We derive the rotational form of Newton's second law from the translational form by performing a force analysis of a simple body consisting of two discrete masses. Curiously, a truly rigid body model leads to an incorrect statement of the rotational second law. The failure of this model is traced to its violation of the strong form of Newton's third law. This leads us to consider a slightly modified non-rigid model that respects the third law, produces the correct rotational second law, and makes explicit the importance of the product of the tangential force with the radial distance: the torque.
The strong form of the third law applies to interatomic forces, which act at a distance. At the macroscopic level, extended objects can exert contact forces on each other that are not in line with their individual centers of mass, e.g., surface friction, generating torque. When these forces respect the weak third law they will automatically respect the strong third law because both forces are exerted at the same point in space: the point of contact.
An important caveat is that the electromagnetic force does not respect these symmetries in general, and mechanical momentum need not be conserved. However, including the electromagnetic field momentum restores conservation, and the resulting field theory respects spacetime symmetries and Noether's theorem.