I'm studying rigid body dynamics lately. I came across the definition of torque, and though I've found a lot of explanations as to why there is an r there (the moment), all of them are mathematical (equating work and so on). None of them explained physically and I still couldn't figure out why the distance from axis of rotation increases the net effect, or torque. 

So I thought about this and came to this line of thought -

Rotation can be thought of as a rigid body have all the infinitesimal masses performing circular motion about a fixed axis. There is pure rotation, hence angular velocity is constant. Thus velocity which is omega times r increase with the distance from the rotation axis. So if force is applied at more distance, this implies more velocity of the point of the application, and since the body is rigid, all the other mass connected to the point of application goes along through inter-atomic interactions and hence more rotational effect. Is this line of thought correct?

So what happens inside a body when it rotates? Do the rest of the atoms go along due to electromagnetic attraction and if so, can someone explain exactly what happens inside the body when it rotates and where does that r come from from an inter-atomic point of view?

The truth is we don't know. But when you think about it, how can we know? If we knew what technology would eventually come out of experiments like this, why would we not build that technology now?

Large expensive machines like the CERN supercollider help us to further understand the laws of nature. And through understanding these laws, new technologies arise. But we, the physicists, have absolutely no idea what wonderful technologies might result tomorrow because we invested so heavily in science today.

It's purported in 1850 after Faraday developed the electric generator, the British minister of finance asked him what practical value there was to electricity. Faraday could not have known that electricity would one day form the backbone of all modern society (but that didn't stop him from making a snarky remark). It's hard to predict the future; we labour in science in the hopes that what we do will prove useful for some new and amazing technologies. But we don't know what technologies will result from our expensive laboratories any more than Faraday knew that electricity would allow you to make a computer.
