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

7.1 Length as a Fundamental Dimension 163

All of us, at one time or another, have experienced not knowing where we are going. In

other words, we were lost! The smarter ones among us use a map or stop and ask someone for

directions and distances (xandycoordinates) to the desired place. An example of using a map

to locate a place is shown in Figure 7.2. Coordinate systems are also integrated into software that

drives computer numerically controlled (CNC) machines, such as a milling machine or a lathe

that cuts materials into specific shapes.

Now that you understand the importance of the length dimension, let us look at its divisions

or units. There are several systems of units in use in engineering today. We will focus on two of

these systems: the International System of Units (SI) and the United States Customary units.

The unit of length in SI is the meter ( m). We can use the multiples and fractions of this unit

according to Table 6.2. Common multipliers of the meter are micrometer (m), millimeter

( mm), centimeter (cm), and kilometer (km). Recall from our discussion of units and multipli-

cation prefixes in Chapter 6 that we use these multiplication prefixes to keep the numbers man-

ageable. The International System of Units is used almost universally, except in the United States.

The unit of length in the U.S. Customary system is foot (ft). The relation between foot and meter

units is given by 1 ft0.3048 m. Table 7.1 shows other commonly used units and their

z

z

x

y

x

y

A

0

Cartesian system

(x, y, z)

z

z

r

x

y

A

Cylindrical system

(r, , z)



z

r

x

y

A

Spherical system

(r, , )





0

0

■Figure 7.1

Examples of coordinate systems.

To locate an object at pointA, with respect to

the origin (point 0) of the Cartesian system,

you move along thexaxis byxamount (or

steps) and then you move along the dashed

line parallel to theyaxis byyamount. Finally,

you move along the dashed line parallel to the

zdirection byzamount. How would you get

to pointAusing the Cylindrical or Spherical

system? Explain.

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