Anything that is measurable in this physical world is called
a physical quantity. For example, the length of a table can be measured. Here,
length is a physical quantity. The mass of your body can be measured, mass is a
physical quantity. The time during which you are reading this book can be
measured, time is a physical quantity. If you apply force to lift something,
that force can be measured. So force is a physical quantity. There are many
such quantities in this physical world. Among these, it is seen that there are
a few quantities which can be measured without any help from any other
quantities. These quantities are `fundamental quantities’. For instance, to
measure the length of a table, you need to measure only the length. To measure
this length, there is no need of measuring any other quantity. So, length is a
fundamental quantity. On the other hand, measurement of some quantities needs
the help of other quantities. For example, to measure the density of copper bar
it is necessary to measure the mass and volume of a piece of copper bar and
then mass is to be divided by the volume. Again, to measure the volume, the
length, the breadth and the height are to be measured, that is, lengths are to
be measured three times in three directions. So, it is seen that, there are
certain quantities which are fundamental. They do not depend on other
quantities. These are called fundamental quantities.
So, the physical quantities which are independent or neutral
that is, they do not depend on other quantity, rather other quantities depend
on them, are called fundamental quantities. Scientists have identified seven
such quantities as fundamental quantities which are used in all branches of
science for measurement. These are (1) length (2) mass (3) time (4) temperature (5) electric current
(6) luminous intensity and (7) amount of substance.
All other quantities may be derived from fundamental
quantities that mean, these are obtained from the product or quotient of one or
more fundamental quantities. These are called derived quantities or compound
quantities.
So, the quantities depend on fundamental quantities or
obtain from fundamental quantities are called derived quantities. Velocity,
acceleration, force, work, heat, electric current etc. are derived quantities
since these are obtain from fundamental quantities.
For
instance,
Hence, force is a derived quantity.
Units of measurement
Measurement is related to most of our daily activities.
Moreover, we need accurate measurement for various research works. The act of
measuring something in our daily life is called measurement. In general,
measurement means the act of determining the quantity of something. For
example, the distance of the school from Jon’s home is 700 meters. Rahat has
bought 5 Kilograms of rice from the shop. Alee takes 50 seconds to go to the
school’s office room. Here, 700 meters is the distance, 5 kilograms is the mass
of rice and 50 seconds is the amount of time spent. We need two things to
measure anything. One is number and another is unit.
A standard is essential, comparing with which any
measurement is done. These standard quantities are called the unit of
measurement. Say, the length of a rod is 4 meters. Here, meter is a unit of
length and 1 meter is a specific measurement. Therefore, length of the rod 4
meters means length of the rod is 4 times of this 1 meter’s unit. There are
different units for measurement of time, volume, velocity, mass, force, energy,
temperature, electric current etc. These units have been designed in such way
that they can be convenient and can be easily and accurately reproduced. Except
some units all these units are interrelated with one another.
Fundamental SI units
We can select fundamental units according to your liking,
since the units of fundamental quantities do not depend on other units. But our
selection must have international recognition. It should have some
characteristics as well. For example, it should be unchangeable, that is,
independent of place, time and person. It will not change due to passage of
time or any other natural change. It could be reproduced easily. The standard
of fundamental units that were accepted in 1960, while introducing the SI
system of units, were changed later on in some cases in order to attain
suitable characteristics. But no change was brought in values of the units. For
example, at present, meter is defined in terms of distance traveled by light.
Earlier, meter was defined using wavelength of a kind of light. Prior to it,
the length of a rod kept at Sevres near Paris in France was taken as the
standard of meter. The latest accepted standard of fundamental units in
International System are described below
Unit of mass: Kilogram: The kilogram is the mass equal to that
of a cylinder made of platinum-iridium alloy (International prototype
kilogram) kept at the International Bureau of Weights and Measures at Severs, France.
The diameter of this cylinder is 3.9 cm; its height is also 3.9 cm.
Unit of time: Second: The time
required to complete 9 192 631 770 vibrations by a cesium-133 atom is
called one second (s).
