Units

• unit of measurement (or unit of measure, or just unit)

SI units

• International System of Units (SI, from Système international d’unités)
• SI base unit
• SI unit

SI base units

	SI unit	dimension	quantities
$\mathrm{s}$	second	$\mathrm{T}$	time $t$
$\mathrm{m}$	metre	$\mathrm{L}$	length $l,r,x$
$\mathrm{kg}$	kilogram	$\mathrm{M}$	mass $m$
$\mathrm{A}$	ampere	$\mathrm{I}$	electric current $I,i$
$\mathrm{K}$	kelvin	$\mathrm{\Theta }$	thermodynamic temperature $T$
$\mathrm{mol}$	mole	$\mathrm{N}$	amount of substance $n$
$\mathrm{cd}$	candela	$\mathrm{J}$	luminous intensity $I_{\mathrm{v}}$

Other units

Length

• mile (or international mile, statute mile) (מִיל)

  • $1mi.=1609.344\mathrm{m}$
  • nautical mile (מיל ימי)
    • $1\mathrm{NM}=1852\mathrm{m}$
  • geographical mile
    • $\approx 1855.3\mathrm{m}$
  • US survey mile $=1609.347\mathrm{m}$

• light-year (ly)

  • $1\mathrm{ly}\approx 9.4607\times 10^{15}\mathrm{m}$

• angstrom (or ångström)

  • $1\mathring{\mathrm{A}}=10^{-10}\mathrm{m}=0.1\mathrm{nm}=100\mathrm{pm}$

area $A$

${\mathrm{m}}^2$

volume $V$

• ${\mathrm{m}}^3$

Mass

• SI unit: $\mathrm{kg}$
• (gram, gramme) $1\mathrm{g}=10^{-3}\mathrm{kg}$
• (tonne, (in US: metric ton)) $1\mathrm{t}=10^3\mathrm{kg}$
• (short ton, tn, st, US ton, (in US: ton)) $=2000\mathrm{lb}$
• (long ton, imperial ton, displacement ton, British ton) $=2240\mathrm{lb}$
• (pound, pound-mass) $1\mathrm{lb}=0.45359237\mathrm{kg}$
  • also denoted like: $5^{\prime \prime }$ or $5\#$
• Unified atomic mass unit

Energy

• joule $\mathrm{J}$
  • $\mathrm{kg}\cdot {\mathrm{m}}^2\cdot {\mathrm{s}}^{-2}$
• (kilowatt-hour)
  • $1\mathrm{kWh}=3.6\times 10^6\mathrm{J}$
  • the energy consumed by a 1-kilowatt appliance in 1 hour
• (electronvolt)
  • $1\mathrm{eV}=1.6\times 10^{-19}\mathrm{J}$
  • the energy acquired by a particle carrying a charge whose magnitude equals that on the electron as a result of moving through a potential difference of $1\mathsf{V}$

calorie

• in physics/chemistry: small calorie, gram calorie, thermochemical calorie
  • $1\mathrm{cal}=4.184\mathrm{J}$
• in nutrition: large calorie, kilocalorie, Calorie, kilogram calorie
  • $1\mathrm{Cal}=4.184\mathrm{kJ}$ (also $\mathrm{kcal}$)

power

• watt ($\mathrm{W}$)
  • $\mathrm{kg}\cdot {\mathrm{m}}^2\cdot {\mathrm{s}}^{-3}$
• ((imperial) horsepower, HP, BHP (brake horsepower)) $1\mathrm{hp}\approx 745.7\mathsf{W}$
• (metric horsepower, CV, PS) $1\mathrm{hp}\approx 735.5\mathsf{W}\approx 75\mathsf{k}{\mathsf{g}}_{\mathsf{f}}\cdot \mathsf{m}\cdot {\mathsf{s}}^{-1}$

intensity

• ”The intensity (or flux) of radiant energy is the power transferred per unit area, where the area is measured on the plane perpendicular to the direction of propagation of the energy” (Wikipedia)
  • also called: flux
  • $I=\frac{\text{power}}{\text{area}}$
• SI unit: $W/{\mathrm{m}}^2=\mathrm{J}\cdot {\mathrm{s}}^{-1}\cdot {\mathrm{m}}^{-2}$
• quantities with the same dimension:
  • sound intensity
  • irradiance
  • radiant exitance
  • radiosity
  • heat flux
• other meanings of intensity

