Until now, we have been concerned with the kinematics of particles where the objective has been to determine the motion of a particle or rigid body without regard to the cause of the motion. Clearly in any physical system motion cannot occur without the application of some kind of external stimulus. In particular, in order for a particle to accelerate, it is necessary to apply a force to the particle. In order to study the motion that results from the application of a force (or, in general, the application of multiple forces) to a particle, it is necessary to study the kinetics of the particle. The objective of kinetics is threefold: (1) to describe quantitatively the forces that act on a particle; (2) to determine the motion that results from the application of these forces using postulated laws of physics; and (3) to analyze the motion.

The first topic in this chapter is the development of models for forces that are commonly used in dynamics. In particular, models are developed for contact forces, spring forces, and gravitational forces. These models will be used throughout the remainder of this book when solving problems.

The next topic in this chapter covers Newton's laws, which are the fundamental postulates that govern the nonrelativistic motion of particles.

The first topic in the study of dynamics is kinematics. Kinematics is the study of the geometry of motion without regard to the forces the cause that motion. For any system (which may consist of a particle, a rigid body, or a system of particles and/or rigid bodies) the objectives of kinematics are fourfold: to determine (1) a set of reference frames in which to observe the motion of a system; (2) a set of coordinate systems fixed in the chosen reference frames; (3) the angular velocity and angular acceleration of each reference frame (and/or rigid body) resolved in the chosen coordinate systems; and (4) the position, velocity, and acceleration of each particle in the system. In order to develop a comprehensive and systematic approach, the study of kinematics given in this Chapter is divided into two parts: (1) the study of kinematics of particles and (2) the study of kinematics of rigid bodies.

This Chapter is organized as follows. First, both a qualitative and precise definition of a reference frame is given. In particular, it is discussed that a reference frame provides a perspective from which to observe the motion of a system.

In Chapter 3 we discussed the important principles and methods used in the formulation, solution, and analysis of the motion of a single particle. In this chapter we extend the results of particle kinetics to systems consisting of two or more particles.

The first topic covered in this chapter is the center of mass of a system of particles. Using the definition of the center of mass, the linear momentum of a system of particles is defined. Then, using the definition of linear momentum, the velocity and acceleration of the center of mass of the system are defined.

The second topic covered in this chapter is the angular momentum of a system of particles. In particular, expressions for the angular momentum are derived relative to an arbitrary point, an inertially fixed point, and the center of mass of the system. Then, relationships between these three different forms of angular momentum are derived.

The third and fourth topics covered in this chapter are Newton's 2nd law and the rate of change of angular momentum for a system of particles. In particular, it is shown that the center of mass of the system satisfies Newton's 2nd law. Furthermore, the key results relating the rate of change of angular momentum for a system of particles to moment applied to the system are derived.

Until now we have been concerned with the kinetics of particles, i.e., the kinetics of objects that have nonzero finite mass but do not occupy any physical space. Furthermore, in Section 2.15 of Chapter 2 we studied the kinematics of motion of a rigid body. In this chapter we turn our attention to the kinetics of rigid bodies. To this end, the objectives of this chapter are threefold: (1) to describe quantitatively the forces and moments that act on a rigid body; (2) to determine the motion that results from the application of these forces and moments using postulated laws of physics; and (3) to analyze the motion.

The key difference between a particle and rigid body is that a particle can undergo only translational motion whereas a rigid body can undergo both translational and rotational motion. In general, for motion in ℝ3 it is necessary to specify three variables for the translational motion and to specify another three variables for the rotational motion of the rigid body.

Mechanics is the study of the effect that physical forces have on objects. Dynamics is the particular branch of mechanics that deals with the study of the effect that forces have on the motion of objects. Dynamics is itself divided into two branches called Newtonian dynamics and relativistic dynamics. Newtonian dynamics is the study of the motion of objects that travel with speeds significantly less than the speed of light while relativistic dynamics is the study of the motion of objects that travel with speeds at or near the speed of light. This division in the subject of dynamics arises because the physics associated with the motion of objects that travel with speeds much less than the speed of light can be modeled much more simply than the physics associated with the motion of objects that travel with speeds at or near the speed of light. Moreover, nonrelativistic dynamics deals primarily with the motion of objects on a macroscopic scale while relativistic dynamics deals with the study of the motion of objects on a microscopic or submicroscopic scale.

The subject of dynamics has been taught in engineering curricula for decades, traditionally as a second-semester course as part of a year-long sequence in engineering mechanics. This approach to teaching dynamics has led to a wide array of currently available engineering mechanics books, including Beer and Johnston (1997), Bedford and Fowler (2005), Hibbeler (2001), and Merriam and Kraige (1997). From my experience, the reasons these books are adopted for undergraduate courses in engineering mechanics are threefold. First, they include a wide variety of worked examples and have more than 1000 problems for the students to solve at the end of each chapter. The variety of problems provides instructors with the flexibility to assign different problems every semester for several years. Second, these books are generic enough that they can be used to teach undergraduates in virtually any branch of engineering. Third, they cover both statics and dynamics, thereby making it is possible for a student to purchase a single book for a year-long engineering mechanics course. Using these empirical measures, it is hard to dispute that these books cover a tremendous amount of material and enable an instructor to tailor the material to the needs of a particular course. Given the vast array of undergraduate dynamics books already available, an obvious question that arises is, why write yet another book on the subject of undergraduate engineering dynamics?