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[[Image:Moment.png|right]]
{{đang dịch|ngôn ngữ=tiếng Anh}}
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]].
== Tổng quan ==
In general, the 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.
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 property when the observation axis is changed. If '''M'''<sub>A</sub> is the moment around ''A'', then the moment around the axis that goes through a point ''B'' is
: <math>\mathbf{M_B} = \mathbf{M_A} + \mathbf{R} \times \mathbf{B} \,</math>
where
:'''R''' is the vector from point ''B'' to point ''A''.
This expression is usually referred to as the [[parallel axis theorem]]. For cases when the moment is the sum of individual "submoments", such as in [[rigid body dynamics]] where each particle of the body contribute to a moment, the axis change is the sum of a macroscopic and microscopic quantity,
: <math>\mathbf{M_B} = \mathbf{R} \times \mathbf{B} + \sum_{i=0}{\mathbf{r_i} \times \mathbf{b_i}} \,</math>
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]] (''L = Iω''), which is typically the cause of rotational motion of a body.
* [[Moment of inertia]] (''I = mω×r''), which is analogous to [[mass]] in discussions of rotational motion.
* [[Torque]] (''τ = rF''), which is a [[force]] applied on a position of a body. When no net torque is applied, angular momentum is conserved.
== Lịch sử ==
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.
==Xem thêm==
* [[mô men (toán học)]]
[[Category:Vật lý]]
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