ABSTRACT
This chapter reviews the rotational motion of a single particle around an arbitrary axis, and the concepts of the moment of inertia and the center of mass. It focuses on how the center of mass simplifies the description of the translational and rotational motion of a system of particles. The chapter explores generalized definitions of the moment of inertia, including products of inertia and the inertia tensor, and demonstrates how to calculate these quantities for a variety of solids. It discusses the parallel axis theorem for rigid bodies and show how it can be used to calculate the moment of inertia tensor. This is followed by a discussion of eigenvalues and eigenvectors of matrices, and how they can be used to describe the principal axes of a rigid body. The chapter concludes with a discussion of the Euler equations and how they can be used to describe the precessional motion of spinning tops and gyroscopes.
