Moment of Inertia Sphere

The moment of inertia of a point mass about a known axis is defined by I = mr²  where m is its mass and r is its perpendicular distance from the axis of rotation.

Introduction :

Definition :  The moment of inertia of a rigid body about an axis is defined as the sum of the products of the masses of different particles, supposed to be constituting the body, and the square of their respective perpendicular distances from the axis of rotation.
                     Moment of inertia of a sphere can be explained in two parts (1) Solid Sphere (2)Hollow Sphere.
(1) Moment of inertia of a Solid Sphere  :  
    (a) About an axis passing through its diameter :   Consider a solid sphere of mass M and radius R. Its moment of inertia about an axis of rotation passing through its diameter is
                                                                            I  =  MR²
   (b) About an axis passing through its tangent  :   Let A'B' the tangent to the solid sphere. A parallel axis through its centre of mass is AB

By parallel axes theorem,
 Moment of inertia about the tangent = Moment of inertia about a diameter + Mr² .
                                                                  =`(2)/(5)` MR² + MR²
                                                         I      =  `(7)/(5)` MR² .

Moment of Inertia Sphere : Hollow Sphere

(2) Moment of Inertia of a Hollow Sphere
(a) Moment of inertia about an axis passing through the diameter of a hollow sphere of mass M and radius R is
                                                I  =`(2)/(3)`   MR² . 
(b)  Moment of inertia about an axis passing through its tangent can be obtained by applying parallel axes theorem. It is given by
                                                  I  =  `(5)/(3)` MR² .

Moment of Inertia Sphere : Example Problem

Problem : If the radius of the earth is suddenly halved keeping its mass constant, find its time period of rotation around its own axis.
Solution :  When the radius of the earth gets reduced suddenly keeping its mass constant, the angular momentum of the earth remains constant.      
                                                I   = constant
     If I changes from I₁ to I₂ ,   changes from`omega` ₁  to`omega`  ₂ so that 
                                          I₁ `omega`₁  =  I₂`omega`₂ .
     Assuming the earth to be a solid sphere, its moment of inertia about its diameter,
                      I  =  MR²
   If the radius changes form R to R/n
                                           `(2)/(5)` MR₁² `omega`₁  =  `(2)/(5)` MR₂² `omega`₂ 
                                                           R²  =  `(2pi)/(24 hours)`  = [R / n]² `(2pi)/(T)`  
          The time period of rotation , T = 24 hours / n² .
      In this problem, the radius changes from  R  to R / 2 .
                         `:.`   `(2)/(5)` MR²  `(2pi)/(24 hours)`   =  `(2)/(5)` M [R/2]² `(2pi)/(T)`
                               T  =  24 / 2²   =  24 / 4  =  6 hours.

Alkaline Metal facts

Introduction :

Alkaline metals are of very keen importance to us. These metals were discovered in the first decade of 19th century by an English chemist Sir Humphry Davy (1778- 829). Along the same time, he also found some elements of other metal families. Alkaline metal facts include all the basic properties shown by them.

About Alkaline Metals
Alkaline metals constituting Group2 of the Periodic Table. These metals show some general properties which are as follows:

• These metals are softer than most other metals
• These metals readily react with water (especially when heated).
• These metals are powerful reducing agents.
• These metals form divalent compounds, etc.

Facts Related to Alkaline Earth Metals

There are various facts related to Alkaline earth metals, some of the important ones are as follows:

