Our goal in this chapter is to understand Newton's laws of motion. Newton's laws are simple to state and they are not mathematically complex, so at first glance the task looks modest. As we shall see, Newton's laws combine definitions, observations from nature, partly intuitive concepts, and some unexamined assumptions about space and time. Newton's presentation of his laws of motion in his monumental Principia (1687) left some of these points unclear. However, his methods were so successful that it was not until two hundred years later that the foundations of Newtonian mechanics were carefully examined, principally by the Viennese physicist Ernst Mach. Our treatment is very much in the spirit of Mach.
Newton's laws of motion are by no means self-evident. According to Aristotle, the natural state of bodies is rest: bodies move only when a force is applied. Aristotelian mechanics was accepted for two thousand years because it seemed intuitively correct. Careful reasoning from observation and a great leap of imagination were needed to break out of the Aristotelian mold.
Analyzing physical systems from the Newtonian point of view requires effort, but the payoff is handsome. To launch the effort, this chapter is devoted to presenting Newton's laws and showing how to apply them to elementary problems. In addition to deepening our understanding of dynamics, there is an immediate reward for these exercises—the power to analyze physical phenomena that at first sight might seem incomprehensible.