moment

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For a random variable X the rth moment (about the origin) is defined to be the expectation of X^r, where r is a non-negative integer. It is usually denoted by μ′_r. So μ′₀=1 and μ′₁=μ, the mean of the distribution of X.

The rth moment about the mean (or central moment or corrected moment) is defined to be the expectation of (X−μ)^r and is usually denoted by μ_r. Thus μ₁=0 and μ₂=σ², the variance of X. The moments about the mean can be expressed as linear combinations of the uncorrected moments, for example:

.

noun

1. A very brief time: crack, flash, instant, minute¹, second¹, trice, twinkle, twinkling, wink. Informal jiff, jiffy. Chiefly British tick. See big/small/amount, time.
2. A particular interval of time that is limited and often crucial: instant, juncture, point. See time.
3. The quality or state of being important: concern, concernment, consequence, import, importance, significance, significancy, weight, weightiness. See important/unimportant.

Idioms beginning with moment:
moment of truth

In addition to the idiom beginning with moment, also see at this point (moment); every minute (moment) counts; for the moment; have one's moments; just a minute (moment); live for the moment; never a dull moment; not for a moment; of the moment; on the spur of the moment; weak moment.

Definition: importance
Antonyms: triviality, unimportance

The property by which a force tends to cause a body, to which it is applied, to rotate about a point or line; equal in magnitude to the product of the force and the perpendicular distance of the point from the line of action of the force.

(DOD, NATO) In air transport, the weight of a load multiplied by its distance from a reference point in the aircraft.

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1. the force exerted by a lever about a fulcrum.
2. statistically, the mean. The first moment is the same as the mean, the second moment is the mean of the square of a variable, and so on.

• Principles of Mechanics, Waves, and Measurement - moment: tendency to produce motion, esp. about an axis; product of physical quantity such as area or mass and its directed distance from axis
• Aviation and Aerodynamics - moment: measure of aircraft’s tendency to produce motion about an axis
• Periods of Time - moment: brief span of time; second, instant

Not to be confused with Momentum (physics).

For a more abstract concept of moments that evolved from this concept of physics, see Moment (mathematics).

Classical mechanics
History of classical mechanics · Timeline of classical mechanics
Branches Statics · Dynamics / Kinetics · Kinematics · Applied mechanics · Celestial mechanics · Continuum mechanics · Statistical mechanics
Formulations Newtonian mechanics (Vectorial mechanics) Analytical mechanics: Lagrangian mechanics Hamiltonian mechanics
Fundamental concepts Space · Time · Velocity · Speed · Mass · Acceleration · Gravity · Force · Impulse · Torque / Moment / Couple · Momentum · Angular momentum · Inertia · Moment of inertia · Reference frame · Energy · Kinetic energy · Potential energy · Mechanical work · Virtual work · D'Alembert's principle
Core topics Rigid body · Rigid body dynamics · Euler's equations (rigid body dynamics) · Motion · Newton's laws of motion · Newton's law of universal gravitation · Euler's laws of motion · Equations of motion · Inertial frame of reference · Non-inertial reference frame · Rotating reference frame · Fictitious force · Linear motion · Mechanics of planar particle motion · Displacement (vector) · Relative velocity · Friction · Simple harmonic motion · Harmonic oscillator · Vibration · Damping · Damping ratio · Rotational motion · Circular motion · Uniform circular motion · Non-uniform circular motion · Centripetal force · Centrifugal force · Centrifugal force (rotating reference frame) · Reactive centrifugal force · Coriolis force · Pendulum · Rotational speed · Angular acceleration · Angular velocity · Angular frequency · Angular displacement
Scientists Galileo Galilei · Isaac Newton · Jeremiah Horrocks · Leonhard Euler · Jean le Rond d'Alembert · Alexis Clairaut · Joseph Louis Lagrange · Pierre-Simon Laplace · William Rowan Hamilton · Siméon Denis Poisson
v t e

In physics, the term moment can refer to many different concepts.

Contents 1 Moment of Force 2 Other definitions 3 External links 4 References

Moment of Force

Moment of force (often just moment) is the tendency of a force to twist or rotate an object; see the article torque for details. A moment is valued mathematically as the product of the force and the moment arm. The moment arm is the perpendicular distance from the point of rotation, to the line of action of the force. The moment may be thought of as a measure of the tendency of the force to cause rotation about an imaginary axis through a point.^[1] (Note: In mechanical and civil engineering, "moment" and "torque" have different meanings, while in physics they are synonyms. See the discussion in the "torque" article, or the article couple (mechanics).)

