"If I have seen further than other men, it is because I stood on the shoulders of giants." - Isaac Newton
Isaac Newton (1642-1727) published his masterwork, Philosophiae Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy") in 1687. In this tome he combined the individually remarkable conceptual achievements of calculus, vectors and an elegant expression of the simple relationship between force and inertia (which in effect gave definition to those entities for the first time) to produce an integrated description of the interactions between objects and exactly how they produce different kinds of motion. This was the true beginning of the science of dynamics, for it marked the adoption of the descriptive paradigms that are still used universally to describe dynamics, even after Quantum Mechanics has exposed Newtonian Mechanics as fundamentally inadequate.1 Newton, like most great thinkers, had a variety of ludicrous foibles and was often a jerk in his dealings with others. I will not attempt to document his personal life, though many have done so [you can consult their work]; although it is interesting and revealing, it doesn't matter to our understanding of the conceptual edifice he built in the Principia. Moreover, I will make no attempt to introduce concepts in the order that Newton did, nor will I hesitate to use a more modern notation or even an updated version of a paradigm, with the rationale that (a) what matters most is getting the idea across clearly; and (b) we may have actually achieved a more elegant, compact understanding than Newton in the intervening centuries. This is one of the endearing (to me) traditions of Physics - and indeed of all genuine pursuit of truth2 - we treasure an æsthetic of searching for a better, more elegant, more reliable, more accurate (with regard to predicting the results of experiments), truer model of the world and rooting out the demonstrably wrong parts of existing models. A frightening number of people who claim to know the Truth share no such æsthetic and in fact are dedicated to suppressing such activities when they threaten their most cherished and unexamined Truths. Grrrr....
Before we go on to expound Newton's "Laws" in their modern form it is useful to examine the "self-evident" [oh, yeah?] concepts of force and mass and their relationship with that relatively rigorously defined kinematic quantity, the acceleration.