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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.
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. 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 ?
No base shall be run, or run scored, when a fair ball has been caught, or momentarily held before touching the ground, unless the base held when the ball was hit is re-touched by the base-runner after the ball has been so caught or held by the fielder.
The euro momentarily sank to 115.55 yen, the lowest in New York since August 2002.
Pause momentarily in the mid-range pike position, and then return under control to the starting position.
Each is poised at a distinct angle, focused on a discrete wave ahead or behind, a swell coming or passed, one momentarily kissing the chin of the moon.
Dining spins of actual hard-boiled eggs at 1,800 rpm, the researchers saw gaps momentarily appear beneath the eggs.
One had to perpetually reorient one's body in order to ascertain which projection linked up (momentarily) with the spoken words on the sound track; screens went suddenly blank; narratives were interrupted and new ones begun midstream.
Now, edited and carefully annotated by two modern historians, one of whom is his great-grandson, his story amazes, engages, and provides rare insight into a momentarily lighter side of the Civil War.
This resulted from the switchover from one component to the other, which caused the flow front to hesitate or stop momentarily. In 1972 Battenfeld developed a simultaneous multi-injection approach using a two-channel nozzle that addressed this issue and helped to eliminate part surface defects and obtain better distribution of the core material within the part.
Saleem Golam shone on Langford in this nail-biting finish, picking up his whip, putting it down when his mount momentarily threatened to hang, and then producing it again late on to see the job through at the main expense of Robert Winston and Frankie Dettori.
Patrols are also called out to a large number of accidents where holidaymakers have momentarily forgotten which country they are in and have driven on the wrong side of the road.
Momentarily heartened by the caption: 'We apologise for the lack of sound and/or vision, this is for legal reasons' I imagined the person responsible for this slurry had been arrested.
The pace decelerates momentarily for another wonderful male solo, this time with the dancer's undulating torso held parallel to the floor but pushing forward with unyielding grace.