Chapters 1 to 10 were devoted to statics, that is, to the analysis of
bodies at rest. We now begin the study of dynamics, the part of mechanics
that deals with the analysis of bodies in motion.
While the study of statics goes back to the time of the Greek
philosophers, the first significant contribution to dynamics was made
by Galileo (1564-1642). Galileo's experiments on uniformly accelerated
bodies led Newton (1642-1727) to formulate his fundamental
laws of motion.
Dynamics includes:
- Kinematics, which is the study of the geometry of motion. Kinematics is used to relate displacement, velocity, acceleration, and time, without reference to the cause of the motion.
- Kinetics, which is the study of the relation existing between the forces acting on a body, the mass of the body, and the motion of the body. Kinetics is used to predict the motion caused by given forces or to determine the forces required to produce a given motion.
Chapters 11 to 14 are devoted to the dynamics of particles; in
Chap. 11 the kinematics of particles will be considered. The use of
the word particles does not mean that our study will be restricted to
small corpuscles; rather, it indicates that in these first chapters the
motion of bodies - possibly as large as cars, rockets, or airplanes -
will be considered without regard to their size. By saying that the
bodies are analyzed as particles, we mean that only their motion as
an entire unit will be considered; any rotation about their own mass
center will be neglected. There are cases, however, when such a
rotation is not negligible; the bodies cannot then be considered as
particles. Such motions will be analyzed in later chapters, dealing with
the dynamics of rigid bodies.
In the first part of Chap. 11, the rectilinear motion of a particle
will be analyzed; that is, the position, velocity, and acceleration of a
particle will be determined at every instant as it moves along a straight
line. First, general methods of analysis will be used to study the
motion of a particle; then two important particular cases will be considered,
namely, the uniform motion and the uniformly accelerated
motion of a particle (Secs. 11.4 and 11.5). In Sec. 11.6 the simultaneous
motion of several particles will be considered, and the concept
of the relative motion of one particle with respect to another will be
introduced. The first part of this chapter concludes with a study of
graphical methods of analysis and their application to the solution of
various problems involving the rectilinear motion of particles (Secs.
11.7 and 11.8).
In the second part of this chapter, the motion of a particle as it
moves along a curved path will be analyzed. Since the position, velocity,
and acceleration of a particle will be defined as vector quantities, the
concept of the derivative of a vector function will be introduced in Sec.
11.10 and added to our mathematical tools. Applications in which the
motion of a particle is defined by the rectangular components of its
velocity and acceleration will then be considered; at this point, the motion
of a projectile will be analyzed (Sec. 11.11). In Sec. 11.12, the motion
of a particle relative to a reference frame in translation will be
considered. Finally, the curvilinear motion of a particle will be analyzed
in terms of components other than rectangular. The tangential
and normal components of the velocity and acceleration of a particle
will be introduced in Sec. 11.13 and the radial and transverse components
of its velocity and acceleration in Sec. 11.14.
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