I wanted to explain torque in the form of fundamental force

I predict that it must be derived from the inverse squared laws of force because of the fact that earth around the sun is acted upon by the torque.

So, I imagine a rod suspended at one end. And in free space I apply force at its free end perpendicular to its alignment . What I see is that the as the distance from the another ends increases the the molecules at the free end path tend to be in straight line . So I think that the force acted upon there produces small but easy change in the alignment of the whole rod

Similarly if a free rod at rest is pushed with a force at its center of mass the inertia of mass both at its right and left is same but if I apply same force and left or right to the center of mass it inertia at one side is more than that of the other side. In big picture I think I can imagine someone pushing me when two of my friends holding me from both side and in other case those friends holding me from same side.

Using these proposition how can I derive torque and generalize it. Can anyone help?

There is no torque acting on the Earth in its orbit around the sun. If there were, the length of the year would be either lengthening or shortening. If a body is in circular motion at constant angular velocity (ω), there is no torque acting.

Apologies if you already know what follows but, from some of the things you say, I can't be sure how much is familiar to you:

ω is the angular equivalent of straight line velocity, v and torque,τ is the angular equivalent of force. If you apply a net torque, you change the angular velocity, in other words imparting an angular acceleration. So it is just like F=ma, but normally written something like: τ = Iώ. (This applies so long as the rotating object is fixed with respect to the axis of rotation.)

The tricky bit is that the angular equivalent of mass is moment of inertia, I. Calculating moments of inertia is not straight forward for extended objects, because you need to integrate mass x distance from the axis of rotation, ∫m(r ) dr, across the whole object.

I do not understand your second paragraph at all, so cannot comment on it. I don't understand why you start talking about molecules, in a discussion of mechanics.

**Edited by exchemist, 28 June 2019 - 11:11 AM.**