SCIENTIFIC NOTATION

SCIENTIFIC NOTATION

DEFINITION
The expressing of a very large or very small number in power of ten is known as scientific notation

DEFINITION
The product of co-efficient 'M' and power 10 'P' is called scientific notation

EXPLANATION
In Physics we deal with a very large or very small numbers. Therefore ,to save time and space we convert the number to standard form. There must be only one-zero digit to the left of a decimal point while writing number in standard form. The power of ten is positive for large numbers while negative for small numbers

STEPS FOR CONVERSION TO SCIENTIFIC NOTATION
STEP 1 :
Locate the position of decimal point
STEP 2 :
Move the decimal point and place it after first non-zero digit
STEP 3 :
If the decimal is moved towards left from its initial position then the power of 10 will be positive and the value of power of 10 will be the number of digit through which the decimal point has been moved
STEP 4
If the decimal is moved towards right from its initial position then power will be negative and the value of power of 10 will be the number of digit through which the decimal point has been moved
EXAMPLE
*) Average distance between earth and moon is 384,400,000 m. For standard form we can write it as
distance = 384,400,000×10^0 m
distance = 3.84400000×10^8 m.
distance =3.844×10^8 m

STERADIAN

STERADIAN
It is the unit of solid angle or three dimensional angle. Steradian can also be called as squared radian

DEFINITION
One steradian is the angle substended at the center of a sphere at the center of a sphere by a surface area equal to the square of radius of the sphere

MATHEMATICALLY
If area taken on sphere =(radius)^2 Then the angle at center by a surface area is 1 steradian

SYMBOL
It is denoted by 'sr'

EXPLANATION
According to the definition of steradian solid angles in a sphere can be calculated as
................ (Equ. 1)
We know that surface area of the sphere is given by
surface area of sphere = 4πr^2
Putting value in Equ. 1 we get
Solid angle = 4πr^2/r^2
................ (Equ. 2)

SUPPLEMENTARY UNITS AND RADIAN

SUPPLEMENTARY UNITS

DEFINITION
The S.I units which are not yet classified either base or derived unit is known as Supplementary Units
NUMBER
In number these are Two 1) RADIAN
2) STERADIAN

RADIAN
DEFINITION
The unit of plane angle subtended by an arc of length equal to its radius at center of circle is known as radian
SYMBOL
It is denoted by 'rad'
EXPLANATION
Consider a circle whose radius is 'r'.If the length of arc AC is equal to radius 'r' of the given circle then
Now we know from trigonometry that the ratio of angles subtended by arcs is equal to the ratio of the length of arcs i.e Ø =s/r × 1rad ........ eq (1)
When s= r (length of arc=radius of the cicle then equation 1 can be written as
Ø=1 rad
When we are finding radians in one complete circle then put s =2πr (circumference of the circle)
Ø=2πr/r × 1rad
Ø= 2πr rad ..........eq (2) Eq .2 gives us radians in one revolution

OTHER UNIT OF PLANE ANGLE
Degree is another unit of plane angle
One revolution=360 degree.........eq .(3)
1 degree has 60 minutes
1 minute has 60 seconds

RELATION BETWEEN DEGREE AND RADIAN
From eq .2 and eq .3 we conclude that in one complete revolution has 2πr radian and 360 degree so comparing these two equations we have that
2πr rad= 360 degree
1 rad =
1 rad = 57.3 degree

DERIVED UNITS

DERIVED UNITS

DEFINITION 1
The standard which is derived from base units is known as derived unit
DEFINITION 2
The units of derived physical quantities are known as derived unit

EXAMPLES

1) The unit of speed is m/s which is a derived unit because it is obtained from base unit meter (m) and second (s)
v= s/t
unit of speed = m/s
So by dividing two base units we get another standard for measuring speed
2) The unit of force is newton (N) which is derived from base units i.e kilogram (kg) meter (m) and second (s)
F= ma
newton= kgm/s^2
3) The unit of work is joule (J) which is also a derived unit
W = Fd
joule =Nm

TYPES OF SI UNITS

TYPES OF SI UNIT
SI units are of three types
*)Base units
*)Derived units
*)Supplementary units

BASE UNITS

DEFINITION
The units of seven base physical quantities are defined and standardized and termed as SI base units

1) METER
The distance traveled in vacuum by light wave in 1/299792458 seconds
And the symbol of meter is (m)

2) KILOGRAM
The mass of platinum-iridium alloy cylinder having length and diameter of 3.9 cm kept at IBWM in paris
The symbol of kilogram is (kg)

3) SECOND
The duration in which a cesium atom completes 9192631770 vibrations
The symbol of second is (s)

4) AMPERE
The amount of current when charge flow at the rate 1coulomb/second through a cross section of a conductor
The symbol of ampere is (A)

5) KELVIN
The fraction 1/273.16 of the thermodynamic temperature of the triple point of water (277.16 k)
The symbol of kelvin is (K)

6) MOLE
The amount of a substance containing 6.022×10^23 atom,molecules and ions etc
The symbol of mole is (mol)

7) CANDELA
The radiations of monochromatic source of frequency 540×10^12 Hz and that has radiant intensity of 1/683 watt per steraidan
The symbol of candela is (cd)

INTERNATIONAL SYSTEM OF UNITS

INTERNATIONAL SYSTEM UNITS
DEFINITION

A complete set of units for all kind of quantities (both base and derived quantities) is called system units

HISTORY
Different system of units have been in use in different countries They are
*) MKS(meter-kilogram-second)
*) CGS(centimeter-gram-second)
*) FPS(foot-pound-second)
SI UNITS
DEFINITION
For the sake of uniformity and universalization of science and technology a set of definitions and standards was defined by an international committee in 1960 to describe all physical quantities. This system was named as system International (SI). The units in this system are termed as SI units

PHYSICAL QUANTITY

PHYSICAL QUANTITY
DEFINITION
A quantity that can be observed measured and laws of physics can expressed in term of those quantity is called physical quantity
EXAMPLE
Length,height,volume,force,temperature,mass etc

CLASSIFICATION OF PHYSICAL QUANTITIES
There are two types of physical quantities
1) Base physical quantity
1) Derived physical quantity

*)BASE PHYSICAL QUANTITY
DEFINITION
The minimum number of physical quantities in term of which other physical quantities are expressed is known as base physical quantities
EXAMPLE
The seven base physical quantities are
1)Length
2)Mass
3)Time
4)Temperature
5)Electric current
6)Luminous intensity
7)Amount of substance

DERIVED PHYSICAL QUANTITIES
DEFINITION
All those quantities which are derived from base physical quantities are known as derived physical quantities
EXAMPLE
Speed,velocity,force,acceleration,power,work etc

EXPLANATION
Speed is derived physical quantity because speed is obtained from the division of two base quantities i.e length and time