The dimensions of energy

Dimensions of energy

Let us use the cases of: [ilmath]F\eq Ma[/ilmath] - force = mass [ilmath]\times[/ilmath] acceleration, and, [ilmath]E\eq F\ell[/ilmath] - Energy = Force [ilmath]\times[/ilmath] distance (here [ilmath]\ell[/ilmath] is used, for "[ilmath]\ell[/ilmath]ength")

Dimensions in play:

• [ilmath][E]\eq ML^2T^{-2} [/ilmath]
  • [ilmath][F]\eq MLT^{-2} [/ilmath]
    • [ilmath][a]\eq LT^{-2} [/ilmath] for ([ilmath]L[/ilmath] being length, [ilmath]T[/ilmath] being time)
    • [ilmath][M]\eq M[/ilmath] for ([ilmath]M[/ilmath] being mass)
  • [ilmath][\ell]\eq L[/ilmath] for ([ilmath]L[/ilmath] being length - as above)

We could also do:

• [ilmath][E]\eq \mathrm{N}\mathrm{M} [/ilmath] "Newton Meters" - from [ilmath][F]\eq \text{Newtons} [/ilmath] and [ilmath][L]\eq M[/ilmath]
• [ilmath][E]\eq \text{Kg M}\ /\ \mathrm{S}\ /\ \mathrm{S} [/ilmath] - Kilogram meters per second per second

This will be expanded on in future