In order to describe rotational motion, we usually ditch the familiar concepts of force, linear momentum and mass, and use instead their moments to describe the motion. Is it just because it makes our calculations easier, or is there a deeper reasoning behind it.
In case of translational motion, where we work with force, mass and momentum, the shape of the body doesn't matter. However, in case of rotation, it seems that the shape of the body does matter, and treating them as point masses would give us incorrect results.
For example, consider a physical pendulum or a compound pendulum. Instead of using force or mass, we try to analyze it using torque/moment of inertia. Is it because the latter considers the distribution of masses, while the former ignores it ? Or is there a deeper theoretical reason for using the moments.
So, if we used force/mass to analyze a compound pendulum, we would get a wrong answer for it's time period, if we compare that to experimental answers. However, the answer we get by analyzing torque would be closer to the experimental ones. Is that the reason we use Torque to analyze rotation - because it considers the distribution of masses, and thus agrees more with experimental results, or is there some theoretical reasoning behind it, and we can just as well describe any compound pendulum, purely using forces ?