Page 182 - Dynamics of Mechanical Systems

0593_C06_fm Page 163 Monday, May 6, 2002 2:28 PM

6

Forces and Force Systems

6.1 Introduction
Kinematics is a study of motion without regard to the causes of the motion. Alternatively,
kinetics is a study of forces causing a motion. While knowledge of forces is based upon
experience and intuition and upon studies in elementary physics and statics, it is helpful
to review the fundamental concepts again, as they are essential in studying the dynamics
of mechanical systems. Unlike unit vectors, position vectors, or velocity vectors, force
vectors are generally associated with a point of application. Force vectors are thus bound
vectors, whereas the other vectors are free vectors.
To illustrate the importance of the point of application, consider the rod shown in Figure
6.1.1. Let a force F be applied perpendicular to the rod, first at end A and then at end B.
The effect upon the rod of the different points of application is that in the first case (end
A) the rod will rotate clockwise, whereas in the second case (end B) the rod will rotate
counterclockwise.
In this chapter, we review and discuss the analysis of forces and sets of forces (force
systems) as they are applied with mechanical systems. We will consider various represen-
tations of force systems, various kinds of force systems, and various methods of analysis.

6.2 Forces and Moments
If we intuitively define a force as a push or pull applied in some direction at a point, the
force may be represented as a bound vector. The force then has (1) a magnitude, (2) a line
of action (defining its orientation), (3) a sense (push or pull), and (4) a point of application.
Figure 6.2.1 depicts a force F acting at a point P with line of action L.
A moment is defined as the rotational effect of a force about a point. This point is generally
distinct from the points on the line of action of the force. Specifically, the moment M of
O
a force F about a point O is defined as:

D
×
M = p F (6.2.1)
O
where p is a position vector locating any point Q, on the line of action of F, relative to O.
Figure 6.2.2 depicts point O, a typical point Q, vectors p and F, and the line of action L of F.

163