Download Units And Measurements

Units & Measurements
International Systems of Units
Measurement
It is the process of assigning a number to an attribute (or phenomenon) according to a rule
or set of rules.
Units
•
•
A unit is the chosen standard of measurement of quantity, which has the same nature
as the quantity.
To express any physical quantity completely, we need the numerical value and the
unit (u).
Physical quantity = nu
FUNDAMENTAL AND DERIVED UNITS
In mechanics, length, mass and time are the three basic or fundamental
quantities,because
(i) they represent our basic scientific notions,
(ii) there is no other quantity which is simpler to them,
(iii) length, mass and time cannot be obtained from one another,
(iv) all other physical quantities in mechanics can be obtained from them.
Fundamental Units: Units for fundamental or base quantities (length, mass and time)
Derived Units: Units obtained from fundamental units
Example:
Unit of speed (ms−1)
Speed =
Distance
Time
∴ Unit of Speed =
Unit of Distance
Unit of Time
The units of physical quantities like density, momentum, acceleration, force, work, power,
energy, pressure etc. can be expressed in terms of fundamental units of length, mass and
time. Their units are all derived units.
CHOICE OF A STANDARD UNIT
The unit chosen for measuring any physical quantity should "meet the following
essential requirements: (i) It should be of suitable size
(ii) It should be accurately defined
(iii) It should be easily accessible;
(iv) It should be easily reproducible i.e. replicas of the unit should be available easily;
(v) It should not change with time, and
(vi) It should not change with the change physical conditions like temperature,
pressure
SYSTEMS OF UNITS
A system of units is the complete set, of units, both fundamental and derived, for all kinds of
physical quantities. Each system is named in terms of fundamental units on which it is
based. The common systems, of units used in mechanics are given below:
(a) The FPS system is the British Engineering system of units, which uses foot as the unit of
length, pound as the unit of mass and second as the unit of time.
(b) The C.G.S system is the Gaussian system which uses centimetre, gram and second as the
three basic units for length, mass and time respectively.
(c) The MKS system is based on metre, kilogram and second as the fundamental units of
length, mass and time respectively.
The CGS and MKS systems are called metric systems or decimal systems because multiples
and sub multiples of basic units are related to the practical units by powers of ten.
FPS system is losing its popularity because of inconvenient multiples and submultiples
involved in it for conversion. The conversion factors in common use are:
(i)
1 foot = 30.48 cm = 0.3048 metre
(iv)1 pound = 453.6 gm = 0.4536 kg
(d) SI The name SI is an abbreviation' of "Le Systeme International d' unites", which is French
equivalent of International system of units. This system of units is essentially a modification
over the MKS system and is, therefore, called rationalised MKS system. This rationalisation
was essential to obtain the units of all the physical quantities in Physics as the fundamental
units of mass, length and time on MKS. system could be used to obtain the units of physical
quantities in mechanics only.
The SI is based on the following seven fundamental units and two supplementary units:
Basic Physical Quantitiy
1. Mass
Fundamental unit Symbol used
kilogram
kg
2. Length
metre
m
3. Time
second
s
4. Temperature
kelvin
K
5. Electric current
ampere
A
6. Luminous intensity
candela
Cd
7. Quantity of matter
mole
mol
1 metre = 100 cm = 3.281 ft. 1 kg = 1000 gm = 2.205 pound.
Supplementary physical quantity
Supplementry Units
Supplementary unit
1. Plane angle
radian
rad
2. Solid angle
steradian
sr
1. Radian (rad)
It is the plane angle' that' an arc of a circle whose length is equal to the radius, subtends at
the center of the circle.
2. Steradian (Sr)One steradian is defined as the solid angle subtended at the centre of a
sphere by its surface wbose area is equal to the Sfluare of the radius of the sphere.
ORDER OF MAGNITUDE OF MASS
The following table gives the order of magnitude from the mass of
electron to the mass of universe:
Object
Order of mass (kg)
Electron
10-30
Proton
10-23
Uranium atom
10-25
Cell
10-10
Dust particle
10-9
Man
102
Elephant
103
Moon
1023
Earth
1025
Sun
1030
Galaxy
1042
Universe
1055
ADVANTAGES OF SI:
Following are the main advantages of 51 over the other systems of units:
1. SI is a coherent system of units i.e. a system based on a certain set of fundamental
units, from
which all derived units are obtained by multiplication or division without introducing
numerical factors.