• The name alkaline metals owes to their oxides that simply give basic alkaline solutions. These metals melt at high temperature and remain solids in heated atmospheres.
• The alkaline metals show good trend in their properties in the periodic table, with well-defined homologous behavior in going down the group.
• Some alkaline metals like Be and Mg, they show a distinguishable flame color , brick-red for Ca (Calcium) , Magenta-Red for Sr (Strontium) , Green for Ba (Barium) and crimson red for Ra (radium).
• The metals coming in this group show patterns in their electronic configuration, especially the behavior of them in their outermost shells, which results in the trend in chemical behavior.
• The alkaline metals are mostly Silver colored, soft metals, which react readily reactions with halogens.
• Alkaline Metal like Beryllium is highly toxic, it is rarely available to biological systems, and it has no known role in living organisms.
• Other Alkaline metal like Magnesium and calcium are essential to all known living things. They are involved in many roles like in some cellular processes, Mg functions as the active centre of the enzymes and Ca salts takes structural roles.
• Strontium and barium have lower availably in the atmosphere. They play very important roles in marine aquatic life, especially hard corals. These two are also used in medicines. Strontium is used to build the exoskeleton.
• The last metal that is Radium has a low availability and is very highly radioactive.

Conclusion

Alkaline earth metals are of very keen importance to us. These metals are highly important for the automobile industries due to their structure qualities. These metals are of great concern, as they are also included in building machines and other important equipment. 

Nomenclature and Structure of Carboxyl Group

Introduction :

In aldehydes the carbonyl compilation is connection to a carbon and hydrogen as in the ketons is attachment to carbon atoms. The carbonyl combine in to carbonyl acids derived as in combine where carbon is attachment to nitrogen with to halogens are identified amides along with acyl correspondingly. The frequent method of these module combine as aldehyde, ketone.

Nomenclature and Structure of Carboxyl Group Carboxylic Acids:

Aldehydes with ketones as well carboxylic acids are huge increase in plant life along with animal empire. They cooperate an important position in biochemical technique of existence. They append smell by flavour to environment.Carbon compound comprise a carboxyl well-organized locate –COOH are identified carboxylic acids. The carboxyl grouping, consists of a carbonyl grouping append to a hydroxyl group, thus the surname carboxyl. 

Nomenclature and structure Carboxylic acids capacity be aliphatic depending list the collection, alkyl or aryl append toward carboxylic carbon. huge digit of carboxylic acids are ascertain in environment. a number of advanced correlate of aliphatic carboxylic acids identified as greasy acids, happen in usual heavy since ester of glycerol.  Carboxylic acids afford as initial substance for a number of supplementary significant organic complex such similar to anhydrides.
They are develop  in amny foodstuff yield also pharmaceuticals toward include flavours. a number of these people are influence for utilize since solvents to is acetone with for categorize equipment similar to adhesives.

Nomenclature and structure of carboxyl group:
Carboxylic acids are amongst the initial organic compounds to subsist isolated from environment a huge quantity of them are accepted by their frequent names.
The normal given name end with the suffix –ic acid also have derived from latin names of their accepted foundation. intended for naming compounds containing supplementary than one carboxyl group, the finale –e of the alkane is retained.
Structure of carboxyl group:
Nomenclature and structure carboxylic acids the acquaintance to the carboxyl carbon be located in one plane as well as are separated by concerning 120°. The carboxylic carbon is with a reduction of electrophilic than carbonyl carbon as of the feasible resonance structure.

Definition of some Important Terms Pertaining to Coordination Compounds

Introduction:
Complex ion, exciting molecular collective consisting of a metallic atom or ion to which is emotionally involved single or additional electron-donating molecules. In a number of complex ions, such as sulfate, the atoms are so tightly bound collectively that they do something as an only unit. A lot of complex ions however are simply loosely aggregated and lean to distance in a water solution until equilibrium is recognized connecting the complex ion and its important components.

Some Important Terms Pertaining to Coordination Compounds:

Definition of Central atom/ion compounds:

