Page 27 - Electric Machinery Fundamentals

INTRODUCTION TO MACHINERY PRlNCIPLES 3

in daily use for a long time. Engineering students and working engineers in the
United States today must be familiar with both sets of units, since they will en-
counter both througbout their professional lives. Therefore, this book includes
problems and examples using both SI and English units. The emphasis in the ex-
amples is on Sl units, but the older system is not entirely neglected.

Notation

In this book, vectors, electrical phasors, and other complex values are shown in bold
face (e.g., F), while scalars are shown in italic face (e.g., R). In addition, a special
font is used to represent magnetic quantities such as magnetomotive force (e.g., g).

1.3 ROTATIONAL MOTION, NEWTON'S
LAW, AND POWER RELATIONSIDPS

Almost all electric machines rotate about an axis, called the shaft of the machine.
Because of the rotational nature of machinery, it is important to have a basic un-
derstanding of rotational motion. This section contains a brief review of the con-
cepts of distance, velocity, acceleration, Newton's law, and power as they apply to
rotating machinery. For a more detailed discussion of the concepts of rotational
dynamics, see References 2, 4, and S.
In general, a three-dimensional vector is required to completely describe the
rotation of an object in space. However, machines normally turn on a fIxed shaft, so
their rotation is restricted to one angular dimension. Relative to a given end of the
machine's shaft, the direction of rotation can be described as either clockwise (eW)
or counterclockwise (CCW). For the purpose of this volume, a counterclockwise an-
gle of rotation is assumed to be positive, and a clockwise one is assumed to be nega-
tive. For rotation about a fixed shaft, all the concepts in this section reduce to scalars.
Each major concept of rotational motion is defined below and is related to
the corresponding idea from linear motion.

Angular Position ()
The angular position 9 of an object is the angle at which it is oriented, measured
from some arbitrary reference point. Angular position is usually measured in
radians or degrees. It corresponds to the linear concept of distance along a line.

Angular Velocity lJ)
Angular velocity (or speed) is the rate of change in angular position with respect
to time. It is assumed positive if the rotation is in a counterclockwise direction.
Angular velocity is the rotational analog of the concept of velocity on a line. One-
dimensional linear velocity along a line is defined as the rate of change of the dis-
placement along the line (r) with respect to time.

dr
v = dt (1-1)