TABLE OF CONTENTS In the previous two chapters we studied methods for analyzing the forces in machines. First, in Chapter 14 we analyzed static or steady-state forces; then, in Chapter 15 we went on to analyze the time-varying dynamic forces caused by acceleration. A brief review will show that vector equations were used throughout and, therefore, most of the equations and techniques presented seem equally applicable in either two or three dimensions. The examples presented, however, were all limited to planar motion.
In this chapter, as implied by its title, we will extend our study to include spatial problems. Thus, the basic principles are not new, but the problems presented may seem more complex because of our difficulty in visualizing in three dimensions. In addition to this added complexity, we will see that our previous treatment of moments and angular motion were not presented in detail enough to deal with three-dimensional rotations.
We will also derive and study methods involving the use of translational and angular impulse and momentum. These additional techniques, while particularly valuable with spatial problems, also provide alternative methods of analysis for planar problems. These may improve our comprehension of the physical principles involved and, sometimes, may also greatly simplify the solution process for certain problems.
Sometimes the shapes of machine parts are so complicated that it is extremely tedious and time-consuming to calculate the moment(s) of inertia. Consider, for example, the problem of finding the mass moment of inertia of an...
