Topics
Rotational Dynamics
 Rotational Dynamics
 Circular Motion and Its Characteristics
 Applications of Uniform Circular Motion
 Vertical Circular Motion
 Moment of Inertia as an Analogous Quantity for Mass
 Radius of Gyration
 Theorems of Perpendicular and Parallel Axes
 Angular Momentum or Moment of Linear Momentum
 Expression for Torque in Terms of Moment of Inertia
 Conservation of Angular Momentum
 Rolling Motion
Circular Motion
 Angular Displacement
 Angular Velocity
 Angular Acceleration
 Angular Velocity and Its Relation with Linear Velocity
 Uniform Circular Motion (UCM)
 Radial Acceleration
 Dynamics of Uniform Circular Motion  Centripetal Force
 Centrifugal Forces
 Banking of Roads
 Vertical Circular Motion Due to Earth’s Gravitation
 Equation for Velocity and Energy at Different Positions of Vertical Circular Motion
 Kinematical Equations for Circular Motion in Analogy with Linear Motion.
Gravitation
 Newton’s Law of Gravitation
 Projection of Satellite
 Periodic Time
 Kepler’s Laws
 Binding Energy and Escape Velocity of a Satellite
 Weightlessness
 Variation of ‘G’ Due to Lattitude and Motion
 Acceleration Due to Gravity and Its Variation with Altitude and Depth
 Communication satellite and its uses
 Composition of Two S.H.M.’S Having Same Period and Along Same Line
Mechanical Properties of Fluids
 Fluid and Its Properties
 Thrust and Pressure
 Liquid Pressure
 Pressure Exerted by a Liquid Column
 Atmospheric Pressure
 Gauge Pressure and Absolute Pressure
 Hydrostatic Paradox
 Pascal’s Law
 Application of Pascal’s Law
 Measurement of Atmospheric Pressure
 Mercury Barometer (Simple Barometer)
 Open Tube Manometer
 Surface Tension
 Molecular Theory of Surface Tension
 Surface Tension and Surface Energy
 Angle of Contact
 Effect of Impurity and Temperature on Surface Tension
 Excess Pressure Across the Free Surface of a Liquid
 Explanation of Formation of Drops and Bubbles
 Capillarity and Capillary Action
 Fluids in Motion
 Critical Velocity and Reynolds Number
 Viscous Force or Viscosity
 Stokes’ Law
 Terminal Velocity
 Equation of Continuity
 Bernoulli's Equation
 Applications of Bernoulli’s Equation
Angular Momentum
 Definition of M.I., K.E. of Rotating Body
 Rolling Motion
 Physical Significance of M.I (Moment of Inertia)
 Torque and Angular Momentum
 Theorems of Perpendicular and Parallel Axes
 M.I. of Some Regular Shaped Bodies About Specific Axes
Kinetic Theory of Gases and Radiation
 Gases and Its Characteristics
 Classification of Gases: Real Gases and Ideal Gases
 Mean Free Path
 Expression for Pressure Exerted by a Gas
 Root Mean Square (RMS) Speed
 Interpretation of Temperature in Kinetic Theory
 Law of Equipartition of Energy
 Specific Heat Capacity
 Absorption, Reflection, and Transmission of Heat Radiation
 Perfect Blackbody
 Emission of Heat Radiation
 Kirchhoff’s Law of Heat Radiation and Its Theoretical Proof
 Spectral Distribution of Blackbody Radiation
 Wien’s Displacement Law
 Stefanboltzmann Law of Radiation
Oscillations
 Periodic and Oscillatory Motion
 Simple Harmonic Motion (S.H.M.)
 Differential Equation of Linear S.H.M.
 Projection of U.C.M.(Uniform Circular Motion) on Any Diameter
 Phase of K.E (Kinetic Energy)
 K.E.(Kinetic Energy) and P.E.(Potential Energy) in S.H.M.
 Composition of Two S.H.M.’S Having Same Period and Along Same Line
 Some Systems Executing Simple Harmonic Motion
Thermodynamics
 Thermodynamics
 Thermal Equilibrium
 Zeroth Law of Thermodynamics
 Heat, Internal Energy and Work
 First Law of Thermodynamics
 Thermodynamic State Variables and Equation of State
 Thermodynamic Process
 Heat Engine
 Refrigerators and Heat Pumps
 Second Law of Thermodynamics
 Carnot Cycle and Carnot Engine
Oscillations
 Oscillations
 Explanation of Periodic Motion
 Linear Simple Harmonic Motion (S.H.M.)
 Differential Equation of Linear S.H.M.
 Acceleration (a), Velocity (v) and Displacement (x) of S.H.M.
 Amplitude (A), Period (T) and Frequency (N) of S.H.M.
 Reference Circle Method
 Phase in S.H.M.
 Graphical Representation of S.H.M.
 Composition of Two S.H.M.’S Having Same Period and Along Same Line
 The Energy of a Particle Performing S.H.M.
 Simple Pendulum
 Angular S.H.M. and It's Differential Equation
 Damped Oscillations
