1  12 Physics and the Laws of Nature & Units of Length, Mass, and Time
The study of
physics
deals with the fundamental laws of nature and many of their applications.
These laws govern the behavior of all physical phenomena. We describe the behavior of physical
systems using various quantities that we create for this purpose; however, there are three
quantities —
length
,
mass
, and
time
— that we take as fundamental quantities and we use
these three to create other quantities.
We define a system of units for these quantities so that we can specify how much length, mass,
or time we have. The system of units used in this book is the
SI
, which stands for Système
International. In this system the unit of length is the
meter
(m), the unit of mass is the
kilogram
(kg), and the unit of time is the
second
(s). This system of units is still sometimes referred to by
its former name, the mks system.
SI units are based on the metric system. An important aspect of this system is its hierarchy of
prefixes used for quantities of different magnitudes. Certain of these prefixes are used very
frequently in physics, so you should become very familiar with them. Some of the more common
ones are listed here:
Power Prefix Symbol
10
15
femto
f
10
12
pico
p
10
9
nano
n
10
6
micro
µ
10
3
milli
m
10
2
centi
c
10
3
kilo
k
10
6
mega
M
Exercise 11 Metric Prefixes
Write the following quantities using a convenient metric prefix.
(a)
0.00025 m,
(b)
25,000 m,
(c)
250 m,
(d)
250,000,000 m,
(e)
.0000025 m
Solution
(a)
0.25 mm
(b)
25 km
(c)
0.25 km
(d)
250 Mm
(e)
2.5 µm
Practice Quiz
1.
Which of the following quantities is not one of
the fundamental quantities?
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1
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your answer: speed
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13 Dimensional Analysis
In physics we derive the physical quantities of interest from the set of fundamental quantities of
length, mass, and time. The
dimension
of a quantity tells us what
type
of quantity it is. When
indicating the dimension of a quantity only, we use capital letters enclosed in brackets. Thus, the
dimension of length is represented by [L], mass by [M], and time [T].
We use many equations in physics, and these these equations must be dimensionally consistent.
It is extremely useful to perform a dimensional analysis on any equation about which you are
unsure. If the equation is not dimensionally consistent, it cannot be a correct equation. The rules
are simple:
•
Two quantities can be added or subtracted only if they are of the same dimension.
•
Two quantities can be equal only if they are of the same dimension.
Notice that only the dimension needs to be the same, not the units. It is perfectly valid to write 12
inches = 1 foot because both of them are lengths, [L] = [L], even though their units are different.
However, it is not valid to write
x
inches =
t
seconds because they have different dimensions, [L]
[T].
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 Spring '08
 RAO
 Physics, Scientific Notation, Mass, Velocity

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