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Units and Dimension & Errors:
1. Review of Basic Concepts :
* Physics is the branch of Science which deals with observation, measurement and description of natural phenomena related to Matter and Energy ‘Physics’ is also defined as the study of nature and its law.
* Mechanics is one of the branches of Physics which deals with the studies of forces acting on the bodies.
* Physical Quantities are the quantities which can be able to describe the Laws of physics. Physical quantities may be divided into fundamental and derived quantities.
* Fundamental quantities can be classified into 7 Quantities .
Namely :
* Mass
* Length
* Time
* Temperature
* Electric current
* Luminous Intensity
* Amount of substance
* In addition to these seven basic units there are two supplementary units – ‘radian’ and ‘steradian’. The units of Fundamental quantities are called ‘fundamental units'.
* In 1960, to measure the physical quantities, International System of Units abbreviated as ‘SI’ in all languages was introduced.
Supplementary units:
Name of Quantity:Plane angle | Solid angle
Name of Unit: Radian | Steradian Fundamental Quantities can be defined as follows :
* The fundamental quantities should be independent to one another.
* All other quantities may be expressed in terms of fundamental quantities.
Derived Quantities and their units :
Fundamental or Basic Quantities:
* Dimension of a physical quantity are the powers to which the fundamental quantities must be raised.
Derived Quantities :
* The quantities derived from the fundamental quantities are called derived quantities.
Eg. Area, Volume, Density
Derived Units :
* The units of derived quantities are called derived units.
Rules and conventions for writing SI Units and their Symbols :
1. The units named after scientists are not written with a capital initial latter.
E.g: Newton, Henry, watt.
2. The symbols of the units named after scientists should be written by a capital letter.
E.g : N for Newton, H for Henry, W for watt
3. Small letters are used as symbols for units not derived from a proper name.
E.g : m for metre, kg for kilogram
4. No full stop or other punctuation marks should be used within or at the end of symbols.
E.g: 50 m and not as 50m
5. The symbols of the units do not take plural form.
E.g: 10kg not as 10kgs
6. When temperature is expressed in Kelvin, the degree sign is omitted.
E.g: 273 K not as 273°K
7. If expressed in Celsius scale, degree sign to be included.
E.g: 100 C not 100C
8. Use of solidus is recommended only for indicating a division of one letter units symbol by another unit symbol. Not more
than one solidus is used.
E.g: ms-1 or m/s J/K or JK-1
mol-1 but not J /K /mol
9. Some space is always to be left between the number and the symbol of the unit and also between the symbols for
compound units such as force,momentum etc.
10.Only accepted symbols should be used.
E.g: ampere is represented as A not as amp. (or) am; second is represented as ‘s’
and not as sec.
11. Numerical value of any physical quantity should be expressed of mercury is 1.36 x 104kg m-3 and not as 13600kg m-3
E.g: density of mercury is 1.36 x 10 4 kg m-3 and not as 13600kg m-3
Light Year:
In order to measure very large distance, the following units are used.
1. Light year
2. Astronomical Unit
Light year is the distance travelled by light in one year in vacuum.
Distance travelled = velocity of light x 1 year
* 1 light year = 3 x 10^8 m x 1 year (In seconds)
= 3 x 10^8 x 365.25 x 24 x 60 x 60
= 9.467x 10^15m
1 light year = 9.467 x 10^15 m.
Greatest Units:
* 1 light year = 9.46 x 10^15 m
* 1 parsec = 3.84 x 10^16 m
* 1 AU = 1.5 x 10^11 m
* 1 metric ton = 10^3 kg
* 1 Quintal = 10^2 kg
Astronomical unit :
* Astronomical unit is the mean distance of the centre of the Sun from the centre of the earth. 1 Astronomical unit = 1.496 x 10^11m
Expressing Larger and smaller Quantities:
* The fundamental units are defined.
* Now it is easier to express larger and smaller units of the same physical quantity.
* The table lists the standard SI prefixes, their meanings and abbreviation.
10-15 femto f
10-12 Pico p
10-9 Nano n
10-6 micro
10-3 milli m
10-2 centime c
10-1 deci d
101 deca da
102 Hecto h
103 Kilo k
106 Mega M
109 Giga G
1012 Tera T
1015 Peta P
Scalar Quantities:
* Physical quantities which have magnitude only and no direction
E.g : Mass, Speed, Volume, Work, Time, Power Energy
Vector Quantities:
Physical quantities which have magnitude and direction both and which obey triangle law.
Eg : Displacement, Velocity, acceleration, force, Momentum
Dimensional Quantities :
* Constant which possess dimensions are called Dimensionless are called ‘Dimensionless quantities’
E.g : Strain, Specific Gravity etc. Uses of Dimensional Analysis :
* The method of dimensional analysis is used in four important ways :
1. It is used to check the dimensional correctness of a given physical equation.
2. To the physical equation
3. Finding the dimensions of constants (or) variables in an equation.
4. Conversion of one unit from one system to another.
Limitation of Dimensional Analysis :
1. If a physical quantity depends more than 3 quantities, the dimensions cannot be applied
2. The dimensional method cannot be applied to equations involving exponential and trigonometric functions.
3. The value of dimensionless constants be determined by this method.
Dimensional quantities:
* Constants which possess dimensions are called dimensional constants. Planck’s constant, universal gravitational
constant are dimensional constants.
* Dimensional variables are those physical quantities which possess dimensions but do not have a fixed value. Example −
velocity, force, etc.
Dimensionless quantities:
* There are certain quantities which do not possess dimensions. They are called dimensionless quantities. Examples are strain, angle, specific gravity, etc. They are dimensionless as they are the ratio of two quantities having the same dimensional formula.