Moment (physics)

In physics, a moment is an expression involving the product of a distance and a physical quantity, and in this way it accounts for how the physical quantity is located or arranged. Moments are usually defined with respect to a fixed reference point; they deal with physical quantities as measured at some distance from that reference point. For example, the moment of force acting on an object, often called torque, is the product of the force and the distance from a reference point. In principle, any physical quantity can be multiplied by distance to produce a moment; commonly used quantities include forces, masses, and electric charge distributions.

In its most simple and basic form, a moment is the product of the distance to some point, raised to some power, multiplied by some physical quantity such as the force, charge, etc. at that point:

where ${\displaystyle Q}$ is the physical quantity such as a force applied at a point, or a point charge, or a point mass, etc. If the quantity is not concentrated solely at a single point, the moment is the integral of that quantity's density over space:

where ${\displaystyle \rho }$ is the distribution of the density of charge, mass, or whatever quantity is being considered.

More complex forms take into account the angular relationships between the distance and the physical quantity, but the above equations capture the essential feature of a moment, namely the existence of an underlying ${\displaystyle r^{n}\,\rho (r)}$ or equivalent term. This implies that there are multiple moments (one for each value of n) and that the moment generally depends on the reference point from which the distance ${\displaystyle r}$ is measured, although for certain moments (technically, the lowest non-zero moment) this dependence vanishes and the moment becomes independent of the reference point.

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