Topics
Rotational Dynamics
 Rotational Dynamics
 Characteristics of Circular Motion
 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
 Torque and Angular Momentum
 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
 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
Angular Momentum
Kinetic Theory of Gases and Radiation
 Kinetic Theory of Gases and Radiation
 Behaviour of a Gas
 Ideal Gas and Real Gas
 Mean Free Path
 The Pressure of Ideal Gas
 Root Mean Square (RMS) Speed
 Kinetic Interpretation of Temperature
 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
 Stefanboltzmann Law of Radiation
Oscillations
 Periodic and Oscillatory Motions
 Simple Harmonic Motion
 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 Motions
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
 Kinetic Theory of Gases Assumptions
 Mean Free Path
 Derivation for Pressure of a Gas
 Degrees of Freedom
 Derivation of Boyle’s Law
 Thermal Equilibrium
 First Law of Thermodynamics
 Heat Engines
 Temperature and Heat
 Qualitative Ideas of Blackbody Radiation
 Wein'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
 Induced Emf in a Stationary Coil in a Changing Magnetic Field
 Generators
 Back Emf and Back Torque
 Induction and Energy Transfer
 Eddy Currents
 SelfInductance
 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
 SelfInductance
 Mutual Inductance
 Transformers
 Need for Displacement Current
 Coil Rotating in Uniform Magnetic Induction
 Alternating Currents
 Reactance and Impedance
 LC Oscillations
 Inductance and Capacitance
 Resonant Circuit
 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
 MassEnergy Relation and Mass Defect
 Nuclear Binding Energy
 Nuclear Fusion – Energy Generation in Stars
 deBroglie Relation
 Wave Nature of Matter
 Wavelength of an Electron
 DavissonGermer 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
 Kinetic Energy of Rolling Motion
notes
Rolling motion
Rolling motion is a combination of rotation and translation.
All the particles on a rolling body have two kinds of velocity

Translational, which is velocity of COM.

Linear velocity on account of rotational motion.
Here in the figure we can see that every point have two velocities, one in the direction of velocity of COM and other perpendicular to the line joining centre and the point.

Point Po have opposite velocities , and if condition of noslipping is there then it must have zero velocity, so `V_(com) = ωR`

At point P1both the velocities add up.

At any other point, add both the velocities vectorially to get the resultant, which are shown for some of the cases in red color in figure.

The line passing through PO and parallel to w is called the instantaneous axis of rotation.

The point PO is instantaneously at rest.

Kinetic Energy of Rolling Motion

`"KE_rolling" = "KE_translation" + "KE_rotation"`
 `KE=1/2Iomega^2 + 1/2mv_(com)^2`
 substituting I =mk^{2}(where K is the radius of gyration) and `V_"com"=Romega`
 we get `"KE"=1/2mv_"com"^2(1+k^2/R^2)`