Torque and its origin What's the origin of the definition of torque, that is, the moment of force about the point in consideration? - (1) 
Is there a proof? 
Why should torque be r x F, and not r² or r³ x F for that matter? I have tried searching many books but none gave the proof as to why torque should be r x F only, and not any other combination of the two. 
I was hoping if it'd be possible to design a thought experiment, that clearly validates equation (1)
Thanks! 
 A: By definition a moment in physics is the product of a physical quantity  and a position. So the quantity $\vec{r}\times\vec{F}$ could by definition be considered a moment of force. The utility of this moment is found when we consider the moment of momentum, $\vec{L}=\vec{r}\times \vec{p}$ ($\vec{p}$ is momentum), also called the angular momentum. It's called this because moments are generally related to rotational or turning or angular behaviors.
If we accept that angular momentum is a conserved quantity, then an important idea to consider is the time rate of change of momentum, which we call torque, often symbolized by $\vec{\Gamma}$ or $\vec{\tau}$. Conservation of angular momentum says
$$\vec{L}_{\mathrm{new}} = \vec{L}_{\mathrm{old}}+\int\Gamma\ \mathrm{d}t.$$
Calculating the time rate of change of $\vec{L}$ we get
$$\frac{\mathrm{d}\vec{L}}{\mathrm{d}t}= \frac{\mathrm{d}\vec{r}}{\mathrm{d}t}\times \vec{p}+\vec{r}\times \frac{\mathrm{d}\vec{p}}{\mathrm{d}t}$$
The first cross product vanishes (I'll let you figure that out), and $\frac{\mathrm{d}\vec{p}}{\mathrm{d}t}=\vec{F}.$
So the time rate of change of momentum, which we name torque, is equal to the moment of a force. [Edit: added "equal to"]
