In this chapter, we extend perhaps the most famous law in mechanics, Newton’s Second Law, to study objects and systems of objects executing rotational motion. Emphasis is placed on developing an intuition for the effects of torques on the rotational dynamics of systems by comparing and contrasting them to the effects that forces have on the linear motion of such systems.

Just as force is a ubiquitous concept in linear mechanics, torque is ubiquitous in rotational mechanics. We, therefore, begin this chapter with the definition and detailed description of torque, which we then use to study static equilibrium. Our discussion includes descriptions of common forces and their points of application, as well as subtleties associated with studying systems of objects in static equilibrium. The chapter ends with some useful theorems commonly found in the literature.

We begin our study of rotational motion with the definitions and detailed examination of the fundamental quantities which we will use throughout this book. We then proceed with a description of kinematics in rotational motion by drawing analogies from our knowledge of one-dimensional kinematics in linear motion.

The classical theory of atmospheric flight mechanics is introduced. The kinematic description of a rigid aircraft is first described using Euler angles. This is followed by the derivation of the Newton-Euler equations describing the aircraft dynamics, with a discussion on the external forces appearing on the vehicle. Steady-state flight conditions are discussed next and used to introduce the concept of load factor and the maneuvering envelope of an aircraft. Finally, dynamic stability is described for both the longitudinal and lateral problem.

The Schwarzschild black holes discussed in Chapter 12 are not the most general black hole spacetimes predicted by general relativity. They are simple objects – exactly spherically symmetric and characterized by a single parameter, the total mass. Remarkably, the most general stationary black hole solutions of the vacuum Einstein equation are not much more complicated. They are described by the family of geometries discovered by Roy Kerr in 1963, and are called Kerr black holes. Members of the family depend on just two parameters – the total mass and total angular momentum. Kerr black holes are the rotating generalizations of the Schwarzschild black hole. This chapter gives an elementary introduction to their properties.