Page 21 - Dynamics of Mechanical Systems

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2 Dynamics of Mechanical Systems

Kinematics is a study of motion without
regard to the cause of the motion. Kine-
matics includes an analysis of the posi-
tions, displacements, trajectories,
velocities, and accelerations of the mem-
bers of the system. Inertia is a study of the
mass properties of the bodies of a system
and of the system as a whole in various
configurations. Kinetics is a study of forces.
Forces are generally divided into two
classes: applied (or “active”) forces and iner-
tia (or “passive”) forces. Applied forces
arise from contact between bodies and FIGURE 1.2.1
Subdivisions of mechanics.
from gravity; inertia forces occur due to the
motion of the system.

1.3 Fundamental Concepts and Assumptions

The study of dynamics is based upon several fundamental concepts and basic assumptions
that are intuitive and based upon common experience: time, space, force, and mass. Time
is a measure of change or a measure of a process of events; in dynamics, time is assumed
to be a continually increasing, non-negative quantity. Space is a geometric region where
events occur; in the study of dynamics, space is usually defined by reference frames or
coordinate systems. Force is intuitively described as a push or a pull. The effect of a force
depends upon the magnitude, direction, and point of application of the push or pull; a
force is thus ideally suited for representation by a vector. Mass is a measure of inertia
representing a resistance to change in motion; mass is the source of gravitational attraction
and thus also the source of weight forces.
In our study we will assume the existence of an inertial reference frame, which is simply
a reference frame where Newton’s laws are valid. More specifically, we will assume the
Earth to be an inertial reference frame for the range of systems and problems considered
in this book.
Newton’s laws may be briefly stated as follows:

1. In the absence of applied forces, a particle at rest remains at rest and a particle
in motion remains in motion, moving at a constant speed along a straight line.
2. A particle subjected to an applied force will accelerate in the direction of the
force, and the acceleration will be proportional to the magnitude of the force
and inversely proportional to the mass of the particle. Analytically, this may be
expressed as

F = m a (1.3.1)
where F is the force (a vector), m is the particle mass, and a is the resulting
acceleration (also a vector).
3. Within a mechanical system, interactive forces occur in pairs with equal magni-
tudes but opposite directions (the law of action and reaction).