Units and Dimension

Units and Dimension

Index:

v   Quantities: Physical quantities, Fundamental quantities, Derived quantities

v   Derived quantities and derived unit with formulas

v   System of Units

v   Supplementary units

v   SI units

v   Dimensions (M L T)

v   Principles of Homogeneity of dimension

v   Application of Dimensional equation:

1).       To check the correctness of any given equation.

2).       To Establish the relation between various quantities.

3).       To find the units of physical quantities.

4).       To change the one system of unit to another system of unit.

·               Physical quantities: 

A physical quantity is a quantity that cannot be measured or quantified.

e.g.: mass, length, volume, momentum etc.

·               Fundamental quantities:

are those physical quantities that cannot be expressed in terms of other quantities

-These are independent

-There are seven types of fundamental quantities:

1). Length (meter)      

2). Mass (kilogram)    

3). Time (second)       

4). Temperature (Kelvin)

5). Luminous intensity (candela)         

6). Electric current (Ampere)

7). Amount of substance (moles)

·               Derived quantities: 

The physical quantities which are expressed in terms of based quantity are called derived quantities.

In simple words one or two base quantities are either multiplies or divided to form new quantity.

e.g.: Area = length × breadth, Volume = Length × Breadth × Height, Momentum = mass × velocity

·               Derived quantities and derived unit with formulas: 

                                                                                                       

 NOTE: Work and Energy both has same dimension and unit because energy is equal to work

Pressure and stress both has same dimensional formulae because both tend to change the state of the object

Angle is a supplementary unit (dimension less unit)

·               System of Units:

-                MKS       Meter     Kilogram     Second

-                CGS        Centimeter     Gram    Second

-                FPS         Foot     Pound     Second

·               Supplementary units:

The supplementary units is referred as a dimensionless unit which is employed with the fundamental unit to create the derived units

e.g.: ‘Angle has a unit radian’

·               SI units: 

The international system of units represented as SI units is the new method of metric system which is mostly used unit system. It is employed in all research and development applications and it is defined to be a coherent system of units.

·               Dimensions (M L T): 

Such forms which represent the relation of physical quantity to fundamental unit is called dimension. 

·               Principles of Homogeneity of dimension:

According to this principle any given equation would be true if the powers of dimension on both sides are same.

e.g.: T = 2π √l/√g

T=time period

l=length

g=gravitational acceleration

2π is constant therefore we not consider it,

[M⁰L⁰T¹] = √ [M⁰L¹T⁰]/ √ [M⁰L¹T^-2]

[M⁰L⁰T¹] = √ [M⁰L⁰T²]

[M⁰L⁰T¹] = [M⁰L⁰T¹]

L.H.S = R.H.S

As the powers of dimension on both sides are equal therefore the give equation is correct.

·               Application of Dimensional equation:

1).       To check the correctness of any given equation.

2).       To Establish the relation between various quantities.

3).       To find the units of physical quantities.

4).       To change the one system of unit to another system of unit.

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