In discussing the principles of dynamics in Chapter 2, we stressed that Newton's second law F = ma holds true only in inertial coordinate systems. We have so far avoided non-inertial systems in order not to obscure our goal of understanding the physical nature of forces and accelerations. Because that goal has largely been realized, in this chapter we turn to the use of non-inertial systems with a twofold purpose. By introducing non-inertial systems we can simplify many problems; from this point of view, the use of non-inertial systems represents one more computational tool. However, consideration of non-inertial systems also enables us to explore some of the conceptual difficulties of classical mechanics. Consequently, the second goal of this chapter is to gain deeper insight into Newton's laws, the properties of space, and the meaning of inertia. We start by developing a formal procedure for relating observations in different inertial systems.
In this section we shall show that any coordinate system moving uniformly with respect to an inertial system is also inertial. This result is so transparent that it hardly warrants formal proof. However, the argument will be helpful in the next section when we analyze non-inertial systems.
Suppose that two physicists, Alice and Bob, set out to observe a series of events such as the position of a body of mass m as a function of time. Each has their own set of measuring instruments and each works in their own laboratory. Alice has confirmed by experiments that Newton’s laws hold accurately in her laboratory, and she concludes that her reference frame is therefore inertial.