2. SI is a rational system of units, as it assigns only one unit to a particular physical
quantity. For example joule is the unit for all types of energy. This is not so in other systems
of units. For example, in MKS system, mechanical energy is in joule, heat energy is in calorie
and electric energy is in watt hour.
3. SI is an absolute system of units. There are no gravitational units on the system. The
use of factor 'g' is thus eliminated.
4. S.I is a metric system i.e. the multiples and submultiples of units are expressed as
powers of 10.
5.In current electricity, the absolute units on the SI, like ampere for current, volt for
potential difference, ohm for resistance, henry for inductance, farad for capacity and so on,
happen to be the practical units for measurement of these quantities.
.
SOME IMPORTANT PRACTICAL UNITS
1. Astronomical Unit (AU). It is the average distance of the center of the sun from the
center of the earth.
1AU = 1.496 * 1011 m ~= 1.5 * 1011 m
2. Light Year (ly): It is another important unit of long distances. One light year is the distance
travelled by light in vacuum in one year. As velocity of light in vacuum is 3 x 108 ms-1 and 1
year = 365 x 24 x 60 x 60 second, therefore, 1 light year = 3 x 108 ms-1 * 365 x 24 x 60 x 60
second =9.46 * 1015 m
3. Par sec. It is yet another unit of long distances and represents a parallactic second. One
Par sec is the distance at which an arc I AU long subtends an angle of 1 second.
1 par sec = 3.1 x 1016 m
Relation Between AU, Ly And Par Sec
11
As 1AU = 1.5 x 10 m and
and
1ly = 9.46 x 1015 m
1 parsec = 3.1 x 1016 m
1 ly = 6.3 * 104 AU
1 par see = 3.26 ly
Clearly, 1 par see is bigger than 1ly, which is bigger than 1 AU It may be of interest to note
that size of universe is nearly 1010 ly The nearest star, Alpha centauri, outside our solar
system is 4.3ly away from the earth.
Some useful units of length
1inch = 0.0254 m
(b) In the micro-cosm measurement, i.e. in the measurement of small distances, we use the
following four units:
(i) 1 micron = 1µ or 1µm = 10-6 m
(ii) 1 nanometre = 1 nm = 10-9 m
(iii) 1 angstrom = lAo = 10-10 m
(iv) 1 fermi = 1 femtometre = 1fm = 10-15 m
For example, the radius of proton is 1.2 fm and radius of hydrogen atom is 0.5 A0 .
(c) For measuring very small areas, the unit used is
1 barn = 10-28 m2
Nuclear cross sections are measured in barns.
(d) For measuring heavy masses, the units used are
(i)
(ii)
1 tonne or 1 metric ton = 1000 kg
1 quintal = 100 kg
(f) Some practical units of standard of time are:
(i) Solar day: It is the time taken by earth to complete one rotation about its axis w.r.t. the
sun.
(ii) Sedrial day. It is the time taken by earth to complete one rotation about its axis w.r.t. a
fixed star.
(iii) Solar year (or year) is the time taken by the earth to complete one revolution around
the sun in its orbit.
1 solar year = 365.25 average solar days = 366.25 sedrial days
Note. The year in which there is total solar eclipse is called a tropical year. The year, which is
divisible by 4, and in which month of February has 29 days, is called leap year.
One hundred years make up one century.
(iv) Lunar month. It is the time taken by moon to complete one revolution around the earth
in its orbit.
1 Lunar month = 27. 3 days.
(v) Shake. It is the smallest practical unit of time. 1 shake = 10-8 sec.
(g) For measuring pressures, the units used are:
(i) 1 bar = 1 atmospheric Pressure = 105 N/m2
As 1 atmospheric pressure = 760 mm of Hg column
1 bar = 760 Torr
(ii) 1 Torr = 1 mm. of Hg column
METRIC PREFIXES FOR POWERS OF 10
The physical quantities whose magnitude is either too large or too small can be expressed
more compactly by the use of certain prefixes. For example, the distance of Delhi from
Ambala is 200,000 metres. It is more compact to represent this distance as 200 km.
The prefixes we commonly use for powers of 10 are listed below in Table:
Power of 10
Prefix
Symbol
10-1
Deci
d
10-2
Centi
c
10-3
Mili
m
10-6
Micro
µ
10-9
Nano
n
10-12
Pico
p
10-15
Femto
f
10-18
Atto
a
101
Deca
da
102
Hecto
h
103
Kilo
k
106
Mega
M
109
Giga
G
1012
Tera
T
1015
Peta
P
1018
Exa
E