(redirected from Moments)
Also found in: Dictionary, Thesaurus, Medical, Legal, Idioms.


in physics and engineering, term designating the product of a quantity and a distance (or some power of the distance) to some point associated with that quantity. The most theoretically useful moments are moments of masses, areas, lines, and forces, including magnetic force. The concept of torque (propensity to turn about a point) is the moment of force. If a force tends to rotate a body about some point, then the moment, or turning effect, is the product of the force and the distance from the point to the direction of the force. The application of this concept is illustrated by pushing open a door: the farther from the hinge the push is applied, the less force is required. The principle of the moment of a force is perhaps best seen in the use of a leverlever,
simple machine consisting of a bar supported at some stationary point along its length and used to overcome resistance at a second point by application of force at a third point. The stationary point of a lever is known as its fulcrum.
..... Click the link for more information.
. Extensions of this concept are important in mechanics, in topics such as inertia, center of gravity, equilibrium, and stability of structures, and in architectural problems. The moment of inertia of a body about a point is the sum, for each particle in the body, of the mass of the particle and the square of its distance from the point. The angular momentum of a body about a fixed axis is equal to the product of the momentum and the length of the moment arm (distance from the body to the axis). A torque acting on a rigid body acts to change its angular momentum by producing an angular acceleration.



a mathematical concept that plays an important role in mechanics and probability theory. If we have a system of point masses m1, m2, … (mi > 0) lying on a line and if their abscissas with respect to some origin O are equal to x1, x2, …, respectively, then the sum

x1km1 + x2km2 + … = Σ ixikmi

is called the kth order moment of the system about the point O. In mechanics the first-order moment is called the static moment and the second-order moment is called the moment of inertia. If in the expression for the moment all the abscissas are replaced by their absolute values, a quantity called the absolute moment is obtained. The point with abscissa (Σiximi)/(Σimi) is called the center of mass of a given system of masses. Moments computed about the center of mass are called central moments. The central, first-order moment for any system is equal to zero. Of all the moments of inertia, the central moment of inertia is the smallest. Chebyshev’s inequality states that the sum of the masses located at a distance greater than a from the point O does not exceed the system’s moment of inertia with respect to O divided by a2. If a mass distribution has a density f(x) ≧ 0, then the integral

is called the moment of order k, provided that it is absolutely convergent. In the case of an arbitrary mass distribution, the sums in the expressions for the moments are replaced by Stieltjes integrals; the Stieltjes integral first arose in this way. All the definitions and theorems mentioned above remain valid in this case.

In probability theory, the different possible values of a random quantity play the role of abscissas, and the corresponding probabilities take the place of the masses. The first-order moment is called the mathematical expectation value of the given random quantity, and the central, second-order moment is called its dispersion. The first-order moment is always the abscissa of the center, since the total mass is unity. Chebyshev’s inequality, referred to above, plays an extremely important role in probability theory. In mathematical statistics, moments usually function as basic, statistical quantities summarizing the characteristics of distributions.

The problem in mathematical analysis of the characterization of the properties of a function f(x) by the properties of the sequence of its moments

is called the problem of moments. This problem was first considered by P. L. Chebyshev in 1874 in connection with his studies in probability theory (the attempt to prove the central limit theorem). Later, powerful new methods of mathematical analysis were developed in the investigation of this problem.


Chebyshev, P. L. Izbr. trudy. Moscow, 1955.
Markov, A. A. Izbr. trudy. Moscow, 1951.
Gnedenko, B. V. Kurs teorii veroiatnostei, 5th ed. Moscow, 1969.
Loève, M. Teoriia veroiatnostei. Moscow, 1962. (Translated from English.)


Static moment of some quantity, except in the term “moment of inertia.”
The n th moment of a distribution ƒ(x) about a point x0 is the expected value of (x - x0) n , that is, the integral of (x - x0) n d ƒ(x), where d ƒ(x) is the probability of some quantity's occurrence; the first moment is the mean of the distribution, while the variance may be found in terms of the first and second moments.


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.


a. a tendency to produce motion, esp rotation about a point or axis
b. the product of a physical quantity, such as force or mass, and its distance from a fixed reference point
References in periodicals archive ?
So the meetings began with stories of the organization's early days and galvanizing moments that shaped its culture.
Among the shortlisted moments are John Lennon's death.
For in the richness of the moment, both conditions are true.
The terror of the modern moment allowed Wright, as Joseph Bodziock puts it, "to bore into the white American psyche and find the anxieties and terrors that dwelled there.
At the moment the members look over their shoulder at each other, allowing the Tokyo players into the Club but desperately needing to be challenged by newcomers.
The search for an electric dipole moment (EDM) of the neutron is perhaps unique in modern physics in that experimental work on this subject has been going on more or less continuously for over 50 years.
Natasha Kaplinsky and Brendan Cole's win in Strictly Come Dancing won Best Entertainment Moment, against Greg Dyke chairing Have I Got News For You?
Elsewhere, news reader Natasha Kaplinsky and dancer Brendan Cole's victory on hit show Strictly Come Dancing won the award for Best Entertainment Moment.
Kelly also won the Best Sport moment, beating Maria Sharapova's Wimbledon glory and Matthew Pinsent's Olympic rowing heroics.
Consider the Mass as meal: bread and wine, stories and prayers, comment and counsel, songs and silences, meditation and murmuring, arrivals and departures, children and elders, sitting and standing--and the guest of honor arriving suddenly in the midst of us in the middle of the meal, there in the bread and the wine, the miracle of the moment.
And unlike Ryan McGinley, whose photographs document a dream of youth freely exposing itself in moments as innocent as nature, Kern exposes the economics and artifice of every situation.
The BBC drew up shortlists of top 10 moments in seven categories which were narrowed down to four by viewing panels.