I'm curious about how equations like $F_{g}=G\frac{m_{1}m_{2}}{r^{2}}$ and $F_{e}=k\frac{q_{1}q_{2}}{r^{2}}$ were derived. Turns out that they're actually inverse square laws. But it's still unclear to me, how they are verified.
The equation for moment of inertia is $I=m\sum_{n=1}^{n} r_{n}^{2}$. Does $r^2$ here indicate that rotational inertia is proportional to the area of a... circle or sphere? (Is it a, um... square law?) Which leads me to the last question—
Why are laws like these inversely proportional to the area of a sphere? Couldn't they be inversely proportional to the volume of a sphere?
Is it even sphere in all cases?
Why prefer area over volume?
Most importantly, how are they verified?
I think the answer to this is interrelated to the previous questions. So I asked all of them at once, instead of making seperate posts. Should I make individual posts instead?
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