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Module 1: Units and Significant Figures
1.1 The Speed of Light
When we observe and measure phenomena in the world, we try to assign numbers to the
physical quantities with as much accuracy as we can possibly obtain from our measuring
equipment.
For example, we may want to determine the speed of light, which we can
calculate by dividing the distance a known ray of light propagates over its travel time,
distance
speed of light
=
.
(1.1.1)
time
In 1983 the General Conference on Weights and Measures defined the
speed of
light
to be
c
=
299,
792,
458
meters/second
.
(1.1.2)
This number was chosen to correspond to the most accurately measured value of
the speed of light and is well within the experimental uncertainty.
1.2 International System of System of Units
The three quantities – time, length, and the speed of light – are directly
intertwined. Which quantities should we consider as “base” and which ones as “derived”
from the base quantities? For example, are length and time base quantities while speed is
a derived quantity?
This question is answered by convention. The basic system of units used
throughout science
and
technology
today
is
the
internationally
accepted
Système
International
(SI).
It consists of seven base quantities and their corresponding base units:
Mechanics is based on just the first three of these quantities, the MKS or meter
kilogramsecond system. An alternative metric system to this, still widely used, is the so
called CGS system (centimetergramsecond). So far as distance and time measurements
are concerned, there is also wide use of British Imperial units (especially in the USA)
based on the foot (ft), the mile (mi), etc., as units of length, and also making use of the
minute, hour, day and year as units of time.
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View Full DocumentBase Quantity
Base Unit
Length
meter (m)
Mass
kilogram (kg)
Time
second (s)
Electric Current
ampere (A)
Temperature
Kelvin (K)
Amount of Substance
mole (mol)
Luminous Intensity
candela (cd)
We shall refer to the dimension of the base quantity by the quantity itself, for example
dim
length
!
length
!
L,
dim
mass
!
mass
!
M,
dim
time
!
time
!
T.
(1.2.1)
1.3 The Atomic Clock and the Definition of the Second
Isaac Newton, in the
Philosophiae Naturalis Principia Mathematica
(“Mathematical
Principles of Natural Philosophy”), distinguished between time as duration and an
absolute concept of time,
“Absolute true and mathematical time, of itself and from its own nature,
flows equably without relation to anything external, and by another name
is called duration: relative, apparent, and common time, is some sensible
and external (whether accurate or unequable) measure of duration by
means of motion, which is commonly used instead of true time; such as an
hour, a day, a month, a year. ”
1
.
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 Spring '11
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