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when measuring any physical quantity we compare it to a standard reference point known as a unit
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i) fundamental units, these are fundamental or base quantities which are not derived
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ii) derived units, these are the units of other physical quantities and can be expressed as a combination of multiple fundamental units
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(together they are know as the system of units)
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CGS system- the system where centimeter (L), gram (M), seconds (T)
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FPS system [british system]- the system where foot (L), pound (M), seconds (T)
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MKS system- the system where meter (L), kilogram (M), seconds (T)
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SI units- it's the present system of units which is internationally accepted for measurement.
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It has seven base units which then can be combined with each other to form the derived units
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quantity
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name
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symbol
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length
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meter
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m
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mass
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kilogram
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kg
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time
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second
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s
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electric
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ampere
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A
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Thermodynamic temperature
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kelvin
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K
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Amount of substance
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mole
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mol
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Luminous intensity
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candela
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cd
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the dimensions of a physical quantity are the powers (or the exponents) to which the base quantities are raised to represent that quantity
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square brackets [ ] are used to indicate the dimensions
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An equation obtained by equating a physical quantity with its dimensional formula is called the dimensional equation of the physical quantity. In other words it can be said that dimensional equations represent the dimensions of a physical quantity in terms of the base quantity
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Volume - [V] = [M0 L3 T0]
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Speed - [v] = [M0 L T-1]
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Force - [F] = [M L T-2]
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Mass density - [p] = [M L-3 T0]
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Dimensional analysis is the practice of checking relations between physical quantities by identifying the dimensions of the physical quantities. These dimensions are independent of the numerical multiples and constants
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It helps us deduce certain relations between different physical quantities and checking the derivation, accuracy and dimensional consistency of the mathematical expressions
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We make use of dimensional analysis for three prominent reasons:
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1) To check the consistency of a dimensional equation
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2) To derive the relation between physical quantities in physical phenomena
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3) To change units from one system to another
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