Part I is about the basics, the fundamentals. Chapters 1 through 3 present the concepts that underlie the rest of the book. Chapter 1 defines thinking, introduces the main types of thinking, and presents what I call the search-inference framework for describing thinking.

Past writers (e.g., Arnauld, 1662/1964) have taken formal logic as a normative model of thinking. Today, people sometimes use the word “logical” as if it simply meant “reasonable” or “rational.” Logic has influenced education – where it served as the basis for the teaching of thinking for centuries – and it has provided us with much of our language for talking about thinking: “premise,” “assumption,” “contradiction.”

Here is a problem: “All families with six children in a city were surveyed. In seventy-two families, the exact order of births of boys (B) and girls (G) was G B G B B G. What is your estimate of the number of families surveyed in which the exact order of births was B G B B B B?”

Two remaining components that affect the overall performance of a turbofan engine are the bypass duct and mixer, as shown in Figure 11.1. Applications have previously been presented in Figures 2.42 and 2.44. These are relatively simple compared with the other components but should be included because they both generate losses in total pressure. Because the length-to-flow-width ratio of the bypass duct is moderate, the duct can incur significant losses. Also, it is desirable to have a uniform temperature gas entering the afterburner or nozzle so that these components operate near peak efficiency. Mixing of two fluid streams at different temperatures is a highly irreversible process, and a mixer consists of 3-D vanes in both the radial and circumferential (annular) directions. Thus, with good mixing of the low-temperature bypassed air and high-temperature primary air, further significant losses can occur. Owing to the temperatures exiting from the turbine, mixers are generally fabricated from a nickel-based alloy. With these losses the thrust and TSFC will both be compromised.

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.

In Chapter 11, we studied the forces in machine systems in which all forces on the bodies were in balance, and therefore the systems were in either static or dynamic equilibrium. However, in real machines this is seldom, if ever, the case except when the machine is stopped. We learned in Chapter 4 that although the input crank of a machine may be driven at constant speed, this does not mean that all points of the input crank have constant velocity vectors or that other links of the machine operate at constant speeds. In general, there will be accelerations, and therefore machines with moving parts having mass are not balanced.

In Part I we examined the form and function ofthe major families of power electronic converters.Our goal was to show how the intended powerconversion function is achieved in each case byappropriate configuration of the circuitcomponents and by proper operation of theswitches. Throughout those earlier chapters, ourconcern was with nominal operating conditions, that is,the ideal operating conditions in which aconverter is designed to perform its primaryconversion function. As nominal operation in mostpower electronic circuits involves a periodic steady state, wefocused on situations in which circuit operationand behavior are the same from cycle to cycle.

The existence of vibrating elements in a mechanical system produces unwanted noise, high stresses, wear, poor reliability, and, frequently, premature failure of one or more of the parts. The moving parts of all machines are inherently vibration producers, and for this reason engineers must expect vibrations to exist in the devices they design. But there is a great deal they can do during the design of the system to anticipate a vibration problem and to minimize its undesirable effects.

In this chapter, we begin by defining the concept of the angular momentum for a point mass, systems of discrete masses, and continuous rigid bodies. We then use the most general form of Newton’s Second Law for rotational motion to study the impulse due to a torque, the angular momentum impulse theorem, and finally the conservation of angular momentum. To develop these theorems, we draw from our understanding of the analogous theorems in linear motion.