7.6 Area 171
7 7..4 (^4) RRaaddiiaannss aass aa RRaattiioo ooff TTwwoo LLeennggtthhss
Consider the circular arc shown in Figure 7.5. The relationship among the arc length,S,
radius of the arc,R, and the angle in radians, u, is given by
(7.1)
Note that radians represents the ratio of two lengths and thus is unitless. As you will learn later
in your physics and dynamics classes, you can use Equation (7.1) as the basis for establishing a
relationship between the translational speed of a point on an object and its rotational speed. Also
note 2pradians is equal to 360 degrees, and 1 radian is equal to 57.30 degrees.
7 7..5 (^5) SSttrraaiinn aass aa RRaattiioo ooff TTwwoo LLeennggtthhss
When a material (e.g., in the shape of a rectangular bar) is subjected to a tensile load (pulling
load), the material will deform. The deformation, L, divided by the original length,L, is called
normal strain, as shown in Figure 7.6. In Chapter 10, we will discuss the concepts of stress and
strain in more detail. We will also explain how stress and strain information is used in engi-
neering analysis. But for now, remember that strain is the ratio of deformation length to orig-
inal length and thus is unitless.
(7.2)
Note that strain is another length-related engineering variable.
7 7..6 6 AArreeaa
Area is a derived, or secondary, physical quantity. It plays a significant role in many engineer-
ing problems. For example, the rate of heat transfer from a surface is directly proportional to
the exposed surface area. That is why a motorcycle engine or a lawn mower engine has extendedstrain
¢L
L
u
S 1
R 1
S 2
R 2
R 1
S 1
S 2
R 2
■Figure 7.5
The relationship among arc
length, radius, and angle.L
L
Load
■Figure 7.6
A bar subjected to a pulling load.Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