Simpsonville, South Carolina and Moment (physics): Difference between pages
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:''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.''
[[Image:Moment.png|right]]
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)
== Overview ==
In general, the (first) moment '''M''' of a [[vector (spatial)|vector]] '''B''' is
: <math>\mathbf{M_A} = \mathbf{r} \times \mathbf{B} \,</math>
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 (mathematics)|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
: <math>\mathbf{B} = \sum_{i=0}{\mathbf{b_i}} \,</math>
or alternatively,
: <math>\mathbf{M_B} = \mathbf{R} \times \mathbf{B} + \mathbf{M_A} \,</math>
== Related quantities ==
Some notable physical quantities arise from the application of moments:
* [[Angular momentum]] (<math> L = I \omega </math> ), the rotational analog of [[momentum]].
* [[Moment of inertia]] (<math>I = \sum m r^2</math>), which is analogous to [[mass]] in discussions of rotational motion.
* [[Torque]] (''τ = rF''), the rotational analog of [[force]].
* [[Magnetic moment]] (''μ = IA''), a [[dipole]] moment measuring the strength and direction of a magnetic source.
== History ==
The history of torques is very interesting.{{Fact|date=April 2007}} 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.
[[Category:Physical quantity]]
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