1.1 Physical Quantities:
Different quantities needs to describe the physical phenomenon or object are called physical phenomenon or object are called physical quantities. Examples: speed, density, mass, length etc.
The physical quantities are divided into two groups:
1. Fundamental Quantities: Those physical quantities which are independent to any other physical quantities are known as Fundamental quantities. Eg: mass, length, time etc.
2. Derived Quantities: Those physical quantities which depend on other physical quantities and only obtained by multiplying and dividing the fundamental quantities are known as Derived quantities. Eg: density, velocity, acceleration, force etc.
1.2 Units:
The physical quantities are measured by comparing with some standard measurement of same kinds are called units.
The units are divided into two groups:
1. Fundamental Unit: Units of the fundamental quantities are called fundamental units. These are independent to any other units.
2. Derived Units: Units of the derived quantities are called derived unit. These units are obtained by multiplying and dividing the fundamental units.
System of measurement:
i. CGS system: The system of measurement in which 3 fundamental quantities mass, length and time are measured in gm, cm and s respectively is known as CGS system. All other derived quantities are also measured in terms of these units of measurement.
ii. MKS system: The system of measurement in which 3 fundamental quantities mass, length and time are measured in kg, m and s respectively is known as MKS system. All other derived quantities are measured in terms of these unit of measurement.
iii. FPS system: The system of measurement in which 3 fundamental quantities mass, length and time are measured in pound (lb), foot (ft) and second (s) respectively is known as FPS system. All other derived quantities are measured in terms of these unit of measurement.
iv. International system of units (S.I) : S.I is an abbreviation " Le systeme International d " units which is french and equivalent of international system of unit. It is used widely throughout the World in which seven different quantities are introduced as fundamental quantities and their units as fundamental units.
Quantity Unit Symbol
1. Mass Kilogram Kg
2. Length Meter m
3. Time Sec S
4. Temperature Kelvin K
5. Electric Current Ampere A
6. Luminious Intensity Candela cd
7. Amount of Mole Mol.
Substance
Two more quantities are introduced as supplementary quantities and their units as supplementary unit.
Some useful practicle units:
1.Plane angle Radian Rad
2.Solid angle Steradian Sr
1.Astronomical unit (AU): Average distance between centre of Earth and centre of Sun.
Therefore, 1AU = 1.496 * 10^11 = 1.5 * 10^11 m
2.Light year(ly): Distance travel by light in a vacuum in 1 year.
Therefore, 1ly = 9.46 * 10^15 m
3. 1 inch = 2.54cm
1 foot = 30.48cm
1 yard = 91.44 cm
1 mile = 1.609 * 10^3 m
1 nautical mile = 1.852 * 10^3 m
1 angstrom = 10^-10 m
1 Fermi = 1femtometre = 10^-15
For Areas
1 barn = 10^-28 m^2
1 acre = 4047 m^2
1 hectare = 10^4 m^2
For mass
1 tonne/metric ton = 1000 kg
1 Quintal = 100 kg
1 slug = 14.57 kg
1 lb = 0.4536 kg
1 amu = 1.67 * 10^-27 kg
For time
1 shake = 10^-8 sec
1 solar year = 365.25 days
For pressure
1 bar = 1 atmospheric pressure = 10^5 N/m^2
1 torr = 1 mm of Hg = 133N/m^2
1 bar = 760 torr
1 atmospheric pressure = 760 mm of Hg = 1.01 * 10^5 N/m^2
1.3 Dimension:
The power of fundamental quantity involved in any physical quantity is called Dimension of that physical quantity. The representation of physical quantity interms of power of fundamental quantities involved in it is called dimensional formula of that physical quantity. Three fundamental quantities mass,length and time are represented by [M] , [L] and [T] respectively. All other derived quantities are also expressed in terms of these representations.
E.g: Force = ma = Kgm/s^2 = [MLT^-2]
Work = F * d = Nm(J) = [ML^2T^-2]
Pressure = F/A = N/m^2 = [ML^-1T^-2]
1.4 Error analysis: (formula)
Least count (LC): The smallest measurement that can be taken by an instrument is called Least count. E.g = Least count of scale graduates in mm is 1mm.
Absolute error: The different between true value and measured value is called Absolute error.
i. Error in sum of quantities
ii. Error in difference of quantities
iii. Error in product of quantities
iv. Error in division of quantities
v. Error in quantities raised to some power.
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