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
- Stefan-boltzmann 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: 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
- 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 Circuit
- 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
- 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-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
- 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
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Translational, which is velocity of COM.
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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.
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Point Po have opposite velocities , and if condition of no-slipping is there then it must have zero velocity, so `V_(com) = ωR`
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At point P1both the velocities add up.
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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.
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The line passing through PO and parallel to w is called the instantaneous axis of rotation.
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The point PO is instantaneously at rest.
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Kinetic Energy of Rolling Motion
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`"KE_rolling" = "KE_translation" + "KE_rotation"`
- `KE=1/2Iomega^2 + 1/2mv_(com)^2`
- substituting I =mk2(where K is the radius of gyration) and `V_"com"=Romega`
- we get `"KE"=1/2mv_"com"^2(1+k^2/R^2)`
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