In terms pertaining of coordination entity is definition; the atom/ion to which a fixed number of ions/group is bound in a definite geometrical arrangement around is called the central atoms or ions.
Ligands compounds:
The terms pertaining ions or molecules bound to the central atoms ion in the coordination entity are called ligands. These may be simple ions such as Cl-, Small molecules such as H2o or NH3, larger molecules such as H2NCH2CH2NH2 or N (CH2CH2NH3) or even macromolecules such as proteins.
Definition of coordination number:
Some terms pertaining of synchronization numeral of a metal ion in a complex can be distinct as the number of ligands donor atoms to which the metal is straight bonded.
Definition of coordination sphere:
The central atom/ions and ligands attached to it are enclosed in square, bracket and are collectively terms pertaining as the coordination sphere. Some ionization groups are written outside the bracket and are called counter ions.
Definition of coordination polyhedron:
The spatial arrangements of the important ligand atoms which are directly attached to the central atoms/ion definition terms a coordination polyhedron about the central atoms.
Definition of oxidation number of central atoms compounds:
The oxidation number of the central atom in a some complex is definition as the charge it would carry if all the ligands are removed along with the electron pair that are shared with the central atoms.

Homoleptic and Heteroleptic Complexes Compounds:

         Important complex in which a metal is bound to only one kind of donor group [CO (NH3)6)3+ are known as homoleptic. Important Complex in which a metal is bound to more than one kind of donor group are known as hetroleptic.

Properties of Transverse Waves

Introduction 

A transverse wave is a type of mechanical wave. They travel in a straight line and carry energy and momentum through medium particles from one point to another.
“If on propagation of a mechanical wave through a medium, the medium particles oscillate along a direction perpendicular to the direction of propagation of the wave, the wave is called a transverse wave.”  In other words, if wave travels in x- direction, medium particles vibrate up or down or along y- direction. For example, when one end of a horizontal rope is tied to a hook and the other end is moved up and down, a transverse wave travel horizontally while particles of rope vibrate up and down.
There are several examples of transverse waves in everyday life.               
Vibrations in string, surface water waves, electromagnetic waves, seismic S (secondary) waves, audience wave.

Properties of Transverse Waves

A transverse wave has all properties of mechanical waves.

1. Amplitude- The maximum vertical displacement of the medium particles on either side of its equilibrium position is called the amplitude. It is denoted by ‘a’.
2. Time period- The time taken by medium particle in completing one oscillation is called as the time period of wave.it is denoted by ‘T’.
3. Frequency- The number of oscillations made by a medium particle in 1 second is called as frequency of wave. It is denoted by ‘f’.
4. Phase- The phase of the wave at any instant denotes the position and direction of motion of medium particle at that instant.
5. Wavelength- The distance travelled by the wave in one complete oscillation

is called as wavelength of wave. It is denoted by ‘λ’.

Properties of Transverse Waves : Speed

Wave speed- The distance travelled by the wave in one second is called as ‘wave speed’. It is denoted by ‘v’.
Transverse waves can be formed only in solids because solids have rigidity.
(i)                Speed of transverse wave is given by the following formula-
                              V =√ (η / d)
Where, η is modulus of rigidity of material and d is the density.
(ii)              Speed of transverse waves in flexible stretched string is given by following formula-
                              V = √ (T / m)
 Where T is the tension in the string and m is the mass per unit length of string.

Longitudinal Waves Compression

Introduction:      

When a stone is dropped into water in a pond. waves are produced at the point where the stone strikes and water. The waves (ripples) travel outward and particles of the water vibrate up and down about their mean positions. This can be clearly seen when the leaves floating on the surface of the pond move up and down as the ripples pass on. They do not travel along the wave. Similarly, when a tuning fork is set into vibrations, waves are produced in the surrounding air making the particles of the air oscillate about their mean positions. Hence a wave motion can be defined as a form of disturbance which travels through the medium due to repeated periodic motion of the particles of the medium about their mean positions, the disturbance being handed over from one particle to the next. in the process the energy and momentum of the particles is successively transmitted through the medium in the wave form known as a progressive wave or a travelling wave. Such a wave travels with a constant speed in the medium.

Longitudinal Waves Compression

The direction of propagation of waves relative to the direction of vibration of the particles of the medium classifies them into two types, namely  longitudinal waves and transverse waves.

Longitudinal waves :
 If the particles of the medium vibrate parallel to the direction of propagation of the waves, the waves are called 'Longitudinal waves'. The propagation of longitudinal waves can be demonstrated as shown in the figure below. 