Image A shows a moment at Point O, when the components are perpendicular to the Point O. Image B and Image C illustrate the components of a Moment at Point O, when the components are not perpendicular to point O.

The moment of a force can be calculated about any point and not just the points in which the line of action of the force is perpendicular. Image A shows the components, the force F, and the moment arm, x when they are perpendicular to one another. When the force is not perpendicular to the point of interest, such as Point O in Images B and C, the magnitude of the Moment, M of a vector F about the point O is

where

is the vector from point O to the position where quantity F is applied.

× represents the cross product of the vectors.^[2]

Image C represents the vector components of the force in Image B. In order to determine the Moment, M of a vector F about the point O, when vector F is not perpendicular to point O, one must resolve the force F, into its horizontal and vertical components. The sum of the moments of the two components of F about the point O is :

M _OF = F * sin (θ) * x + F * cos(θ) * 0

The moment arm to the vertical component of F is a distance x. The moment arm to the horizontal component of F does not exist. There is no rotational force about point O due to the horizontal component of F. Thus, the moment arm distance is zero, or 0.^[1]

Thus M can be referred to as "the moment M with respect to the axis that goes through the point O, or simply "the moment M about point O". If O is the origin, or, informally, if the axis involved is clear from context, one often omits O and says simply moment, rather than moment about O. Therefore, the moment about point O is indeed the cross product,

,

since the cross product = F * x sin (θ)^[1]

When F is the force, the moment of force is the torque as defined above.

Other definitions

• The Principle of moments is if an object is balanced then the sum of the clockwise moments about a pivot is equal to the sum of the anticlockwise moments about the same pivot.
• A pure moment is a special type of moment of force. See the article couple (mechanics).
• Moment of inertia () is analogous to mass in discussions of rotational motion.
• Moment of momentum or angular momentum () is the rotational analog of momentum.
• Magnetic moment () is a dipole moment measuring the strength and direction of a magnetic source.
• Electric dipole moment is a dipole moment measuring the charge difference and direction between two or more charges. For example, the electric dipole moment between a change of -q and q separated by a distance of d is ()

External links

Wikimedia Commons has media related to: Moment (physics)

Look up moment in Wiktionary, the free dictionary.

References

1. ^ ^{a b c} Roberts, Adrian (2003). Statics and Dynamics with a Background in Mathematics. United Kingdom: The Press Syndicate of the University of Cambridge. pp. 1–300. ISBN 0-521-52087-8. http://books.google.com/books?id=DYPWQ-83xr8C&printsec=frontcover&dq=statics#v=onepage&q=moment&f=false. 
2. ^ Hall, A, S; Archer, F,E Gilbert, R,I (2005). Engineering Statics (Second ed.). Sydney, Australia: UNSW Press. pp. 39–227. ISBN 086840425. http://books.google.com/books?id=nsQd5r7J6WkC&printsec=frontcover&dq=statics#v=onepage&q=moment&f=false. Retrieved 2011-03-25. 

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Common misspelling(s) of moment

• moent

Dansk (Danish)
n. - øjeblik

idioms:

• any moment now    hvert øjeblik
• at the moment    i øjeblikket
• for a moment    i et øjeblik
• for the moment    for øjeblikket
• have one's moments    have sine (store) øjeblikke
• of the moment    dagens (mand/kvinde)
• Wait a moment    vent et øjeblik

Nederlands (Dutch)
ogenblik, moment, belang, tijdstip

Français (French)
n. - moment, instant, importance, (Phys) moment

idioms:

• any moment now    d'un moment à l'autre, incessamment
• at any moment    à tout instant
• at the moment    en ce moment, pour l'instant
• at this moment    en ce moment
• for a moment    l'espace d'un instant
• for the moment    pour l'instant
• have one's moments    (fig) avoir ses bons côtés
• in a moment    dans un moment
• not for a moment    pas un seul instant, jamais de la vie (excl)
• of the moment    du moment
• one moment    un instant
• Wait a moment    Attendez un moment/un instant, minute/pas si vite (excl) (d'indignation)

