Unifying Concepts for Planar Motion

Chapter 4 is a reformulation of the concepts presented in Chap. 3, but with the goal of creating a unified framework for deriving equations of motion. In essence, this chapter is devoted to the derivation of Euler’s laws of motion. While Chap. 3 provides the necessary background to fully understand the derivations in Chap. 4, the latter sheds important light on what might have seemed like arbitrary choices when solving problems in the former. It is also a good warmup for the full three-dimensional problem addressed in the next chapter. Here we encounter the key ideas of center of mass and mass moment of inertia, which had been implicit all along but not yet named. While many authors prefer to start by defining and learning how to compute these quantities, here we see them emerge naturally from balance of momentum and energy principles.