Editing Dimensional analysis (section)

== Dimensional equivalences ==
Following are tables of commonly occurring expressions in physics, related to the dimensions of energy, momentum, and force.<ref>{{citation |last=Woan |first=G. |title=The Cambridge Handbook of Physics Formulas |publisher=Cambridge University Press |year=2010 |isbn=978-0-521-57507-2 |url-access=registration |url=https://archive.org/details/cambridgehandboo0000woan }}</ref><ref>{{citation |last1=Mosca |first1=Gene |last2=Tipler |first2=Paul Allen |title=Physics for Scientists and Engineers – with Modern Physics |publisher=W. H. Freeman |location=San Francisco |year=2007 |isbn=978-0-7167-8964-2 |edition=6th}}</ref><ref name=Martin08>{{citation |last1=Martin |first1=B.R. |last2=Shaw |first2=G. |author3=Manchester Physics |title=Particle Physics |publisher=Wiley |year=2008 |isbn=978-0-470-03294-7 |edition=2nd}}</ref>

=== SI units ===
{{main|International System of Units}}

{| class="wikitable"
|-
! scope="col" style="width:100px;" | Energy, {{math|''E''}}
T<sup>−2</sup>L<sup>2</sup>M
! scope="col" style="width:100px;" | Expression
! scope="col" style="width:350px;" | Nomenclature
|-
|rowspan="4"| Mechanical
| <math> Fd </math>
| {{math|''F''}} = [[force]], {{math|''d''}} = [[distance]]
|-
| <math> S/t \equiv Pt </math>
| {{math|''S''}} = [[action (physics)|action]], {{math|''t''}} = time, {{math|''P''}} = [[power (physics)|power]]
|-
| <math> mv^2 \equiv pv \equiv p^2/m </math>
| {{math|''m''}} = [[mass]], {{math|''v''}} = [[velocity]], {{math|''p''}} = [[momentum]]
|-
| <math> I\omega^2 \equiv L\omega \equiv L^2/I </math>
| {{math|''L''}} = [[angular momentum]], {{math|''I''}} = [[moment of inertia]], {{math|''ω''}} = [[angular velocity]]
|-
| Ideal gases
| <math> p V \equiv NT </math>
| {{math|''p''}} = pressure, {{math|''V''}} = volume, {{math|''T''}} = temperature, {{math|''N''}} = [[amount of substance]]
|-
| Waves
| <math> AIt \equiv ASt </math>
| {{math|''A''}} = [[area]] of [[Huygens–Fresnel principle|wave front]], {{math|''I''}} = wave [[intensity (physics)|intensity]], {{math|''t''}} = [[time]], {{math|''S''}} = [[Poynting vector]]
|-
| rowspan="3" | Electromagnetic
| <math> q\phi </math>
| {{math|''q''}} = [[electric charge]], {{math|''ϕ''}} = [[electric potential]] (for changes this is [[voltage]])
|-
| <math> \varepsilon E^2V \equiv B^2V/\mu </math>
| {{math|''E''}} = [[electric field]], {{math|''B''}} = [[magnetic field]], <br /> {{math|''ε''}} = [[permittivity]], {{math|''μ''}} = [[permeability (electromagnetism)|permeability]], <br />{{math|''V''}} = 3d [[volume]]
|-
| <math> pE \equiv m B \equiv I A B </math>
| {{math|''p''}} = [[electric dipole moment]], {{math|''m''}} = magnetic moment, <br /> {{math|''A''}} = area (bounded by a current loop), ''I'' = [[electric current]] in loop
|}

{| class="wikitable"
|-
! scope="col" style="width:100px;" | Momentum, {{math|''p''}} 
T<sup>−1</sup>LM
! scope="col" style="width:100px;" | Expression
! scope="col" style="width:350px;" | Nomenclature
|-
| rowspan="2" | Mechanical
| <math> mv \equiv Ft </math>
| {{math|''m''}} = mass, {{math|''v''}} = velocity, {{math|''F''}} = force, {{math|''t''}} = time
|-
| <math> S/r \equiv L/r </math>
| {{math|''S''}} = action, {{math|''L''}} = angular momentum, {{math|''r''}} = [[displacement (vector)|displacement]]
|-
| Thermal
| <math> m \sqrt{\left\langle v^2 \right\rangle} </math>
| <math> \sqrt{\left\langle v^2 \right\rangle} </math> = [[root mean square velocity]], ''m'' = mass (of a molecule)
|-
| Waves
| <math> \rho V v </math>
| {{math|''ρ''}} = [[density]], {{math|''V''}} = [[volume]], {{math|''v''}} = [[phase velocity]]
|-
| Electromagnetic
| <math> q A </math>
| {{math|''A''}} = [[magnetic vector potential]]
|}

{| class="wikitable"
|-
! scope="col" style="width:100px;" | Force, {{math|''F''}}
T<sup>−2</sup>LM
! scope="col" style="width:100px;" | Expression
! scope="col" style="width:350px;" | Nomenclature
|-
| Mechanical
| <math> ma \equiv p/t </math>
| {{math|''m''}} = mass, {{math|''a''}} = acceleration
|-
| Thermal
| <math> T \delta S/\delta r </math>
| {{math|''S''}} = entropy, {{math|''T''}} = temperature, {{math|''r''}} = displacement (see [[entropic force]])
|-
| Electromagnetic
| <math> Eq \equiv Bqv </math>
| {{math|''E''}} = electric field, {{math|''B''}} = magnetic field, {{math|''v''}} = velocity, {{math|''q''}} = charge
|}