 Free Oscillations, Forced Oscillations and Resonance Oscillations
 Periodic and Oscillatory Motion
Elasticity
 Eneral Explanation of Elastic Property
 Plasticity
 Deformation
 Definition of Stress and Strain
 Hooke’s Law
 Elastic Energy
 Elastic Constants and Their Relation
 Determination of ‘Y’
 Behaviour of Metal Wire Under Increasing Load
 Application of Elastic Behaviour of Materials
Surface Tension
 Molecular Theory of Surface Tension
 Surface Tension
 Capillarity and Capillary Action
 Effect of Impurity and Temperature on Surface Tension
Superposition of Waves
 Superposition of Waves
 Progressive Waves
 Reflection of Waves
 Superposition of Waves
 Stationary Waves
 Free and Forced Vibrations
 Harmonics and Overtones
 Sonometer
 Beats
 Characteristics of Sound
 Musical Instruments
 The Speed of a Travelling Wave
 Speed of Wave Motion
 Study of Vibrations of Air Columns
Wave Motion
 Wave Motion Introduction
 Simple Harmonic Progressive Waves,
 Reflection of Transverse and Longitudinal Waves
 Change of Phase
 Principle of Superposition of Waves
 Formation of Beats
 Beats
Wave Optics
 Introduction of Wave Optics
 Nature of Light
 Light as a Wave
 Huygens’ Theory
 Reflection of Light at a Plane Surface
 Refraction of Light at a Plane Boundary Between Two Media
 Polarization
 Interference
 Diffraction of Light
 Resolving Power
Stationary Waves
 Study of Vibrations in a Finite Medium
 Formation of Stationary Waves on String
 Study of Vibrations of Air Columns
 Free and Forced Vibrations
 Forced Oscillations and Resonance
Electrostatics
 Electrostatics
 Application of Gauss' Law
 Electric Potential and Potential Energy
 Electric Potential Due to a Point Charge, a Dipole and a System of Charges
 Equipotential Surfaces
 Electrical Energy of Two Point Charges and of a Dipole in an Electrostatic Field
 Conductors and Insulators, Free Charges and Bound Charges Inside a Conductor
 Dielectrics and Electric Polarisation
 Capacitors and Capacitance, Combination of Capacitors in Series and Parallel
 Displacement Current
 Energy Stored in a Capacitor
 Van De Graaff Generator
 Uniformly Charged Infinite Plane Sheet and Uniformly Charged Thin Spherical Shell (Field Inside and Outside)
Current Electricity
 Current Electricity
 Kirchhoff’s Laws of Electrical Network
 Wheatstone Bridge
 Potentiometer
 Galvanometer
 Moving Coil Galvanometer
Kinetic Theory of Gases and Radiation
 Concept of an Ideal Gas
 Assumptions of Kinetic Theory of Gases
 Mean Free Path
 Derivation for Pressure of a Gas
 Degrees of Freedom
 Derivation of Boyle’s Law
 Thermal Equilibrium
 First Law of Thermodynamics
 Heat Engine
 Heat and Temperature
 Qualitative Ideas of Black Body Radiation
 Wien's Displacement Law
 Green House Effect
 Stefan's Law
 Maxwell Distribution
 Specific Heat Capacities  Gases
 Law of Equipartition of Energy
Magnetic Fields Due to Electric Current
 Magnetic Fields Due to Electric Current
 Magnetic Force
 Cyclotron Motion
 Helical Motion
 Magnetic Force on a Wire Carrying a Current
 Force on a Closed Circuit in a Magnetic Field
 Torque on a Current Loop in Magnetic Field
 Magnetic Dipole Moment
 Magnetic Potential Energy of a Dipole
 Magnetic Field Due to a Current: Biotsavart Law
 Force of Attraction Between Two Long Parallel Wires
 Magnetic Field Produced by a Current in a Circular Arc of a Wire
 Axial Magnetic Field Produced by Current in a Circular Loop
 Magnetic Lines for a Current Loop
 Ampere's Law
 Magnetic Field of a Solenoid and a Toroid
Wave Theory of Light
Magnetic Materials
 Magnetic Materials
 Torque Acting on a Magnetic Dipole in a Uniform Magnetic Field
 Origin of Magnetism in Materials
 Magnetisation and Magnetic Intensity
 Magnetic Properties of Materials
 Classification of Magnetic Materials
 Hysteresis
 Permanent Magnet and Electromagnet
 Magnetic Shielding
Interference and Diffraction
 Interference of Light
 Conditions for Producing Steady Interference Pattern
 Interference of Light Waves and Young’s Experiment
 Analytical Treatment of Interference Bands
 Measurement of Wavelength by Biprism Experiment
 Fraunhofer Diffraction Due to a Single Slit
 Rayleigh’s Criterion
 Resolving Power of a Microscope and Telescope
 Difference Between Interference and Diffraction
Electromagnetic Induction