Unit of electric current : Ampere : The ampere
is that current which produces a force of 2x10-7 Newton per
meter in vacuum between two parallel infinitely long conductors of negligible
cross-sectional area 1 meter apart when each conductor carries the same
current.
Unit of amount of substance: Mole: The mole is
defined as the amount of substance which contains elementary entities
(e.g. atoms, molecules, ions, electrons etc. or any specified group of these
particles) equal to the number of atoms in 0.012 kilogram of Carbon-12.
Fundamental
quantities and their units
|
SL No
|
Name of
Physical Quantities
|
Symbol
of
|
SI Unit
|
Symbol
|
|
|
|
quantities
|
|
for unit
|
|
1
|
Length
|
L
|
meter
|
m
|
|
2
|
Mass
|
m
|
kilogram
|
kg
|
|
3
|
Time
|
T
|
second
|
s
|
|
4
|
Temperature
|
θ,T
|
Kelvin
|
k
|
|
5
|
Electric
current
|
I
|
ampere
|
A
|
|
6
|
Luminous
intensity
|
IV
|
candela
|
cd
|
|
7
|
Amount
of substance
|
n
|
mole
|
mol
|
Multiple and sub-multiple of units
Sometimes it is beneficial to use the fractions or multiples
of fundamental units. When the value of a quantity is very big or small, the
prefixes mentioned in the following table is very essential. For example, if we
consider the distance of two molecules of air, we can see the distance is very
small and it is 0.00000001 m. If we use this number frequently, we have to be
careful about the number of zero’s every time to see whether it is mentioned
accurately or not. But if we mentioned the number by a prefix we will write
0.01µm instead of
0.00000001m. Here the symbol µrefers
to the prefix 10-6.
Similarly if we mentioned the power of newly built electricity production
center is 2000 x 106
w = 2000mw instead of 2000000000w, it will be more convenient. The use of
indices of 10 before the unit of the following prefixes is approved to be use
in SI system.
|
|
Multiple/Sub-
|
Factor
|
Symbol
|
Example
|
|
|
|
|
multiple
|
|
|
|
|
|
|
Multiple
|
exa
|
1018
|
E
|
1 exa
meter = 1 E.M = 1018m
|
|
|
|
peta
|
1015
|
P
|
1 peta
meter = 1 pm = 1015m
|
|
||
|
tera
|
1012
|
T
|
1 tera
gram = 1 tg = 1012g
|
|
||
|
giga
|
109
|
G
|
1 giga
bite = 1 GB = 109B
|
|
||
|
|
mega
|
106
|
M
|
1 mega
watt = 1 MW = 109W
|
|
|
|
|
kilo
|
103
|
K
|
1 kilo
volt = 1 kV = 103V
|
|
|
|
|
hecto
|
102
|
h
|
1 hecto
joule = 1 hj = 102j
|
|
|
|
Su
|
deca
|
101
|
da
|
1 deca
newton = 1 da N =101N
|
|
|
|
|
desi
|
10-1
|
d
|
1 deci
ohm = 1 dΩ = 10-1Ω
|
||
|
|
centi
|
10-2
|
c
|
1
centimeter = 1 cm = 10-2m
|
||
|
|
milli
|
10-3
|
m
|
1 mili
ampere = 1 mA = 10-3A
|
||
|
|
micro
|
10-6
|
µ
|
1 micro
volt = 1 µV = 10-6V
|
||
|
|
nano
|
10-9
|
n
|
1 nano
second = 1ns = 10-9s
|
||
|
|
pico
|
10-12
|
p
|
1 pico
farad = 1 pf = 10-12f
|
||
|
|
femto
|
10-15
|
f
|
1 femto
meter = 1 fm = 10-15m
|
||
|
|
atto
|
10-18
|
a
|
1 atto
watt = 1 aW = 10-18W
|
||
When a number is expressed as the product of any power of 10
and another number between 1 and 10, it is called a scientific notation. As for
example, 6733000000 are 6.733 x 109 and 0.00000846 is 8.46 x 10-6.
So it is seen that the original number is obtained from a number expressed in
notation by placing the decimal point to the right by the number of digits
equal to the power of 10 if the power is positive and to the left if the power
is negative.
