Definition:Density (Physics)
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Definition
Density is a physical quantity.
The density of a body is its mass per unit volume.
For a homogeneous body it is found by finding its total mass and dividing it by its total volume.
However, if the substance of the body varies throughout, then its density may be a function of position within the body.
The usual symbol used to denote density is $\rho$ (Greek letter rho).
Dimension of Density
The dimension of density is $M L^{-3}$: mass per unit volume.
Units of Density
- The SI units of density are $\mathrm {kg} \ \mathrm m^{-3}$ (kilograms per cubic metre).
- The CGS units of density are $\mathrm g \ \mathrm{cm}^{-3}$ or, less formally: $\mathrm g / \mathrm {cc}$ (grams per cubic centimetre).
Thus:
- $1 \ \mathrm g \ \mathrm {cm}^{-3} = 1000 \ \mathrm {kg} \ \mathrm m^{-3}$
Area Density
The area density of a two-dimensional body is its mass per unit area.
The usual symbol used to denote area density is $\rho_A$, although some sources simply use $\rho$ if the context makes it clear that it refers to area density rather than volume density.
Occasionally, $\sigma$ (Greek letter sigma) is also used, but this is more commonly used for surface charge density.
Dimension of Area Density
The dimension of area density is $M L^{-2}$: mass per unit area.
Units of Area Density
- The SI units of area density are $\mathrm {kg} \ \mathrm m^{-2}$ (kilograms per square metre).
- The CGS units of density are $\mathrm g \ \mathrm{cm}^{-2}$ (grams per square centimetre).
Thus:
- $1 \ \mathrm g \ \mathrm{cm}^{-2} = 10 \ \mathrm{kg} \ \mathrm m^{-2}$
Linear Density
The linear density of a one-dimensional body is its mass per unit length.
The usual symbol used to denote linear density is $\mu$ (Greek letter mu).
Sometimes $\lambda$ (Greek letter lambda) is also used.
Dimension of Linear Density
The dimension of linear density is $M L^{-1}$: mass per unit length.
Units of Linear Density
- The CGS units of density are $\mathrm g \ \mathrm{cm}^{-1}$ (grams per centimetre).
Thus:
- $1 \ \mathrm{kg} \ \mathrm m^{-1} = 10 \ \mathrm g \ \mathrm{cm}^{-1}$
Also see
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- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: density