 Electromagnetic Induction
 Faraday's Laws of Electromagnetic Induction
 Lenz's Law
 Flux of the Field
 Motional Electromotive Force (e.m.f.)
 Induced Emf in a Stationary Coil in a Changing Magnetic Field
 Generators
 Back Emf and Back Torque
 Induction and Energy Transfer
 Eddy Currents
 Self Inductance
 Energy Stored in a Magnetic Field
 Energy Density of a Magnetic Field
 Mutual Inductance
 Transformers
Electrostatics
 Applications of Gauss’s Law
 Mechanical Force on Unit Area of a Charged Conductor
 Energy Density of a Medium
 Dielectrics and Polarisation
 Concept of Condenser
 The Parallel Plate Capacitor
 Capacity of Parallel Plate Condenser
 Effect of Dielectric on Capacity
 Energy of Charged Condenser
 Condensers in Series and Parallel,
 VandeGraaff Generator
AC Circuits
 AC Circuits
 A.C. Generator
 Average and RMS Values
 Phasors
 Different Types of AC Circuits: AC Voltage Applied to a Resistor
 Different Types of AC Circuits: AC Voltage Applied to an Inductor
 Different Types of AC Circuits: AC Voltage Applied to a Capacitor
 Different Types of AC Circuits: AC Voltage Applied to a Series LCR Circuit
 Power in AC Circuit
 LC Oscillations
 Electric Resonance
 Sharpness of Resonance: Q Factor
 Choke Coil
Current Electricity
 Kirchhoff’s Rules
 Wheatstone Bridge
 Meter Bridge
 Metre Bridge
 Potentiometer
Dual Nature of Radiation and Matter
 Dual Nature of Radiation and Matter
 The Photoelectric Effect
 Waveparticle Duality of Electromagnetic Radiation
 Photo Cell
 De Broglie Hypothesis
 Davisson and Germer Experiment
 Waveparticle Duality of Matter
Magnetic Effects of Electric Current
Structure of Atoms and Nuclei
 Structure of Atoms and Nuclei
 Thomson’s Atomic Model
 Geigermarsden Experiment
 Rutherford’s Atomic Model
 Atomic Spectra
 Bohr’s Atomic Model
 Atomic Nucleus
 Constituents of a Nucleus
 Isotopes, Isobars and Isotones
 Atomic and Nuclear Masses
 Size and Density of the Nucleus
 Mass Defect and Binding Energy
 Binding Energy Curve
 Nuclear Energy
 Nuclear Binding Energy
 Radioactive Decays
 Law of Radioactive Decay
Magnetism
Semiconductor Devices
 Semiconductor Devices
 pn Junction Diode as a Rectifier
 Special Purpose Junction Diodes
 Bipolar Junction Transistor (BJT)
 Logic Gates
Electromagnetic Inductions
 Electromagnetic Induction
 Faraday’s Law of Induction
 Self Inductance
 Mutual Inductance
 Transformers
 Need for Displacement Current
 Coil Rotating in Uniform Magnetic Induction
 Alternating Currents
 Reactance and Impedance
 LC Oscillations
 Inductance and Capacitance
 Resonant Circuits
 Power in AC Circuit: the Power Factor
 Lenz’s Law and Conservation of Energy
Electrons and Photons
Atoms, Molecules and Nuclei
 Alphaparticle Scattering and Rutherford’s Nuclear Model of Atom
 Bohr’s Model for Hydrogen Atom
 Hydrogen Spectrum
 Atomic Masses and Composition of Nucleus
 Introduction of Radioactivity
 Law of Radioactive Decay
 Atomic Mass, Mass  Energy Relation and Mass Defect
 Nuclear Binding Energy
 Nuclear Fusion – Energy Generation in Stars
 deBroglie Relation
 Wave Nature of Matter
 Wavelength of an Electron
 Davisson and Germer Experiment
 Continuous and Characteristics Xrays
 Mass Defect and Binding Energy
Semiconductors
 Energy Bands in Solids
 Extrinsic Semiconductor
 Applications of ntype and ptype Semiconductors
 Special Purpose Pn Junction Diodes
 Semiconductor Diode
 Zener Diode as a Voltage Regulator
 IV Characteristics of Led
 Transistor and Characteristics of a Transistor
 Transistor as an Amplifier (Ceconfiguration)
 Transistor as a Switch
 Oscillators
 Digital Electronics and Logic Gates
Communication Systems
 Elements of a Communication System
 Basic Terminology Used in Electronic Communication Systems
 Bandwidth of Signals
 Bandwidth of Transmission Medium
 Need for Modulation and Demodulation
 Production and Detection of an Amplitude Modulated Wave
 Space Communication
 Propagation of Electromagnetic Waves
 Modulation and Its Necessity
 Law of orbits
 Law of areas
 Law of periods
Notes
KEPLER’S LAWS
The three laws of Kepler can be stated as follows:
Kepler’s First law (Law of orbits): All planets move in elliptical orbits with the Sun situated at one of the foci of the ellipse.
Kepler’s 1^{st} law Vs. Copernicus Model

