Definition:Mass Density
This page is about mass density. For other uses, see density.
Definition
Mass density is a physical quantity.
The mass density of a body is its mass per unit volume.
Mass density is a scalar quantity.
For a homogeneous body it is found by finding its total mass and dividing it by its total volume:
- $\rho = \dfrac m V$
where:
However, if the substance of the body varies throughout, then its mass density may be a function of position within the body.
Symbol
The usual symbol used to denote (mass) density of a body is $\rho$ (Greek letter rho).
Some sources use $d$, but that has so many other uses that it may become confused with other things.
Dimension
The dimension of (mass) density is $\mathsf {M L}^{-3}$: mass per unit volume.
Units
- The SI units of mass density are $\mathrm {kg} \, \mathrm m^{-3}$ (kilograms per cubic metre).
- The CGS units of mass density are $\mathrm g \, \mathrm{cm}^{-3}$ or, less formally: $\mathrm g / \mathrm {cc}$ (grams per cubic centimetre).
- The FPS units of mass density are $\mathrm {lb} \, \mathrm {ft}^{-3}$ (pounds per cubic foot).
Area Mass Density
The area mass density of a two-dimensional body is its mass per unit area.
Linear Mass Density
The linear mass density of a one-dimensional body is its mass per unit length.
Also known as
Mass density is usually known just as density, but there are multiple usages for that term.
If it is necessary to distinguish between mass density, area mass density and linear mass density, the term volumetric mass density can be used.
$\mathsf{Pr} \infty \mathsf{fWiki}$ will generally use the unadorned term density in its exposition unless there is cause for confusion.
Also see
- Results about mass density can be found here.
Sources
- 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Definitions: $1$. Scalar and vector quantities
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $1$. Scalar and Vector Quantities
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): density: 1.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): scalar quantity
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): density: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): scalar quantity
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- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): density