A system of units is a collection of units in which certain units are
chosen as fundamental and all others are derived from them. This system is also
called an absolute system of units. In most systems, the mass, length, and time
are considered to be fundamental quantities, and their units are called
fundamental units. The following are some systems of units which are in common
use.
·
c.g.s.
system of units: The unit of length is centimetre
(cm). The unit of mass is gram (g). The unit of time is second (s)
·
m.k.s.
system of units: The unit of length is the metre (m). The
unit of mass is the kilogram (kg). The unit of time is second (s)
·
f.p.s.
system of units: The unit of length is a foot (ft). The
unit of mass is a pound (Lb). The unit of time is second (s). This system is no
more in use. This system is also known as Imperial system or the British
Imperial system. Temperature is measured in Fahrenheit.
S.I. System of Units:
In the year 1960, the Eleventh General Conference of Weights and
Measures introduced the International System of Units. The International
Standard Organization (ISO) and the International Electrochemical Commission
endorsed the system in 1962. In October 1971 a replacement of the metric
system of units was done with a new system called Systeme Internationale d’
Unites. The International System of Units, commonly known as the SI system, is
the modern form of the metric system and is the most widely used system of
measurement in the world. It provides a standard and coherent set of units for expressing
physical quantities.
Fundamental Units:
|
Fundamental Quantity |
S.I. Unit |
Symbol |
|
|
1 |
Length |
Metre |
m |
|
2 |
Mass |
Kilogram |
kg |
|
3 |
Time |
Second |
s |
|
4 |
Temperature |
Kelvin |
K |
|
5 |
Electric current |
Ampere |
A |
|
6 |
Luminous intensity |
Candela |
cd |
|
7 |
Amount of substance |
mple |
mol |
Besides these seven basic units, there are two supplementary units. S.I.
unit for the plane angle is radian (rad) and that of solid angle is steradian
(sd).
Supplementary Units:
|
Quantity |
S.I. Unit |
Symbol |
|
|
1 |
Plane angle |
radian |
rad |
|
2 |
Solid angle |
steradian |
sr |
This system of units is an improvement and extension of the traditional
metric system. Now, this system of units has replaced all other systems of
units in all branches of science, engineering, industry, and technology.
Guidelines for Writing SI Units
and Their Symbols:
·
All units and their symbols should be
written in small case letters e.g. centimetres (cm), metre (m), kilogram per metre
cube ( kg m-3).
·
The units named after scientists are not
written with a capital initial letter but its symbol is written in capital
letter. Thus the unit of force is written as ‘newton’ or’ N’ and not as
‘Newton’. Similarly unit of work and energy is joule (J), S.I. unit of electric
current is ampere (A). The S.I. nit of pressure is pascal (Pa) and that of
temperature is kelvin (K).
·
No full stop should be placed after the
symbol.
·
The denominators in a compound unit should
be written with negative powers. Thus an index notation should be used to write
a derived unit. for example unit of velocity should be written as ms-1 instead of m/s. The unit of density is kilogram per metre cube (
kg m-3 and
not kg/m3)
·
No plural form of a unit or its symbol
should be used. example 5 newtons should be written as 5 N and not as 5 Ns.
·
A compound unit obtained from units of two
or more physical quantities is written either by putting a dot or leaving a
space between symbols of two units. Example unit of torque is newton metre is
written as Nm ot N.m. Unit of impulse is newton second is written as N s or
N.s.
·
Some space should be maintained between
the number and its unit
Advantages of S.I. System of Units:
·
Units are simple to express
·
This system uses only one unit for one physical
quantity. Hence it is a rational system of units.
·
Units of many physical quantities are
related to each other through simple and elementary relationships For
example 1 ampere = 1 volt / 1 ohm.
·
It is a metric system of units. There is a
decimal relationship between the units of the same quantity and hence it is
possible to express any small or large quantity as a power of 10. i.e.
inter-conversion is very easy. For e.g. 1kg = 1000 gm
= 10³ gm
·
The physical quantities can be expressed
in terms of suitable prefixes.
·
a joule is a unit of all forms of energy
and it is a unit of work. Hence it forms a link between mechanical and
electrical units. Hence S.I. the system is a rational system because it uses
only one unit for one physical quantity.
·
This system forms a logical and
interconnected framework for all measurements in science, technology, and
commerce.
·
All derived units can be obtained by
dividing and multiplying the basic and supplementary units and no numerical
factors are introduced as in another system of units. Hence S.I. system of
units is a coherent system. Hence S.I. system of units is used worldwide.
General Steps to Find Derived
Unit:
·
Step -1 Write the formula for the quantity
whose unit is to be derived.
