E1C01 09/14/2010
15:40:35 Page 26
section and placed 1 m apart in vacuum, would produce a force equal to 2 Â 10
À7 newtons per meter
of length between these conductors.
Measure of Substance
The unit of quantity of a substance is defined by the mole. One mole (mol) is the amount of
substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram
of carbon 12.
Luminous Intensity
The intensity of light is defined by the candela. One candela (cd) is the luminous intensity, in a given
direction, of a source that emits monochromatic radiation of frequency 5:40 Â 10
14 hertz and that
has a radiant intensity in that direction of 1/683 watt per steradian.
Derived Units
Other dimensions and their associated units are defined in terms of and derived from the base
dimensions and units (9,12).
Force
From Newton’s law, force is proportional to mass times acceleration:
Force ¼
Mass  Acceleration
g c
where g c is a proportionality constant used to maintain consistency in units.
Force is defined by a derived unit called the newton (N), which is derived from the base
dimensions of mass, length, and time:
1 N ¼ 1
kg À m
s 2
ð1:17Þ
So for this system the value of g c must be 1.0 kg-m/s
2 -N. Note that the resulting expression for
Newton’s second law does not explicitly require the inclusion of g c to make units match and so is
often ignored.
However, in I-P units, the units of force and mass are related through the definition: One poundmass (lb m ) exerts a force of 1 pound (lb) in a standard gravitational field. With this definition,
1 lb ¼
1 lb m
ð
Þ 32:174 ft/s
2
ð
Þ
g c
ð1:18Þ
and g c must take on the value of 32.174 lb m -ft/lb-s
2 . In I-P units, the pound is a defined quantity and
g c must be derived through Newton’s law.
Similarly, in the gravitational mks (metric) system, which uses the kilogram-force (kg f ),
1 kg f ¼
1 kg
ð
Þ 9:80665 m/s
2
ð
Þ
g c
ð1:19Þ
and the value for g c takes on a value of exactly 9.80665 kg-m/s
2 -kg f .
26 Chapter 1 Basic Concepts of Measurement Methods
15:40:35 Page 26
section and placed 1 m apart in vacuum, would produce a force equal to 2 Â 10
À7 newtons per meter
of length between these conductors.
Measure of Substance
The unit of quantity of a substance is defined by the mole. One mole (mol) is the amount of
substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram
of carbon 12.
Luminous Intensity
The intensity of light is defined by the candela. One candela (cd) is the luminous intensity, in a given
direction, of a source that emits monochromatic radiation of frequency 5:40 Â 10
14 hertz and that
has a radiant intensity in that direction of 1/683 watt per steradian.
Derived Units
Other dimensions and their associated units are defined in terms of and derived from the base
dimensions and units (9,12).
Force
From Newton’s law, force is proportional to mass times acceleration:
Force ¼
Mass  Acceleration
g c
where g c is a proportionality constant used to maintain consistency in units.
Force is defined by a derived unit called the newton (N), which is derived from the base
dimensions of mass, length, and time:
1 N ¼ 1
kg À m
s 2
ð1:17Þ
So for this system the value of g c must be 1.0 kg-m/s
2 -N. Note that the resulting expression for
Newton’s second law does not explicitly require the inclusion of g c to make units match and so is
often ignored.
However, in I-P units, the units of force and mass are related through the definition: One poundmass (lb m ) exerts a force of 1 pound (lb) in a standard gravitational field. With this definition,
1 lb ¼
1 lb m
ð
Þ 32:174 ft/s
2
ð
Þ
g c
ð1:18Þ
and g c must take on the value of 32.174 lb m -ft/lb-s
2 . In I-P units, the pound is a defined quantity and
g c must be derived through Newton’s law.
Similarly, in the gravitational mks (metric) system, which uses the kilogram-force (kg f ),
1 kg f ¼
1 kg
ð
Þ 9:80665 m/s
2
ð
Þ
g c
ð1:19Þ
and the value for g c takes on a value of exactly 9.80665 kg-m/s
2 -kg f .
26 Chapter 1 Basic Concepts of Measurement Methods