This document discusses systems of units and the International System of Units (SI). It describes the three fundamental SI units - the meter (length), kilogram (mass), and second (time) - and how other units are derived from these. It provides details on how the definitions and standards for the meter, kilogram, and second have changed over time to become more precise and based on fundamental physical constants. The document also lists the seven base units in SI and the two supplementary units of plane angle and solid angle. It introduces prefixes used to denote multiples and submultiples of units.

1. 1
Module # 04
Units & Systems of Units
Systems of Units
Different systems of units have been in use in science at different
times. The commonly used systems were:
1. The F.P.S. i.e., the foot pound second system.
2. The C.G.S. i.e., the centimeter, gram and second system.
3. The M.K.S. i.e. the meter, kilogram and second system.
Fundamental Units
All physical quantities are expressed in terms of the following
three fundamental quantities.
(1) Length (L)
(2) Mass (M)
(3) Time (T)
In System International (SI) meter is the unit of length, Kilogram is
the unit of mass and second is the unit of time.
Length, mass and time are fundamental quantities and their units
are called fundamental units. All other units are derived from
fundamental units and are called derived units.

2. 2
Length
In scientific laboratories all over the world, the length is measured
in meters.
In I960, in accordance with an international agreement, the meter
was redefined in terms of the wavelength of the orange light
emitted by Krypton-86 atoms in an electrical discharge. The meter
was defined as 1,650763.73 wavelengths of orange light emitted
from a Krypton 86 lamp.
By 1983, the demand for high precision had reached such a point
that even the Krypton-86 standard could not meet them and the
meter was redefined as "the distance travelled by a light wave in
vacuum during a time of 1/299792458 seconds". This definition of
meter was adopted as standard by the 17th General Conference
on Weights and Measures. All precise measurements are now
made with light waves.
Mass
The unit of mass is known as kilogram. It is defined as the mass
of a platinum (90%) and iridium (10%) alloy cylinder, 3.9 cm in
diameter and 3.9 cm in height, kept at the International Bureau of
Weights and Measures in France. This mass standard was
established in 1901 and there has been no change since that time

3. 3
because platinum-iridium is an unusually stable alloy. The same
standard has been adopted for SI units.
Time
Second is the basic unit of time in all systems of units. Before
1960, the standard of time was defined in terms of the mean solar
day. Thus second was originally defined as [1/60] [1/60] [1/24], of
a mean solar day. In 1967, the SI unit of time, the second was
redefined by 13th General Conference on Weights and Measures
using the characteristic frequency of cesium-133 atom. According
to this standard:
1 second = duration of 9,192,631,770 vibrations of cesium-133
atom.
SI Units
In 1960, the eleventh General Conference on weights and
measures introduced a system known as International System or
SI (the abbreviation for the French equivalent, Systeme
International). The units included in this system are known as SI
units. The SI units are now used all over the world.
The SI units, unlike the three basic units of the F.P.S., the C.G.S
and the M.K.S. systems, comprise the seven basic units. These
are:

4. 4
Quantity Unit Name Unit Symbol
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
In addition to these seven fundamental units (listed above), the SI
units also include two supplementary units. These supplementary
units are those of plane angle and solid angle. Their units are
radian and steradian respectively.
Candela
The SI unit of luminous intensity is candela. It is defined as the
luminous intensity in the perpendicular direction of a surface of
1/600000 square meter of a black body radiator at the
solidification temperature of platinum under standard atmospheric
pressure. This definition was adopted by the 13th
General
Conference of Weights and Measures in 1967.

5. 5
Steradian
It is used for the measurement of solid angles i.e. unit of solid
angle.
Derived Units
Some units are expressed in terms of other units, which are
derived from fundamental units, are known as derived units e.g.,
the unit of velocity, acceleration, pressure, Area, volume, density,
force, power, work done etc.
Thus, the nine physical quantities, as mentioned in SI Units, are
regarded as the fundamental quantities and their units are called
the fundamental units. Other physical quantities which can be
defined in terms of these fundamental quantities are, therefore,
called derived quantities and their units are, thus, called derived
units.
Examples
(1) Speed is defined as distance travelled in unit time. In SI
units, the distance is measured in meters and time in seconds.
So, the units for speed would be meter per second.
(2) Acceleration is defined as the time rate of change of velocity.
As the unit of velocity is same as that of speed, therefore, the SI
unit of acceleration is meter per second per second.

6. 6
(3) Force is defined as mass times (multiplication) acceleration.
The SI unit of mass is kilogram and that of acceleration is meter
per second per second. Thus, the SI unit of force is kg ms-2
and is
known as Newton.
Conversion Factors
Sometimes, it becomes necessary to convert units from one
system to another. Conversion factor between the S.I. and
conventional units of lengths are as follows:
1 mile = 1609 m = 1.609 km
1 ft. = 0.3048 m = 30.48cm
1 m = 39.37 inches = 3.281ft
1 inch = 0.0254 m = 2.54 cm
1 gallon = 4.5461 liters
1 tola = 11.636 grams
1 pound = 0.4536 kg
1 ft. = 0.3048 m = 30.48cm
1 m = 39.37 inches = 3.281ft
1 inch = 0.0254 m = 2.54 cm
1 newton = 105
dyne

7. 7
Prefix
In physics, sometimes, we deal with very large numbers and
sometimes with very small numbers. Prefixes are used to express
these large or small numbers as multiple of ten. For example, (in
case of large number)
1 light year = 9460000000000000 m = 946 x 1013 m = 9.46xl015m.
Similarly, (in case of small number)
Radius of Proton = 0.0000000000000012m
= 12x 10-16
m = 1.2x10-15
m
Other Use of Prefix
Sometimes, we use prefix to express appropriate units. For
example, centi means 1/100, therefore, centimeter means 1/100
meter, or;
1/100 m = 1 centimeter
Similarly, 1000 m = 103
meter = 1 kilometer
1/1000m = 10-3m = 1 millimeter
Hence, centi, kilo, milli are called prefixes. The commonly used
prefixes are given below in the table.

8. 8
Prefix Symbol Multiple
tera T 1012
giga G 109
mega M 106
kilo k 103
hecto h 102
deca da 101
deci d 10-1
centi c 10-2
milli m 10-3
micro  10-6
nano n 10-9
pico P 10-12
femto f 10-15
atto a 10-18