For a long time I have wondered if there is a way to show that the rotational analogs of Newton's Laws are a direct consequence of just those laws, or are we adding more to them?
I understand mathematically that we take Newton's second law and do "r cross both sides," but that has always struck me as using more than just the 2nd law.
Here it matters where forces on the body are applied, but I don't see where Newton's Laws talk about points where forces are applied to a body. For translational motion it doesn't matter. So are we adding a sort of "extra law" when we do this for rotation?
The only thing I can think of would be to "disassemble" an extended body into differential point masses and work with internal constraint forces that make the body rigid. If every mass is just a point mass it would get around the issue I'm having. I've never seen any discussion along those lines, though.
Best Answer
I believe this may be of use to you.
The Physical Origin of Torque and of the Rotational Second Law, Daniel J. Cross
According to him, no.
Basically, He explains how an additional "constraint" is required on Newton's original third law such that the idealized rigid body model is no longer feasible, stating that
Obviously, if the forces they exert on each other only lie along the line connecting them, then it would be impossible for a mass to tangentially accelerate another mass about an axis while remaining collinear (or rigid) with it and the axis.
He then goes on to demonstrate that, if the body is NOT idealized as a rigid body, then Newton's laws (coupled with his additional constraint) perfectly predict the torque effect of a force applied to it.
(Please comment if you think I misinterpreted the text of if you feel my summary is not sufficient)