I used to think that torque and force were equally “fundamental”. In other words, my understanding was that we usually use Cartesian coordinates in many common problems because it is a convenient system, so as a result instantaneous forces which act in straight lines seem “easier” mathematically but torques require some extra “baggage”. This baggage includes typically teaching that torque is defined in terms of force.
But if say we happened to choose polar coordinates for the problem the situation would appear the other way around. So it would be arbitrary if we chose to define forces in terms of torques instead.
But later on I learned that angular momentum is conserved independently of regular linear momentum (IIRC). Given the definitions of force & torque as derivatives of momentum, this makes it seem much less certain that one should define either torque in terms of force or vice versa — it gives the impression they are more distinct than it first seemed.
That said, as far as I know a lot of physics is about defining & describing “fundamental forces” — not “fundamental torques”.
So is choosing to use either force or torque as the basis of laws & problems arbitrary? Or is there an actual fundamental rationale to when one or the other should be used?
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