A\}\; ,$

Related quantities

Some notable physical quantities arise from the application of moments:

★ Angular momentum ($L\; =\; I\; omega$ ), the rotational analog of momentum.

★ Moment of inertia ($I\; =\; sum\; m\; r^2$), which is analogous to mass in discussions of rotational motion.

★ Torque ($mathbf\{\; au\}=mathbf\{r\}\; imesmathbf\{F\}$), the rotational analog of force.

★ Magnetic moment ($mathbf\{mu\}=Imathbf\{A\}$), 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. In the lever one applies a force, in his day most often human muscle, to an ''arm'', a 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.