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
Kinetic Theory of Gases and Radiation
 Gases and Its Characteristics
 Classification of Gases: Real Gases and Ideal Gases
 Mean Free Path
 Pressure of Ideal 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
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
Surface Tension
Superposition of Waves
Wave Motion
Wave Optics
Stationary Waves
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
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
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
Current Electricity
Dual Nature of Radiation and Matter
Magnetic Effects of Electric Current
Structure of Atoms and Nuclei
Magnetism
Semiconductor Devices
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
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
description
 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)