·
Step -2 Substitute units of all the
quantities in one system of units in their fundamental or standard form.
·
Step -3 Simplify and obtain derive unit of
the quantity.
Example: To find the unit of velocity.
Velocity is a derived quantity.
Hence its unit is a derived unit.
The velocity is given by,
velocity = displacement/time
S.I. unit of velocity = S.I.
unit of displacement/ S.I. unit of time = m/s
Thus S.I. unit of velocity is
m/s
Definitions of Fundamental Units in S. I. System:
1 metre:
·
The unit of length is a
metre. Its symbol is ‘m’.
·
The distance travelled by electromagnetic
waves in the vacuum in 1/299, 792, 458 seconds is called 1 metre. The
denominator is the velocity of light in the vacuum which is in m/s and is known
accurately.
·
One metre is 1,650, 763.73 times the
wavelength of orange light emitte by a krypton atom at normal pressure. The
wavelength of light is precisely defined in terms of electron transition in an
atom, is easily reproducible and is not affected by the change in place, time,
temperature and pressure, etc. Hence metre is defined in terms of wavelength of
orange light.
1 kilogram:
·
The unit of mass is a
kilogram. Its symbol is ‘kg’.
·
1 kilogram is defined is the total mass of
5.0188 × 1025 atoms of C12 isotopes of carbon. Or The mass of a cylinder made
up of platinum-iridium alloy kept at the International Beuro of Weights and
Measure is defined as 1 kilogram. Reason for Using Platinum iridium alloy for
the cylinder is that it is least affected by environment and time.
1 second:
·
The unit of time is second. Its symbol
is ‘s’.
·
1 second is a time duration of
9,192,631,770 periods of the radiation corresponding to the transition between
two hyperfine levels of the ground state of the Cesium-133 atom. Period of
vibration of the atom of Cesium – 133 is used for defining the standard
of time because the period of vibration of the atom of Cesium – 133 are
precisely defined, is easily reproducible and is not affected by a change in
place, time, temperature and pressure, etc.
1-degree kelvin:
·
The unit of temperature is degree
kelvin. Its symbol is ‘K’.
·
1-degree kelvin is a fraction 1/ 273.16 of
the thermodynamic temperature of the triple point of the water. The triple
point of the water is a temperature at which ice, water, and water vapour are
in equilibrium.
1 candela:
·
The unit of luminous intensity is
candela. Its symbol is ‘cd’.
·
1 candela is luminous intensity in the
normal direction of a surface of area 1/600000 m2 of a black body at the freezing point of platinum under pressure
of 1.01325 × 105 N/m2.
1 ampere:
·
The unit of electric current is the
ampere. Its symbol is ‘A’.
·
1 ampere is the constant current, which is
maintained in each of two infinitely long straight parallel conductors of a
negligible cross-section, situated one metre apart in vacuum, will produce
between the conductors a force of 2 × 10-7 N/m.
1 mole:
·
The unit of the amount of substance is
mole. Its symbol is ‘mol’
·
1 mole is the amount of substance which
contains as many elementary entities (atoms, molecules, ions, electrons, etc.)
as there are atoms in 0.012 kg of pure C12. The number of entities in one mole
is 6.02252 X 1023. It is
called as Avagadro’s number.
1 radian:
·
The unit of plane angle is the radian. Its
symbol is ‘rad’
·
One radian is defined as the angle
subtended at the centre of a circle by an arc equal in length to the radius of
the circle.
1 steradian:
·
The unit of solid angle is
steradian. Its symbol is ‘sr’
·
One steradian is defined as the solid
angle that encloses a surface on the sphere of an area equal to the square of
its radius.
·
Maintaining
Uniformity of Standards
An international body Conference Generale des Poids et Measures or CGPM
(General Conference of Weight and Measures) has been given the authority to
decide the standards and units by international agreement. It holds its
meetings and any change in the standard units are communicated through the
publications of the Conference.
India adopted the metric system of units in 1956 by Parliament Act
“Weights and Measures Act- 1956”. The function of manufacturing, maintaining,
monitoring, and improving the standards of measurements is discharged by the
National Physical Laboratory (NPL), New Delhi. The uniformity in standards is
maintained as follows:
·
Measures (e.g. balances and weights) used
by shopkeepers are expected to be certified by the Department of Measures and
Weights of the local government.
·
The working standards of these local
departments have to be calibrated against the state-level standards, or any
laboratory which is entitled to do so.
·
The state-level laboratories are required
to get their standards calibrated from the National Physical Laboratory at the
national level, which is equivalent to international standards. Thus,
measurements made at any place in the world are connected with the
international system.
Prefixes Used in SI System:
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