According to Copernicus planets move in circular motion whereas according to Kepler planets revolve in elliptical orbit around the sun.

Copernicus model is based on one special case because circle is a special case of ellipse whereas Kepler’s laws aremore of ageneral form.
To Show ellipse is a special form of Circle

Select two points F1 and F2.

Take a pieceof string and fix its ends at F1 and F2.

Stretch the string taut with the help of a pencil and then draw a curve by moving the pencil keeping the string taut throughout.

The resulting closed curve is an ellipse. For any point T on the ellipse, the sum of distances from F1 and F2 is a constant. F1,F2 are called the foci.

Join the points F1 and F2,and extend the line to intersect the ellipse at points P and A.

The centre point of the line PA is the centre of the ellipse O and the length PO = AO, which is also known as the semimajor axis of the ellipse.

For a circle, the two foci merge onto one and the semimajor axis becomes the radius of the circle.

A string has its ends fixed at F1 and F2. The tip of the pencil holdsthe string taut and is moved around and we will get an ellipse.
Kepler’s second law (law of areal velocities):
 A planet moves round the sun in such a way that its areal velocity is constant.
 Planet moves faster when it is near to the sun and slower when it is farther from the sun.
 The areal velocity of a planet is constant.

Area covered by the planet while revolving around the sun will be equal in equal intervals of time. This means the rate of change of area with time is constant.

Suppose position and momentum of planet is denoted by ‘r’ and ‘p’ and the time taken will be Δt.
 `Delta"A"=1/2xx"r"xx"v"Delta"t"` (where `"v"Delta"t"` is distance travelled by a planet in `Delta"t"` time)
`(Delta"A")/(Delta"t")=1/2(rxxv)` `becausev=p/m` `
=`1/2((rxxp))/m`
= `"L"/"2m"`
where 'v' ia the velocity, L is the angular momentum equal to `("r"xx"p")`. For a central force, which is directed along r, L is a constant as the planet goes around. Hence, `(Delta"A")/(Delta"t")`is a constant according to the last equation. This is the law of areas. Gravitation is a central force and hence the law of areas follows.
Kepler’s third law (law of time period): A planet moves round the sun in such a way that the square of its period is proportional to the cube of semi major axis of its elliptical orbit.
Statement:
Accourding to this law the square of time period of a planet is `prop` to the cube of the semimajor axis of its orbit.
suppose earth is revolving around the sun then the square of the time period is `prop` to the cube of the semi major axis.
It is known as the law of periods as it is dependent on the time period of planets.
Derivation of 3rd law: Let us assume that the path of planet is circular
let m = mass of the planet
M = mass of the sun
according to newtons law of gravitation:
`"F"="GMm"/"r"^2`
`"F"_c = "mv"^2/r`
where `"F"_c`= Centripetal force which helps the planet to move around the sun.
`"F"="F"_c`
`"GMm"/"r"^2 = "mv"^2/"r"`
`"GM"/"r" = "v"^2` ...(1)
`"v" = (2pi"r")/"T"`
squaring both the sides in the above eq.
`"v"^2 = (4pi^2"r"^2)/"T"^2`
Substituting this value in eq (1) we get
`"GM"/"r" = (4pir^2)/T^2`
`"T"^2 = (4pi^2"r"^3)/"GM"` Where `((4pi^2)/"GM")="constant"`
`"T"^2 = "r"^3`(In ellipse semimajor axis is same as radius of the circle)