See also moment (mathematics) for a more abstract concept of moments that evolved from this concept of physics.

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. The SI unit for moment is the newton meter (Nm).

Moment = Magnitude of Force x Perpendicular distance to the pivot (Fd)

Overview

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In general, the moment M of a vector B is

$\backslash mathbf\{M\_A\}\; =\; \backslash mathbf\{r\}\; \backslash times\; \backslash mathbf\{B\}\; \backslash ,$;

where

r is the position where quantity B is applied.

× represents the cross product of the vectors.

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

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Since the moment is dependent on the given axis, the moment expression possess a common y,

$\backslash mathbf\{M\_B\}\; =\; \backslash mathbf\{R\}\; \backslash times\; \backslash mathbf\{B\}\; +\; \backslash sum\_\{i=0\}\{\backslash mathbf\{r\_i\}\; \backslash times\; \backslash mathbf\{b\_i\}\}\; \backslash ,$

where

$\backslash mathbf\{B\}\; =\; \backslash sum\_\{i=0\}\{\backslash mathbf\{b\_i\}\}\; \backslash ,$

or alternatively,

$\backslash mathbf\{M\_B\}\; =\; \backslash mathbf\{R\}\; \backslash times\; \backslash mathbf\{B\}\; +\; \backslash mathbf\{M\_A\}\; \backslash ,$

Related quantities

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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.

History

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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.

References

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Physical quantity

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