# [Physics] Why do we need torque separately from force

forcestorque

I'm studying physics for a couple of month now and and I am currently finding it a bit unsatisfying how the basic physical concepts are presented, meaning often times we only get a formula ($\tau=r \times F$, for example) without much discussion or any derivation.
So I was trying to build up a bit of background knowledge and intuition from the Feynman lectures.

From what I understand he derived torque (firstly without vectors) simply by inserting angular coordinates into the displacement in the work formula and rearranged it:

\Delta W=F_x\,\Delta x+F_y\,\Delta y.

angular coordinates ("angular displacement"?):

\Delta x=-PQ\sin\theta=-r\,\Delta\theta\cdot(y/r)=-y\,\Delta\theta.

\Delta y=+x\,\Delta\theta.

inserted:

\Delta W=(xF_y-yF_x)\Delta\theta.

He then calls the part without the angle "torque".

So isn't the torque just a special kind of force, one that acts on a circular displacement? Why do we treat force and torque so seperately when torque just seems to emerge when we work with angular coordinates? Isn't this just a special case, why can't we not use just force all the time (and not separate force/momentum/… and torque/angular momentum/… so strictly)?

Obviously I'm thinking about it the wrong way and have some major misunderstandings regarding the concept of torque and thus angular momentum etc. Are there any "better"/other derivations of this concept? After weeks of frustration I signed up here, maybe you have a better way of getting some intuition with torque.
Thanks.