In the case of numbers expressed in scientific notation the
following general rule of multiplication is applicable:
10m x 10n = 10m+n
Here, m and n may be any positive or negative number. For
example, 106 x 107 = 1013, 107 x 10-20
= 10-13
Dimensions
By now, we know that a physical quantity is a
combination of one or more fundamental quantities. So, any physical quantities
may be expressed as the product of one or more fundamental quantities of
different powers. The power of fundamental quantities in a physical quantity is
called its dimension.
Now, if we take that the dimension of length as L, the dimension
of mass as M and the dimension of time as T, then the dimension of force is
ML/T2 or MLT-2 , that is, force has the dimension of mass
(1) dimension of length (1) dimension of time (-2). (The equation to express
the dimension of physical quantity is called the dimensional equation). Third
bracket [ ] is used to indicate dimensions in any quantity. As for example, the
dimensional equation of force is [ F ] = [ MLT-2 ]
Except these above mentioned three physical quantities of length,
mass and time others dimension of physical quantities are:
The dimension of temperature as θ(Capital
alphabet of Greek letter θ), the
dimension of electric current as I, the dimension of luminous intensity as J
and the dimension of amount of substance as N.
We can verify the validity of any equation or formula by analyzing
dimension. For example, the following equation may be considered:
S = ut + 12
at2
We know that addition, subtraction or equivalence is possible for
any same kind of quantities. Hence every term of an equation must indicate the
same kind of quantity, that is, the dimension of every term must be the same.
Now there are three terms in the above equation, one to the left and two to the
right.
In this equation, s is displacement: its dimension is L, u is
initial velocity; its dimension is L/T = LT-1 ,
a is acceleration ; its dimension is L/T2 = LT-2
, t is time ; its dimension is T.
∴The
dimension is ut = LT-1 x T = L The dimension of at2 = LT-2
x T2 = L
Thus it is seen that the dimension of each of the term on both
sides of the above equation is the same L. Therefore, the equation is valid.
Scientific symbols and notations
Mathematics is said to be the language of physics. We
usually express the laws of physics in the form of mathematical equation and
physicists solved many problems by applying these laws or equations. Various
symbols and notations are used according to the SI system for different
quantities and units. This SI system of units is not only used in physics but
also used in other branches of science now a day for measurement.
The following methods are followed for expressing symbol of units
of different quantities.
1.
The symbol of units is to be expressed by
writing a number and a space after it (actually expresses multiplication) for
expressing the value of a quality. For example “2.21 Kg’’, “7.3 x 102
m2’’, “22 k’’. The sign of % also follows the same rule. However
space after number is not used to express the unit of angle i.e. degree,
minute, and second (°, ` and " ).
2.
Derived unit produced by multiplication is
expressed using a space between two units e.g. N m.
3.
Derived unit produced by division is expressed
as negative power e.g. meter/second is expressed as ms-1 .
4.
No punctuation mark or full stop is used with
the notations as – they are not the abbreviated from anything but the form of
mathematical expression.
5.
The symbol of unit is written in Roman type
font, for example m for meter, s for second but the symbol of quantities are
written in italic type font, for example, m for mass, s for displacement etc.
It does not matter what kind of language or font is used after of before of
these symbols and units to express.
6.
The symbols of unit are expressed in small
letters, for example “m’’, “s’’, “mol’’, but capital letters are used to write
the unit which is derived from name of a person, for example, the unit N is
derived from the name of Newton and Pa from Pascal. However, while expressing
full form of unit small letters are used. For example, Newton or Pascal.
7.
As prefix of a unit is the part of it, no
space is used to express its symbol. For example, km for kilometer (k), MW for
megawatt (M) GHz for giga Hertz (G). More than one prefix is not allowed to use
such as µµF, but pF.
8.
Prefixes more than kilo (103) must
be in capital letter.
9.
The symbols of units are always singular. Such
as ``25 kg’’ instead of ``25 kgs’’.
10.
Line-break should be avoided for expressing
any number or compound unit or number and unit. Only for important purposes
line-break may be acceptable.
End
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