SI units and derivations SIUnitsAndDerivations 2007-07-01 06:55:14 2007-07-01 14:04:08 Topic \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{psfrag} \usepackage{graphicx} \usepackage{amsthm} \usepackage{xypic} The seven SI base units are given in the table below. These units are assumed to be independent of each other. \begin{center} \begin{tabular}{|c||c|c|} \hline \textbf{base quantity} & \textbf{SI base unit} & \textbf{symbol} \\ \hline \hline length & meter & $\mathrm{m}$ \\ \hline mass & kilogram & $\mathrm{kg}$ \\ \hline time & second & $\mathrm{s}$ \\ \hline current & ampere & $\mathrm{A}$ \\ \hline temperature & Kelvin & $\mathrm{K}$ \\ \hline amount of substance & mole & $\mathrm{mol}$ \\ \hline intensity & candela & $\mathrm{cd}$ \\ \hline \end{tabular} \end{center} There are many quantities that can be measured using units that are derived from the base units. Some of these are written in terms of the base units. Some examples are given in the table below. \begin{center} \begin{tabular}{|c||c|c|} \hline \textbf{quantity} & \textbf{SI derived unit} & \textbf{symbol} \\ \hline \hline area & square meter & $\mathrm{m^2}$ \\ \hline volume & cubic meter & $\mathrm{m^3}$ \\ \hline speed, velocity & meter per second & $\mathrm{m/s}$ \\ \hline acceleration & meter per second squared & $\mathrm{m/s^2}$ \\ \hline density & kilogram per cubic meter & $\mathrm{kg/m^3}$ \\ \hline specific volume & cubic meter per kilogram & $\mathrm{m^3/kg}$ \\ \hline concentration & mole per cubic meter & $\mathrm{mol/m^3}$ \\ \hline wave number & reciprocal meter & $\mathrm{m^{-1}}$ \\ \hline current density & ampere per square meter & $\mathrm{A/m^2}$ \\ \hline magnetic field strength & ampere per cubic meter & $\mathrm{A/m^3}$ \\ \hline luminance & candela per square meter & $\mathrm{cd/m^2}$ \\ \hline \end{tabular} \end{center} Other derived units have their own names. Some examples are given in the table below. \begin{center} \begin{tabular}{|c||c|c|c|} \hline \textbf{quantity} & \textbf{SI unit} & \textbf{symbol} & \textbf{derivation from other SI units} \\ \hline \hline volume & liter & $\mathrm{L}$ or $\mathrm{\ell}$ & $\mathrm{10^{-3}m^3}$ \\ \hline plane angle & radian & $\mathrm{rad}$ & \\ \hline solid angle & steradian & $\mathrm{sr}$ & \\ \hline frequency & hertz & $\mathrm{Hz}$ & $\mathrm{s^{-1}}$ \\ \hline force & newton & $\mathrm{N}$ & $\mathrm{kg \cdot m/s^2}$ \\ \hline pressure, stress & pascal & $\mathrm{Pa}$ & $\mathrm{N/m^2}$ \\ \hline energy, work & joule & $\mathrm{J}$ & $\mathrm{N \cdot m}$ \\ \hline power & watt & $\mathrm{W}$ & $\mathrm{J/s}$ \\ \hline charge & coulomb & $\mathrm{C}$ & $\mathrm{A \cdot s}$ \\ \hline potential difference & volt & $\mathrm{V}$ & $\mathrm{W/A}$ \\ \hline resistance & ohm & $\mathrm{\Omega}$ & $\mathrm{V/A}$ \\ \hline temperature & degree Celsius & $\mathrm{{}^{\circ}C}$ & $\mathrm{K}+273.15$ \\ \hline \end{tabular} \end{center} Reference: National Institute of Standards and Technology, \PMlinkexternal{http://physics.nist.gov/cuu/Units/}{http://physics.nist.gov/cuu/Units/}