Units and Dimensions DIMENSIONAL ANALYSIS
Fundamental and Derived Quantities Experiments require measurements, and we generally use numbers to describe the results of measurements. Any number that is used to describe a physical phenomenon quantitatively is called a Physical Quantity. Physics is the study of Physical Phenomenonwith the help of the Physical Quantities. There are Seven Fundamental Physical Quantities namely Mass, Length, Time Temperature, Electric Current, Luminous Intensity and Amount of Substance. All other Physical quantities like Velocity, Momentum, Acceleration, Force etc. can be represented in terms of the seven Fundamental Physical quantities and are known as Derived Quantities Angle and Solid Angle are termed as Supplementary Quantities.
All the Derived Quantities can be expressed in terms of Fundamental Quantities and therefore the units of all the derived quantities can be expressed in the form of units of Fundamental Quantities The following table contains the Fundamental quantities with their SI Units S. No. Physical quantity 1. 2. 3. 4 5. 6. 7 Name of unit Symbol of unit Mass Length Time Temperature Luminous Intensity Candela Electric Current Amount of Substance Mole Kilogram Meter Second Kelvin Cd Ampere mol
The powers to which the fundamental quantities mustbe raised in order to represent a Physical quantity is known as dimension of that Physical quantity. For example Momentum can be represented in the form of Fundamental Quantities as p = mw therefore, is known as dimensional formula of momentum. m- M 1 LIT-1 Fundamental quantities cannot be written in the terms of other fundamental quantities. Mathematical constants like etc are dimensionless. Physical constants such as, 'Universal Gravitational constants (G)', 'Permittivity of Free Space (Eo Y etc. generally have dimensions. Pure ratios are always dimensionless and generally unitless but may not always be unitless. For example, Relative Density is unitless and dimensionless whereas Angle is dimensionless but not unitless, it has a unit Radian.
Nikhil Mishra is an engineer and has been a Faculty of Physics in some of the most premier institutes of the country and has been involved