Systems of Units. Some Important Conversion Factors
The most important systems of units are shown in the table below. The mks system is also known as
the International System of Units(abbreviated SI), and the abbreviations sec (instead of s),
gm (instead of g), and nt (instead of N) are also used.
System of units Length Mass Time Force
cgs system centimeter (cm) gram (g) second (s) dyne
mks system meter (m) kilogram (kg) second (s) newton (nt)
Engineering system foot (ft) slug second (s) pound (lb)
1 inch (in.) &amp#22.540000 cm 1 foot (ft) &amp#212 in. &amp#230.480000 cm
1 yard (yd) &amp#23 ft &amp#291.440000 cm 1 statute mile (mi) &amp#25280 ft &amp#21.609344 km
1 nautical mile &amp#26080 ft &amp#21.853184 km
1 acre &amp#24840 yd
2
&amp#24046.8564 m
2
1 mi
2
&amp#2640 acres &amp#22.5899881 km
2
1 fluid ounce &amp#21/128 U.S. gallon &amp#2231/128 in.
3
&amp#229.573730 cm
3
1 U.S. gallon &amp#24 quarts (liq) &amp#28 pints (liq) &amp#2128 fl oz &amp#23785.4118 cm
3
1 British Imperial and Canadian gallon &amp#21.200949 U.S. gallons &amp#24546.087 cm
3
1 slug &amp#214.59390 kg
1 pound (lb) &amp#24.448444 nt 1 newton (nt) &amp#210
5
dynes
1 British thermal unit (Btu) &amp#21054.35 joules 1 joule &amp#210
7
ergs
1 calorie (cal) &amp#24.1840 joules
1 kilowatt-hour (kWh) &amp#23414.4 Btu &amp#23.6•10
6
joules
1 horsepower (hp) &amp#22542.48 Btu/h &amp#2178.298 cal/sec &amp#20.74570 kW
1 kilowatt (kW) &amp#21000 watts &amp#23414.43 Btu/h &amp#2238.662 cal/s
°F &amp#2°C•1.8 &amp#332 1° &amp#260
&amp#4&amp#23600&amp#5&amp#20.017453293 radian
For further details see, for example, D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics.9th ed., Hoboken,
N. J: Wiley, 2011. See also AN American National Standard, ASTM/IEEE Standard Metric Practice, Institute of Electrical and
Electronics Engineers, Inc. (IEEE), 445 Hoes Lane, Piscataway, N. J. 08854, website at www.ieee.org.
fendpaper.qxd 11/4/10 12:05 PM Page 2
Integration
&amp#2uv&amp#4dx&amp#2uv&amp#6&amp#2u&amp#4vdx (by parts)
&amp#2x
n
dx&amp#2&amp#3c(n&amp#7&amp#61)
&amp#2dx&amp#2ln&amp#3x&amp#3&amp#3c
&amp#2e
ax
dx&amp#2e
ax
&amp#3c
&amp#2sinxdx&amp#2&amp#6cosx&amp#3c
&amp#2cosxdx&amp#2sinx&amp#3c
&amp#2tanxdx&amp#2&amp#6ln&amp#3cosx&amp#3&amp#3c
&amp#2cotxdx&amp#2ln&amp#3sinx&amp#3&amp#3c
&amp#2secxdx&amp#2ln&amp#3secx&amp#3tanx&amp#3&amp#3c
&amp#2cscxdx&amp#2ln&amp#3cscx&amp#6cotx&amp#3&amp#3c
&amp#2&amp#2arctan&amp#3c
&amp#2&amp#2arcsin&amp#3c
&amp#2&amp#2arcsinh&amp#3c
&amp#2&amp#2arccosh&amp#3c
&amp#2sin
2
xdx&amp#2
1_
2
x&amp#6
1_
4
sin 2x&amp#3c
&amp#2cos
2
xdx&amp#2
1_
2
x&amp#3
1_
4
sin 2x&amp#3c
&amp#2tan
2
xdx&amp#2tanx&amp#6x&amp#3c
&amp#2cot
2
xdx&amp#2&amp#6cotx&amp#6x&amp#3c
&amp#2lnxdx&amp#2xlnx&amp#6x
...