force

• newton
  • $\mathrm{N}={\mathrm{kg}\cdot \mathrm{m}\cdot \mathrm{s}}^{-2}$
• (kilogram-force) $1\mathrm{k}{\mathrm{g}}_{\mathrm{f}}\approx 9.8\mathsf{N}$
• (pound-force) $1\mathrm{l}{\mathrm{b}}_{\mathrm{f}}\approx 4.4482\mathsf{N}$

torque

• newton-metre
  • $\mathrm{N}\cdot \mathrm{m}$
  • $\mathrm{kg}\cdot {\mathrm{m}}^2\cdot {\mathrm{s}}^{-2}$
• (kilogram-force meter, (קג”מ)) $1\mathrm{k}{\mathrm{g}}_{\mathrm{f}}\cdot \mathrm{m}\approx 9.8\mathsf{N}\cdot \mathsf{m}$
• (pound-force foot) $1\mathrm{l}{\mathrm{b}}_{\mathrm{f}}\cdot \mathrm{ft}\approx 1.3558\mathsf{N}\cdot \mathsf{m}$

velocity

• meter per second: $\mathrm{m}\cdot {\mathrm{s}}^{-1}$

• kilometer per hour ($km/h$)

• mile per hour ($\mathrm{mph}$)

• knot (קֶשֶר)

  • = 1 nautical mile per hour
  • $\mathrm{kn}$, $\mathrm{kt}$

frequency

• frequency $f$

• rotational frequency $\nu$

• hertz ($\mathrm{Hz}$)

  • ${\mathrm{s}}^{-1}$

• revolutions per minute (RPM) (סיבובים לדקה (סל”ד))

  • ($\mathrm{r}\cdot \mathrm{mi}{\mathrm{n}}^{-1}$) $1\mathrm{rpm}=\frac{1}{60}\mathsf{Hz}$

• beats per minute (bpm)

• angular frequency $\omega$

  • SI unit: radian per second ($\mathrm{rad}\cdot {\mathrm{s}}^{-1}$)

decibels

• A power quantity is a physical quantity $X$ that is directly proportional to power: $X\propto P$
  • examples: power, energy density, acoustic intensity
• A root-power quantity (or field quantity) is a physical quantity $X$ whose square is directly proportional to power: $X^2\propto P$ (or $X\propto \sqrt{P}$)
  • examples: voltage, current, sound pressure, electric field strength, speed, or charge density
• bel ($\mathrm{B}$)
• decibel (dB): $1\mathrm{dB}=0.1\mathrm{B}$
• for any power quantities $P$ and $P_0$ (reference):
  • $L_P=10{\log }_{10}\left(\frac{P}{P_0}\right)\mathrm{dB}={\log }_{10}\left(\frac{P}{P_0}\right)\mathrm{B}$
  • $P$ and $P_0$ said to differ by $L_P$ decibels
  • $L_P$ is a power level
  • examples:
    • sound power level
    • sound intensity level
    • decibel watt (dBW): $\text{power}[\mathrm{dBW}]=10{\log }_{10}\frac{\text{power}[\mathrm{W}]}{1\mathrm{W}}$
    • dBm (or dBmW): $\text{power}[\mathrm{dBm}]=10{\log }_{10}\frac{\text{power}[\mathrm{mW}]}{1\mathrm{mW}}$
• for any root-power quantities $F$ and $F_0$ (reference):
  • $L_F=20{\log }_{10}\left(\frac{F}{F_0}\right)\mathrm{dB}=10{\log }_{10}\left(\frac{F^2}{F_0^2}\right)\mathrm{dB}=2{\log }_{10}\left(\frac{F}{F_0}\right)\mathrm{B}$
  • $L_F$ is a root-power level (or field level)
  • examples:
    • sound pressure level
    • decibel volts: $\text{voltage}[\mathrm{dBV}]=20{\log }_{10}\frac{\text{voltage}[\mathrm{V}]}{1\mathrm{V}}$
    • dBu: ${\text{voltage}}_{\text{rms}}[\mathrm{dBu}]=20{\log }_{10}\frac{{\text{voltage}}_{\text{rms}}[\mathrm{V}]}{\sqrt{0.0006}\mathrm{V}}$

Specific quantities

• A specific (or massic) quantity
  • Per unit of mass: “an intensive quantity obtained by dividing an extensive quantity of interest by mass” (Wikipedia)
    • specific activity
    • specific energy
    • specific enthalpy
  • Per unit of other types:
    • specific gravity
    • specific capacity