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
- Stefan-boltzmann 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: Biot-savart 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,
- Van-deGraaff 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
- Alpha-particle 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
- de-Broglie Relation
- Wave Nature of Matter
- Wavelength of an Electron
- Davisson and Germer Experiment
- Continuous and Characteristics X-rays
Semiconductors
- Energy Bands in Solids
- Extrinsic Semiconductor
- Applications of n-type and p-type Semiconductors
- Special Purpose P-n Junction Diodes
- Semiconductor Diode
- Zener Diode as a Voltage Regulator
- I-V Characteristics of Led
- Transistor and Characteristics of a Transistor
- Transistor as an Amplifier (Ce-configuration)
- 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 1st law Vs. Copernicus Model
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According to Copernicus planets move in circular motion whereas according to Kepler planets revolve in elliptical orbit around the sun.
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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
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Select two points F1 and F2.
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Take a pieceof string and fix its ends at F1 and F2.
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Stretch the string taut with the help of a pencil and then draw a curve by moving the pencil keeping the string taut throughout.
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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.
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Join the points F1 and F2,and extend the line to intersect the ellipse at points P and A.
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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.
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For a circle, the two foci merge onto one and the semi-major axis becomes the radius of the circle.
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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.
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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.
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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 semi-major 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 semi-major axis is same as radius of the circle)