The variety of explanatory modes in dynamics

We have seen that dynamics is a theory with a multiplicity of explanatory structures that can be used to formulate its lawlike conclusions and to provide explanations of the behavior of systems within its purview. We have also seen that the threads of some of these structures can be traced back to the earliest days of the development of the theory.

One pattern of explanation in dynamics we might call the “Newtonian.” Here one must first posit an appropriate structure that admits a preferred metric of time and the existence of the preferred inertial reference frames to which all motion is to be referred. Inertial motion with constant speed and direction is taken as the “natural,” “unforced,” state of a body.

Inertial mass and force are introduced. The former is an intrinsic property of a piece of matter representing its resistance to having its state of motion changed, and the latter is the (vector) measure of the influences that can change the state of motion of a system. The fundamental law, of course, is the proportionality of the linear momentum change of the system to the force applied to it. This initial Newtonian framework must be supplemented, as was first seen by Euler, by a corresponding notion of moment of inertia as intrinsic resistance to change of state of rotation and of moments of forces (or torques) as the measure of the influences generating changes of angular momentum.