...
ener: © Denis Jr. Tangney/iStockphoto
Part B Opener: © Jill Fromer/iStockphoto
Part C Opener: © Science Photo Library/Photo Researchers, Inc
Part D Opener: © Rafa Irusta/iStockphoto
Part E Opener: © Alberto Pomares/iStockphoto
Chapter 19, Figure 437: © Eddie Gerald/Alamy
Part F Opener: © Rainer Plendl/iStockphoto
Part G Opener: © Sean Locke/iStockphoto
Appendix 1 Opener: © Ricardo De Mattos/iStockphoto
Appendix 2 Opener: © joel-t/iStockphoto
Appendix 3 Opener: © Luke Daniek/iStockphoto
Appendix 4 Opener: © Andrey Prokhorov/iStockphoto
Appendix 5 Opener: © Pedro ellano/iStockphoto
P1
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Some Constants
e&amp#22.71828 18284 59045 23536
&amp#2e
&amp#3&amp#21.64872 12707 00128 14685
e
2
&amp#27.38905 60989 30650 22723
&amp#3&amp#23.14159 26535 89793 23846
&amp#3
2
&amp#29.86960 44010 89358 61883
&amp#2&amp#3
&amp#3&amp#21.77245 38509 05516 02730
log
10&amp#3&amp#20.49714 98726 94133 85435
ln
&amp#3&amp#21.14472 98858 49400 17414
log
10e&amp#20.43429 44819 03251 82765
ln 10 &amp#22.30258 50929 94045 68402
&amp#22
&amp#3&amp#21.41421 35623 73095 04880
&amp#2
3
2&amp#3&amp#21.25992 10498 94873 16477
&amp#23
&amp#3&amp#21.73205 08075 68877 29353
&amp#2
3
3&amp#3&amp#21.44224 95703 07408 38232
ln 2 &amp#20.69314 71805 59945 30942
ln 3 &amp#21.09861 22886 68109 69140
&amp#4&amp#20.57721 56649 01532 86061
ln
&amp#4&amp#2&amp#50.54953 93129 81644 82234
(see Sec. 5.6)
1°&amp#20.01745 32925 19943 29577 rad
1 rad &amp#257.29577 95130 82320 87680°
&amp#257°17
&amp#644.806&amp#7
Greek Alphabet
&amp#8Alpha Nu
Beta &amp#11Xi
&amp#4,&amp#12Gamma Omicron
&amp#14,&amp#15Delta &amp#3Pi
&amp#16, &amp#17Epsilon &amp#18Rho
&amp#19Zeta &amp#20,&amp#21Sigma
&amp#22Eta &amp#23Tau
&amp#24,&amp#25,&amp#26Theta &amp#27,&amp#28Upsilon
&amp#29Iota &amp#30,&amp#31, Phi
! Kappa Chi
#,$Lambda %,&ampPsi
&amp#39Mu (,)Omega
Polar Coordinates
x&amp#2rcos &amp#24 y&amp#2rsin &amp#24
r &amp#2&amp#2x
2
*y&amp#3
2
&amp#3 tan &amp#24&amp#2
dx dy&amp#2rdrd
&amp#24
Series
&amp#2&amp#4
`
m&amp#20
x
m
(&amp#5x&amp#5+1)
e
x
&amp#2&amp#4
`
m&amp#20
sinx&amp#2&amp#4
`
m&amp#20
cosx&amp#2&amp#4
`
m&amp#20
ln (1 &amp#5x) &amp#2&amp#5&amp#4
`
m&amp#21
(&amp#5x&amp#5+1)
arctanx&amp#2
&amp#4
`
m&amp#20
(&amp#5x&amp#5+1)
Vectors
a•b&amp#2a
1b
1*a
2b
2*a
3b
3
a &amp#2b&amp#2ll
grad ƒ &amp#2,ƒ &amp#2i* j* k
divv&amp#2,•v&amp#2**
curlv&amp#2,&amp#2v&amp#2ll
k
-
.
.
z
-
v
3
j
-
.
.
y
-
v
2
i
-
.
.
x
-
v
1
.v
3
-
.z
.v
2
-
.y
.v
1
-
.x
.ƒ
-
.z
.ƒ
-
.y
.ƒ
-
.x
k
a
3
b
3
j
a
2
b
2
i
a
1
b
1
(&amp#51)
m
x
2m*1
2m*1
x
m
-
m
(&amp#51)
m
x
2m
(2m)!
(&amp#51)
m
x
2m*1
(2m*1)!
x
m
-
m!
1
-
1 &amp#5x
y
-
x
bendpaper.qxd 11/4/10 12:24 PM Page 2
