Page 29 - Electric Machinery Fundamentals

INTRODUCTION TO MACHI NERY PRINCIPLES 5

I
I I I
• •

F
F T
Torque is counterclockwise

Torque is zero
(a) (b)

FIGURE 1- 1
(a) A force applied to a cylinder so that it passes through the axis of rotation. 'j' = O.
(b) A force applied to a cylinder so that its line of action misses the axis of rOlation. Here'T is
counterclockwise.

Torque T
In linear motion, aforce applied to an object causes its velocity to change. In the
absence of a net force on the object, its velocity is constant. The greater the force
applied to the object, the more rapidly its velocity changes.
There exists a similar concept for rotation. When an object is rotating, its
angular ve!odty is constant unless a torque is present on it. The greater the torque
on the object, the more rapidly the angular velocity of the object changes.
What is torque? It can loosely be called the "twisting force" on an object.
Intuitively, torque is fairly easy to understand. Imagine a cylinder that is free to
rotate about its axis. If a force is applied to the cylinder in such a way that its line
of action passes tbrough the axis (Figure I-la), then the cylinder will not rotate.
However, if the same force is placed so that its line of action passes to the right of
the axis (Figure I-I b), then the cylinder will tend to rotate in a counterclockwise
direction. The torque or twisting action on the cylinder depends on (I) the magni-
( tude of the applied force and (2) the distance between the axis of rotation and the
line of action of the force.
The torque on an object is defined as the product of the force applied to the
object and the smallest distance between the line of action of theforce and the object's
axis of rotation. If r is a vector pointing from the axis of rotation to the point