Page 31 - Electric Machinery Fundamentals

INTRODUCTION TO MACHINERY PRINCIPLES 7

A similar equation describes the relationship between the torque applied to
an object and its resulting angular acceleration. This relationship, called Newton s
law of rotation, is given by the equation
(1-8)
where 'T is the net applied torque in newton-meters or pound-feet and a is the re-
sulting angular acceleration in radians per second squared. The term J serves the
same purpose as an object's mass in linear motion. It is called the moment of
inertia of the object and is measured in kilogram-meters squared or slug-feet
squared. Calculation of the moment of inertia of an object is beyond the scope of
this book. For information about it see Ref. 2.

WorkW
For linear motion, work is defined as the application of aforce through a distance.
In equation form,
W = J F dr (1-9)

where it is assumed that the force is collinear with the direction of motion. For the
special case of a constant force applied collinearly with the direction of motion,
this equation becomes just

W=Fr (1-10)
The units of work are joules in SI and foot-pounds in the English system.
For rotational motion, work is the application of a torque through an angle.
Here the equation for work is
W = J Tde (1-11)

and if the torque is constant,
(1-12)

PowerP
Power is the rate of doing work, or the increase in work per unit time. The equa-
tion for power is
p =dW (1-13)
dt

It is usually measured in joules per second (watts), but also can be measured in
foot-pounds per second or in horsepower.
By this definition, and assuming that force is constant and collinear with the
direction of motion, power is given by

p = dd; = ~ (Fr) = F (~~) = Fv (1-14)