Physical Quantities and Their Units

Angular momentum

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Orbital angular momentum and velocity of a mass during a circular motion

Symbol: $L$
Unit of angular momentum: $\mathrm{Js}$ (Joule second)
Example: $ L ~=~ 10^{-34} \, \mathrm{Js} $ is the magnitude of the orbital angular momentum of an electron in the atom.

$$ \begin{align} \mathrm{Js} ~=~ \mathrm{Nm}\,\mathrm{s} ~=~ \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{s} } \end{align} $$

Energy

Symbol: $W$
Unit of energy: $\mathrm{J}$ (Joule)
Example: $ W ~=~ 30 \, 000 \, 000 \, \mathrm{J} $ is the energy released when one kilogram of coal is burned.

$$ \begin{align} \mathrm{J} ~=~ \mathrm{Nm} ~=~ \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{s}^2 } \end{align} $$

Power

Symbol: $P$
Unit of power: $\mathrm{W}$ (Watt)
Example: $ P ~=~ 2000 \, \mathrm{W} $ is the power of a kettle.

$$ \begin{align} \mathrm{W} ~=~ \frac{ \mathrm{J} }{ \mathrm{s} } ~=~ \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{s}^3 } \end{align} $$

Pressure

Symbol: $\mathit{\Pi}$
Unit of pressure: $\mathrm{Pa}$ (Pascal)
Example: $ \mathit{\Pi} ~=~ 100 \, 000 \, \mathrm{Pa} $ is the air pressure of the earth's atmosphere.

$$ \begin{align} \mathrm{Pa} ~=~ \frac{ \mathrm{N} }{ \mathrm{m}^2 } ~=~ \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{s}^2 } \end{align} $$

Charge

Symbol: $Q$
Unit of charge: $\mathrm{C}$ (Coulomb)
Example: $Q ~=~ 1.6 \cdot 10^{-19} \, \mathrm{C} $ is the charge of an electron.

$$ \begin{align} \mathrm{C} ~=~ \mathrm{As} \end{align} $$

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Positive and negative charges.

Voltage

Symbol: $U$
Unit of voltage: $\mathrm{V}$ (Volt)
Example: $U ~=~ 100 \, 000 \, 000 \, \mathrm{V} $ is the voltage between a thundercloud and the earth.

$$ \begin{align} \mathrm{V} ~=~ \frac{ \mathrm{J} }{ \mathrm{C} } ~=~ \frac{ \mathrm{Nm} }{ \mathrm{As} } ~=~ \frac{ \mathrm{kg} \, \mathrm{m}^3 }{ \mathrm{A} \, \mathrm{s}^3 } \end{align} $$

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Voltage is energy per charge.

Resistance

Symbol: $R$
Unit of resistance: $\mathrm{\Omega}$ (Ohm)
Example: $R ~=~ 100 \, \mathrm{\Omega} $ is the resistance of an ohmic conductor to which 200 volts are applied and through which 2 amps flow.

$$ \begin{align} \mathrm{\Omega} ~=~ \frac{ \mathrm{V} }{ \mathrm{A} } ~=~ \frac{ \mathrm{kg} \, \mathrm{m}^3 }{ \mathrm{A}^2 \, \mathrm{s}^3 } \end{align} $$

Electric field

Symbol: $E$
Unit of electric field: $ \frac{ \mathrm{V} }{ \mathrm{m} } $ (Volt per meter)
Example: $E ~=~ 1000 \, 000 \, \frac{ \mathrm{V} }{ \mathrm{m} } $ is the electric field between the bottom and top of a thundercloud.

$$ \begin{align} \frac{ \mathrm{V} }{ \mathrm{m} } ~=~ \frac{ \mathrm{N} }{ \mathrm{As} } ~=~ \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A} \, \mathrm{s}^3 } \end{align} $$

Magnetic field

Symbol: $\class{violet}{B}$
Unit of magnetic field: $ \mathrm{T} $ (Tesla)
Example: $\class{violet}{B} ~=~ 20 \, \mathrm{T} $ creates a superconducting coil in a nuclear fusion reactor.

$$ \begin{align} \mathrm{T} ~=~ \frac{ \mathrm{Vs} }{ \mathrm{m}^2 } ~=~ \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A} \, \mathrm{s}^2 } \end{align} $$

Capacitance

Symbol: $C$
Unit of capacitance: $ \mathrm{F} $ (Farad)
Example: $C ~=~ 100 \, \mathrm{\mu}\mathrm{F} $ is the capacitance of a given capacitor.

$$ \begin{align} \mathrm{F} ~=~ \frac{ \mathrm{As} }{ \mathrm{V} } ~=~ \frac{ \mathrm{A}^2 \, \mathrm{s}^4 }{ \mathrm{kg} \, \mathrm{m}^3 } \end{align} $$

Inductance

Symbol: $L$
Unit of inductance: $ \mathrm{H} $ (Henry)
Example: $L ~=~ 500 \, \mathrm{mH} $ is the inductance of a given coil with current flowing through it.

$$ \begin{align} \mathrm{H} ~=~ \frac{ \mathrm{Vs} }{ \mathrm{A} } ~=~ \frac{ \mathrm{kg} \, \mathrm{m}^3 }{ \mathrm{A}^2 \, \mathrm{s}^2 } \end{align} $$

Thermal capacity (heat capacity)

Symbol: $C$
Unit of thermal capacity: $ \frac{\mathrm{J}}{\mathrm{K}} $ (Joule per Kelvin)
Example: $C ~=~ 4190 \, \frac{\mathrm{J}}{\mathrm{K}} $ is the heat capacity of one liter of water.

$$ \begin{align} \frac{ \mathrm{J} }{ \mathrm{K} } ~=~ \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{s}^2 \, \mathrm{K} } \end{align} $$