The dimensions of energy

Dimensions of energy

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

Dimensions in play:

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

We could also do:

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

This will be expanded on in future