If m is length, $\mathrm m^2$ is area and $\mathrm m^3$ is volume; given $\mathrm s$ is time, is there such a thing as $\mathrm s^2$ and so on?

Question

If $\mathrm m$ is length, $\mathrm m^2$ is area and $\mathrm m^3$ volume (and so on into hyper dimensions).

Can the same principle of derived units of the product/exponent of the same fundamental unit, be applied to time $\mathrm s$ and weight ($\mathrm {kg}$) e.g $\mathrm s^2$ or $\mathrm {kg}^3$?

Is there such a thing as those derived units? If so what does do they mean/ represent / how could they be used?

I can't think of what they would mean; but jounce is not obviously intuitive, but is a thing. I want to make sure I am not being naïve to just write off $\mathrm s^2$.

Concerning multiple time dimensions, see https://physics.stackexchange.com/q/43322/2451 — Qmechanic, May 10 '17 at 03:11

score 2 · Answer 1 · answered May 09 '17 at 22:51

Each physical quantity has dimensions and hence units. For example, force is measured in Newtons, but 1 Newton is 1 kgms$^{-2}$. This means energy is measured in kgm$^2$s$^{-2}$, power in kgm$^2$s$^{-3}$, power per unit area (such as light shining on a solar panel) as kgs$^{-3}$ etc. Feel free to work out some more examples; they can lead to some surprising results, such as that last one. (What does a kilogram per cubic second "look like"? Well, apparently it looks like power incident on solar panels per unit area.) No physical quantities with units of s$^2$ or s$^3$ come to mind, although s$^{-2}$ does (consider $G\rho$, $\rho$ a density and $G$ Newton's gravitational constant).

Angular acceleration is also s^-2. The inverse of angular acceleration would represent "steadiness of rotation" and have units of s^2. — k-l, May 11 '17 at 22:40

If m is length, $\mathrm m^2$ is area and $\mathrm m^3$ is volume; given $\mathrm s$ is time, is there such a thing as $\mathrm s^2$ and so on?

1 Answers1