Page 28 - Electric Machinery Fundamentals

4 ELECTRlC MACHINERY FUNDAMENTALS

Similarly, angular velocity w is defined as the rate of change of the angular dis-
placement e with respect to time,
de
w=- (1-2)
dt
If the units of angular position are radians, then angular velocity is measured in ra-
dians per second.
In dealing with ordinary electric machines, engineers often use units other
than radians per second to describe shaft speed. Frequently, the speed is given in
revolutions per second or revolutions per minute. Because speed is such an im-
portant quantity in the study of machines, it is customary to use different symbols
for speed when it is expressed in different units, By using these ditIerent symbols,
any possible confusion as to the units intended is minimized. The following sym-
bols are used in this book to describe angular velocity:

Wm angular velocity expressed in radians per second
1,,, angular velocity expressed in revolutions per second
nm angular velocity expressed in revolutions per minute

The subscript m on these symbols indicates a mechanical quantity, as opposed to
an electrical quantity. If there is no possibility of confusion between mechanical
and electrical quantities, the subscript is often left out.
These measures of shaft speed are related to each other by the following
equations:
(1-3a)

(1-3b)

Angnlar Acceleration a

Angular acceleration is the rate of change in angular velocity with respect to
time. It is assumed positive if the angular velocity is increasing in an algebraic
sense. Angular acceleration is the rotational analog of the concept of accelera-
tion on a line. Just as one-dimensional linear acceleration is defined by the
equation
dv
a=- (1-4)
dt
angular acceleration is defined by

dw
a: =~ (1- 5)
dt
If the units of angular velocity are radians per second, then angular acceleration is
measured in radians per second squared.