QUANTITY
Quantity means size, amount, vastness, magnitude, or simply stated as the answer for "how much?" or "how many?".
Physical quantity : A Quantity which can be 'measured' is called physical quantity.
Eg : Length, Area, Volume, Speed, Force, Energy etc.
Eg : Length, Area, Volume, Speed, Force, Energy etc.
Physical quantities are organised into various ways in various systems like FPS, CGS, MKS and SI.
Now the scientists of all countries are following SI for all their research work.
Now the scientists of all countries are following SI for all their research work.
In SI. physical quantities are organised into three groups. They are :
 Fundamental physical quantities
 supplementary physical quantities
 Derived physical quantities
Set of Fundamental Physical Quantities :
Consider a set of physical quantities. If no quantity can be derived from the remaining physical quantities, then the set is called set of fundamental physical quantities.
Examples :

(a) { Mass, Length, Time }

In SI, there are seven fundamental physical quantities. They are Length, Mass, Time, Thermodynamic, Temperature, Strength of Electrical Current, Amount of substance and Luminous Intensity.
Find your self : What is the difference between Mass and Amount of Substance?
Supplementary Physical Quantities : In SI, they are two supplementary physical quantities. They are :

Physical quantities derived from fundamental or supplementary physical quantities are called derived physical quantities.
Eg : Force, Area, Volume, Speed etc.
Eg : Force, Area, Volume, Speed etc.
Fundamental physical quantities are like alphabet in English language and derived physical quantities are like words.
Vectors Tip!
Is ordinary algebra sufficient to find the sum when direction is included?
For example consider the following situation :
We know that 5x + 5x = 10x
Is 5m in one direction + 5m in another direction = 10m ?
Application :
we make use of quantity to distinguish between the object like , 50 ml cup, 2 litre bottle,
UNIT
Unit is a "standard measure" of any physical quantity.
Measurement of a Physical Quantity
It involves two steps :


 Unit is also a value. We should not think of its a name. Hence all algebraic operations are possible with units.
 Every physical quantity is expressed as number (N) followed by its Unit (U).
 Magnitude of the quality (P) does not change with the choice of unit.
Example :

Height of a boy = 1.5m = 150cm
In 1.5m, unit is meter and numerical value is 1.5 In 150cm, unit is centimeter and numerical value is 150 
Vector Tip!
Physical quantities that follow simple algebraic rules are called scalar physical quantities. In short we call them scalars
Eg : mass, distance, time, etc.
Desirable Features of a standard Unit
A standard unit should be consistent, reproducible, invariable, and easily available for usage.
Fundamental Units
Units of fundamentals physical quantities are called fundamental physical units.
In SI, fundamental physical units are as follows :
In SI, fundamental physical units are as follows :
Physical QuantityLength
Mass
Time
Strength of electric current
Thermodynamic temperature
amount of substance
Luminous intensity

Unitmeter
kilogram
second
ampere
kelvin
mole
candela

Symbolm
kg
s
A
K
mol
cd

Note : Fundamental units in some of the old systems are as follows :
SystemF P S
C G S
M K S

Lengthfoot (ft)
centimeter (cm)
meter (m)

Masspound (lb)
gram (g)
kilogram (kg)

Timesecond (s)
second (s)
second (s)

Supplementary Units
Units of supplementary physical quantities are called supplementary units.
In SI, units of supplementary physical quantities are as follows :
In SI, units of supplementary physical quantities are as follows :
Supplementary QuantityPlane angle
solid angle

Unitradian
steradian

Symbolrad
sr

Derived Units :
Units of derived physical quantities are called derived units.
SI units of some derived physical qualities are as follows :
SI units of some derived physical qualities are as follows :
Vector Tip!
Directions means Spatial orientation.
Scalars have only magnitude, but no direction.
Statement of a scalar just consists of its magnitude along with a proper algebraic sign.
Eg : Time (t) = 5 s, Mass (m) = 5 kg
Rules for writing Units in SI :
 All the symbols of fundamental units should be written as they appear in the table of SI units.
 In compound units all the symbols of the fundamental units should be written as they appear in the table of SI units.
 Some of the unit are represented by the names of the scientists as an honour for their research in the respective fields. the full name of such units should be written with a lower initial letter. ( Eg : newton, joule, watt, ampere, kelvin, etc. ).
 The symbol of unit named after a scientist should always be written with the capital letter ( Eg : 5 N ).
 Punctuations like full stop (.), comma (,) etc., should not be used after the symbol of unit.
 A unit should always be represented in singular form. ( 5kg ).
Need of Multiple and Submultiples :
Multiples & Submultiples are introduced to change the size of the units to fulfill the needs of various branches in physics.
Some practical units in various branches of physics ( These are not SI units )


Nature of the Physical quantity is described by its dimensions
Dimensions
The dimensions of a physical quantity are the powers to which the base quantities are raised to represent that quantity.
The physical quantity that is expressed in terms of the base quantities is enclosed in square brackets "[ ]".
The physical quantity that is expressed in terms of the base quantities is enclosed in square brackets "[ ]".
Dimensional Formula
The expression which shows how and which of the base quantities represent the dimensions of a physical quantity is called the dimensional formula of the given physical quantity.
Dimensional formulae of fundamental quantities in SI are as follows :
Dimensional formulae of fundamental quantities in SI are as follows :
QuantityMass
Length
Time
Strength of electric current
Amount of substance
Luminous Intensity

Dimensional Formula[ M ]
[ L ]
[ T ]
[ I ]
[ mol ]
[ cd ]

Supplementary physical quantities have no dimensions.
some authors use [ A ] for strength of electric current instead of [ I ].
some authors use [ A ] for strength of electric current instead of [ I ].
Vector Tip!
Physical quantities which follow vector algebra are called vector physical quantities.
in short we call them vectors.
Eg : displacement, velocity, force etc.
Dimensional Equation :
An equation obtained by equating a physical quantity with its dimensional formula is called the Dimensional Equation of the physical quantity
Conversion of Units :
To convert a unit from one system to another, the steps to be followed are :
 First convert the given unit into SI unit.
 Then, convert it into the desired system of units.