# Moment (physics)

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Not to be confused with Momentum.
For the mathematical concept, see Moment (mathematics). For the moment of a force, see Torque.

In physics, moment is a tendency to produce motion, especially, a rotation about a point or axis. Moment is about a physically measurable quantity in relation to a reference point. It is the product of a physical quantity, such as mass or force, and the distance of the body or point, for which such physical quantity pertains, from a fixed reference point.

## Elaboration

Moment is frequently used in combination with other physical quantities, as in moment of inertia, moment of force, moment of momentum, magnetic moment and so on. For example, in engineering and kinesiology the term moment is often used instead of the more complete term moment of force. A moment of force is the product of the distance of a force from an axis times the magnitude of the force, i.e., F × d, where F is the magnitude of the force and d is the distance of the force. See torque for a more complete description of moments of force or couple for the related concept free moment of force also known as a force couple.

It may also be used when the distance is squared, as in moment of inertia. The moment of inertia is the "second moment" of mass of a physical object. This is the object's resistance or inertia to changes in its angular motion. It is roughly the sum of the squared distances (i.e., moments) of the object's mass particles about a particular axis $(I = \int r^2 dm)$.

## History

The concept of moment in physics is derived from the mathematical concept of moments.[1][clarification needed]. 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.[2] However, historical evolution of the term 'moment' and its use in different branches of science, such as mathematics, physics and engineering, is unclear.

## See also

• Mechanical equilibrium – applies when an object is balanced so that the sum of the clockwise moments about a pivot is equal to the sum of the anticlockwise moments about the same pivot
• Moment of force – see also the article couple (mechanics)
• Moment of inertia$(I = \Sigma m r^2)$ is analogous to mass in discussions of rotational motion. It is a measure of an object's resistance to changes in its rotation rate
• Moment of momentum$(\mathbf{L} = \mathbf{r} \times m\mathbf{v})$ is the rotational analog of linear momentum.
• Magnetic moment$(\mathbf{\mu}=I\mathbf{A})$ is a dipole moment measuring the strength and direction of a magnetic source.
• Electric dipole moment – a dipole moment measuring the charge difference and direction between two or more charges. For example, the electric dipole moment between a charge of –q and q separated by a distance of d is $(\mathbf{p}=q \mathbf{d})$
• Torque or moment, the tendency of a force to rotate an object about an axis
• Bending moment, a moment that results in the bending of a structural element
• First moment of area, a property of an object related to its resistance to shear stress
• Second moment of area, a property of an object related to its resistance to bending and deflection
• Polar moment of inertia, a property of an object related to its resistance to torsion
• Image moments, statistical properties of an image
• Seismic moment, quantity used to measure the size of an earthquake
• Plasma moments, fluid description of plasma in terms of density, velocity and pressure
• List of area moments of inertia
• List of moments of inertia

## References

1. ^ Robertson, D.G.E.; Caldwell, G.E.; Hamill, J.; Kamen, G.; and Whittlesey, S.N. (2004) Research Methods in Biomechanics. Champaign, IL:Human Kinetics Publ., p. 285.
2. ^ simple.wikipedia.org/wiki/Moment_(physics)