Deutsch (German)
n. - Augenblick, Moment

idioms:

• any moment now    sehr bald
• at any moment    jeden Augenblick od. Moment
• at the moment    zur Zeit
• at this moment    in diesem Moment od. Augenblick
• for a moment    für einen Augenblick
• for the moment    für den Augenblick
• have one's moments    manchmal eindrucksvoll, froh o.ä. sein
• in a moment    im Nu (ugs.), sofort, gleich
• not for a moment    keinen Moment [lang]
• of the moment    des Augenblicks
• one moment    einen Moment od. Augenblick!, Moment[chen] od. Augenblick mal!
• Wait a moment    Moment mal!

Ελληνική (Greek)
n. - (χρονική) στιγμή, σπουδαιότητα, βαρύτητα, (φυσ.) ροπή
int. - μια στιγμή!

idioms:

• any moment now    από στιγμή σε στιγμή
• at the moment    για την ώρα
• for a moment    προς στιγμήν, για λίγο
• for the moment    για την ώρα, προς το παρόν
• have one's moments    έχω τις καλές μου στιγμές
• of the moment    αυτού του καιρού, στην επικαιρότητα
• Wait a moment    Για μια στιγμή!

Italiano (Italian)
momento, istante, rilievo

idioms:

• at the moment    per il momento
• for a moment    per un istante
• for the moment    per il momento
• have one's moments    avere momenti felici
• of the moment    del momento

Português (Portuguese)
n. - momento (m), conseqüência (f), fator essencial (m) (Filos.)
int. - só um momento!

idioms:

• at the moment    neste momento
• for a moment    por um momento
• for the moment    por enquanto
• have one's moments    ter seus momentos
• of the moment    o mais importante do momento

Русский (Russian)
момент, минута, определенное время, важность

idioms:

• at the moment    в данный момент
• for a moment    на минутку
• for the moment    в настоящее время
• have one's moments    испытывать минуты счастья
• of the moment    важный в данный момент времени

Español (Spanish)
n. - momento, instante, oportunidad, importancia

idioms:

• any moment now    en cualquier momento
• at any moment    de un momento a otro
• at the moment    en el momento
• at this moment    en este preciso instante, en este momento
• for a moment    por un momento
• for the moment    por el momento, de momento, por ahora
• have one's moments    tiene sus (buenos) momentos
• in a moment    en un instante, en un momento
• not for a moment    ni por un momento, ni por un instante
• of the moment    del momento
• one moment    un momento, un instante
• Wait a moment    ¡un momento!, ¡momentito!, espere un momento

Svenska (Swedish)
n. - ögonblick, betydelse, moment, beståndsdel
int. - ett ögonblick!

中文（简体）(Chinese (Simplified))
瞬间, 指定时刻, 片刻, 时机

idioms:

• any moment now    任何时候, 随时
• at the moment    现在, 当时
• for a moment    一会儿, 片刻
• for the moment    暂时, 目前
• have one's moments    得意的时刻, 出风头的时刻, 走红的时刻
• of the moment    此刻
• Wait a moment    等一会儿

中文（繁體）(Chinese (Traditional))
n. - 瞬間, 指定時刻, 片刻, 時機

idioms:

• any moment now    任何時候, 隨時
• at the moment    現在, 當時
• for a moment    一會兒, 片刻
• for the moment    暫時, 目前
• have one's moments    得意的時刻, 出風頭的時刻, 走紅的時刻
• of the moment    此刻
• Wait a moment    等一會兒

한국어 (Korean)
n. - 순간, 위기, 중요성, 계기

idioms:

• at the moment    그 순간에, 당장에는
• have one's moments    최고로 행복할 때가 있다

日本語 (Japanese)
n. - 瞬間, 時, 時期, 今, 現在, 運動率, 重要性

idioms:

• at the moment    ちょうど今, ちょうどその時
• for a moment    しばらく, 一瞬たりとも
• for the moment    さしあたり
• have one's moments    最高の時である
• of the moment    目下の

العربيه (Arabic)
‏(الاسم) لحظه, أهميه‏

עברית (Hebrew)
n. - ‮הרף-עין, רגע, נקודת-זמן מדויקת, חשיבות, מומנט, תנופה‬

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