Units and System of Units

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What is Units?

◘ The internationally accepted reference standard used for the measurement of a physical quantity is called the unit of that physical quantity.

◘ To measure a physical quantity, a widely accepted standard value of the same physical quantity is used.

◘ It Indicates that how many times the standard physical quantity is used to measure that whole physical quantity.The standard physical quantity known as the Unit.

◘ Consider the following example, Suppose the mass of an object is 20 kg.
• Here 20 indicates that how many unit mass (1 kg) is used to measure the mass of 20 kg
• The answer is 20 times that is 20 unit mass (20 * 1 kg = 20 kg) is used to measure the 20 Kgs of physical quantity (Here Mass). • Here kg is the unit of mass.
• Both the numerical value and unit formed the measurement of the particular physical quantity.

• The unit of a physical quantity always written in small letter even if the  unit is named after the  scientist.   For example – Unit of Force  ‘newton’, Unit of electric current ‘ampere’,  Unit of temperature ‘kelvin’, unit of  luminous intensity ‘candela’.

• If the unit represented by a single letter, then it must be written in Capital letters. For example: Unit of force ‘newton’ (N),  Unit of temperature ‘kelvin’ (K).

Classification of Units

♦ Units are also divided into the following categories _
• 1. Fundamental Units or Base units
• 2. Derived Units
• 3. Supplementary Units

Fundamental Units or Base units
• The number of physical quantities appears to be very large, that is why we need only a limited number of units for expressing all the physical quantities, since they are interrelated with one another.

• These limited number of units for expressing all the physical quantities are called fundamental or base units.

• In another way we can say that the units of fundamental physical quantities are called fundamental units or base units.

♦ Fundamental Units or Base units are independent of each other.There are 7 fundamental units, They are
• 1. Meter (Symbol – m)
• 2. Kilogram (Symbol – Kg)
• 3. Second (Symbol – s)
• 4. Kelvin (Symbol – K)
• 5. Candela (Symbol – cd)
• 6. Mole (Symbol – mol)
• 7. Ampere (Symbol – A)

Derived Units
• The units of all other physical quantities that can be expressed as combinations of the fundamental or base units.


• The units of all other physical quantities except fundamental physical quantities which are obtained with the help of base units are called derived units.

♦ Some Examples_
• Force
• Power
• Work
• Energy
• Acceleration
• Momentum
• Area
• Volume
• Speed
• Density

Supplementary Units
• The Units of Supplementary physical quantities like_
• Plane angle (Unit – Radian)
• Solid angle (Unit – Steradian)

✪ System of Units

• The common systems of units are classified into four categories_
• 1. MKS System
• 2. CGS System
• 3. FPS System
• 4. SI System

MKS (Meter Kilogram Second) System
• In this system of units the unit of length, mass and time are respectively – meter, kilogram and second.

CGS (Centimeter Gram Second) System
• In this system of units the unit of length, mass and time are respectively – centimeter, gram and second.

FPS (Foot Pound Second) System
• In this system of units the unit of length, mass and time are respectively – foot, pound and second.
•  FPS (Foot Pound Second)  system, also known as British system.

SI System
• At present the SI system of units are internationally accepted for measurement.
• Full form – Système Internationale d’ Unites (French for International System of Units) abbreviated as SI.

• For the international usage in scientific, technical, industrial and commercial field the standard SI symbols, units and abbreviations, was developed by the General Conference on Weights and Measures held at Geneva in 1971

• Conversions of SI unit within the system are quite simple and convenient, because the SI unit system used decimal systems.

• SI system is extended and modified form of MKS system.
• Both the MKS and CGS system are called metric or decimal system.

Systems of Unit
Systems of Unit

✪ The 7 Fundamental SI units and their symbol

Base Quantity Name Symbol Definition
Length meter m Presently the meter is defined as the length of the path traveled by light in a vacuum in 1/299 792 458 of a second.
Mass kilogram kg The kilogram is defined as the equal  mass of the  platinum-iridium alloy cylinder (International Prototype) kept at the International Bureau of Weights and Measures, at  Paris, France.
Time second s The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.(1967)
Electric current ampere A The ampere is defined by the force produced by constant  current in two parallel conductors which is equal to 2×10–7 newton per meter of length between the two conductors.

• The two straight parallel conductor should be  infinite in length

•  Also negligible circular cross-section

• And both the conductor  placed 1 meter apart in vacuum

Thermodynamic temperature kelvin K The Kelvin, is the fraction 1/273.16 of the thermodynamic of the triple point of water. (1967)
Luminous intensity Candela cd It is defined by the   luminous intensity, in a given direction, of a source.

• The source of  radiation  should be monochromatic

• Frequency of the radiation  540×1012 hertz

• Also it has a radiant intensity in that direction of 1/683 watt per steradian.

Amount of substance mole mol The mole is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon – 12. (1971)


Supplementary Units and their Symbols in SI unit System

Name of the Quantity Name of the Unit Symbol
Plane angle Radian rad
• ‘Radian’ is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
• π radian = 180°
• 1 radian = 180° / π.

• Length of the Arc AB equal to the radius of the circle.

Solid angle Steradian Sr


Some units retained for general use (Though outside SI)

Name of Unit Symbol Value in SI unit
Minute min 60 s
Hour h 60 min = 3600 s
Day d 24 h= 86400 s
Year y 365.25 d=3.156 x 10^7
Degree o 1o = ( π / 180) rad
Litre L 1 dm3= 10-3m3
Tonne t 103Kg
Carat c 200mg
Bar bar 0.1  Mpa  = 105 Pa
curie Ci 3.7 x 1010 S-1
Rontgen R 2.58 x 10-4 C/Kg
Quintal q 100 Kg
Barn b 100 fm2 = 10-28m2
Are a 1 dam2 =102m2
Hectare ha 1 hm2 = 104 m2
Standard atmospheric pressure atm 101325 Pa = 1.013  105 Pa

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