#### 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

- Circular motion

- Terms involved in a circular motion

1) Angular displacement

2) Angular Velocity

3) Angular Acceleration

- Uniform Circular Motion (UCM)
- Time Period of UCM
- Frequency of UCM

- Centripetal acceleration (Radial acceleration)

1) For non-uniform circular motion - Centripetal force
- Centrifugal force

## Notes

### Circular Motion

Circular motion is the movement of an object in a circular path.

#### Uniform Circular Motion

This motion refers to the circular motion if the magnitude of the velocity of the particle in circular motion remains constant. The non-uniform circular motion refers to the circular motion when the magnitude of the velocity of the object is not constant. Another special kind of circular motion is when an object rotates around itself also known by spinning motion.

**Variables in Circular Motion:-**

**Angular Displacement**

"The angle which is subtended by the position vector at the centre of the circular path refers to the angular displacement."

"The angle which is subtended by the position vector at the centre of the circular path refers to the angular displacement."

Angular Displacement (Δθ) = `(ΔS)/(r)`

where Δ’s refers to the linear displacement while r is the radius. Radian is the unit of Angular Displacement.

**Angular Acceleration"It refers to the rate of time of change of angular velocity (dῶ)."**

Angular acceleration (α) = `(dῶ)/dt` = `(d^2θ) / (dt^2)`

Its unit is `(rad)/(s^2)` and dimensional formula `[T^(-2)]`. The relation between linear acceleration (a) and angular acceleration (α)

A = rα, where r is the radius.

**Angular Velocity"It refers to the time rate change of angular displacement (dῶ)."**

Angular Velocity (ῶ) = `(Δθ)/(Δt)`

Angular Velocity is a vector quantity. Its unit is rad/s. The relation between the linear velocity (v) and angular velocity (ῶ) is

v = rῶ

**Centripetal Acceleration"It refers to an acceleration that acts on the body in circular motion whose direction is always towards the centre of the path."**

Centripetal Acceleration (α) = `v^2/r = rῶ^2`.

The magnitude of this acceleration by comparing ratios of velocity and position around the circle. Since the particle is travelling in a circular path, the ratio of the change in velocity to velocity will be the same as the ratio of the change in position to position. It is also known as radial acceleration as it acts along the radius of the circle. Centripetal Acceleration is a vector quantity and the unit is in `m/s^2`.