Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

10.3 Moment, Torque —Force Acting at a Distance 263

this force will make the door rotate about its hinges. In mechanics, this tendency of force is mea-

sured in terms of a moment of a forceabout an axis or a point.Moment has both direction and

magnitude. In our example, the direction is defined by the sense of rotation of the door. As

shown in Figure 10.11, looking at the door from the top, when you open the door by applying

the force shown, the direction of moment is clockwise, and when you close the same door, the

force creates a counterclockwise moment. The magnitude of the moment is obtained from the

product of the moment arm times the force. Moment arm represents the perpendicular distance

between the line of action of the force and the point about which the object could rotate.

In this book, we will only consider the moment of a force about a point. Most of you will

take a mechanics class, where you will learn how to calculate the magnitude and the direction

of moment of a force about an arbitrary axis. For an object that is subject to force F, the rela-

tionship between the line of action of the force and moment arm is shown in Figure 10.12. The

magnitude of moment about arbitrary pointsA,B, andCis given by

(10.8)

(10.9)

(10.10)

Note that the moment of the forceFabout pointCis zero because the line of action of the force

goes through pointC, and thus the value of moment arm is zero. When calculating the sum of

moments created by many forces about a certain point, make sure you use the correct moment

arm for each force, and also make sure to ask yourself whether the tendency of a given force is

MC 0



MBd 2 F

MAd 1 F (^) 
Open
Distance
Force
■Figure 10.11 Moment of the force created by someone opening or closing a door.
A
C
B
F
d 2
d 1
Line of
action
■Figure 10.12
The moment of the force FF
about pointsA,B, andC.
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