Longitudinal Waves Compression : Simulation

Let a light spring held horizontally be given a push in the same direction. The spring gets compressed sending a pulse of pressure along the spring. Soon this compression tends to release the pressure in the region by pushing the neighbouring (particles) layers of the spring. This is known as rarefaction. Thus the compressions transmitted horizontally along the length of the spring .If the pushing at the end of the spring is repeated at regular intervals of time a periodic longitudinal progressive wave takes place along the length of the spring.
Sound waves are longitudinal waves. Longitudinal waves can travel in solids, liquids and in gases as well.

Electromagnetic Spectrum Animation

Introduction:

The waves do not require medium for their propagation are called electromagnetic waves. These waves propagate in vacuum with speed of light c=3`xx` 10^-7m/s and on account of being chargeless they are not deflected by electric and magnetic fields. These electromagnetic spectrum is done in an animation.

Newton obtained the spectrum of sun and observed that all colours from red to violet exist continuously in the sun’s spectrum. The wavelength of violet colour is 4.0`xx` 10^-7m and the wavelength of red colour is 7.8`xx`10^-7m.

Electromagnetic Spectrum Animation

Visible spectrum in electromagnetic spectrum animation:

The region of spectrum from the wavelength 4.0`xx` 10^-7m to 7.8`xx`10^-7m is called visible spectrum, because all colours between this wavelength range are visible.

Infrared spectrum in electromagnetic animation:
The region of spectrum below violet is called ultraviolet spectrum while that above red is called infrared spectrum. The ultraviolet and infrared radiations are invisible.

According to the wavelength range, the whole electromagnetic spectrum animation is divided from very short gamma rays to long radiowaves.

Properties:
Electromagnetic spectrum animation properties:
Gamma rays ( - rays):

• They lie in the upper frequency range of electromagnetic spectrum.
• Their wavelength range from 10^-13m to 10^-10m.

 Discoverer: Becquerel in 1986.
 Origin: They are produced in nuclear reactions and emitted by disintegration of atomic-nuclei.
Properties: Chemical reaction on photographic plates, fluorescence, phosphorescence, less ionizing but high penetrating power.
 X-rays:

• Wavelength range from 10^-10 m to 10^-8.

Discover: Roentgen in 1896.
Origin: They are emitted due to bombardment of high energetic electrons on heavy target
Properties: All properties of  - rays but less penetrating and more ionizing power.

Ultraviolet Radiation:

• Wavelength range from 10^-8 m to 4.0`xx` 10^-7m.

Discover: Ritter in 1801.
Origin: They are emitted due to bombardment of high energetic electrons on heavy target.
Properties: Less penetration and produce photoelectric effect. Fortunately most of ultraviolet rays are absorbed by ozone layer of atmosphere.
Visible Light:

• Wavelength range from 4.0`xx` 10^-7m to 7.8`xx`10^-7m.

Discover: Newton in 1666.
Origin: Produced by incandescent bodies and ionized gases.
Properties: Produce photoelectric effect and sensation of vision.
Infrared Radiation:

• Wavelength range from 7.8`xx`10^-7m to 10^-3_.

Discover: Hershell in 1800.
Origin: Produced by hot bodies.
Properties: Prodominant heating effect, night photography.
Hertzian Waves:

• Wavelength range from 10^-3m to 1m.

Origin: By spark discharge.
Discover: Hertz in 1888.
Properties: Produce sparks in gaps of receiving circuits. The waves of wavelength range from 1mm to 3cm are also called microwaves.

I like to share this Electromagnetic Spectrum Radio Waves with you all through my article.

Long  Radio Waves:

• Wavelength range from 1m to 10⁵m. The frequency range of radio wave is 0.5MHz to 1000MHz.

Discover: Marconi in 1895.
Origin: These waves are generated by accelerated motion of charges in conducting waves or oscillating circuits.
Properties: Reflected  by layers of atmosphere.

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