#### Topics

##### Physical World and Measurement

##### Physical World

##### Units and Measurements

- International System of Units
- Measurement of Length
- Measurement of Mass
- Measurement of Time
- Accuracy Precision of Instruments and Errors in Measurement
- Significant Figures
- Dimensions of Physical Quantities
- Dimensional Formulae and Dimensional Equations
- Dimensional Analysis and Its Applications
- Need for Measurement
- Units of Measurement
- Fundamental and Derived Units
- Length, Mass and Time Measurements
- Introduction of Units and Measurements

##### Kinematics

##### Motion in a Plane

- Scalars and Vectors
- Multiplication of Vectors by a Real Number
- Addition and Subtraction of Vectors — Graphical Method
- Resolution of Vectors
- Vector Addition – Analytical Method
- Motion in a Plane
- Motion in a Plane with Constant Acceleration
- Projectile Motion
- Uniform Circular Motion
- General Vectors and Their Notations
- Motion in a Plane - Average Velocity and Instantaneous Velocity
- Rectangular Components
- Scalar and Vector Product of Vectors
- Relative Velocity in Two Dimensions
- Cases of Uniform Velocity
- Cases of Uniform Acceleration Projectile Motion
- Motion in a Plane - Average Acceleration and Instantaneous Acceleration
- Angular Velocity
- Introduction

##### Motion in a Straight Line

- Position, Path Length and Displacement
- Average Velocity and Average Speed
- Instantaneous Velocity and Speed
- Kinematic Equations for Uniformly Accelerated Motion
- Acceleration
- Relative Velocity
- Elementary Concepts of Differentiation and Integration for Describing Motion
- Uniform and Non-Uniform Motion
- Uniformly Accelerated Motion
- Position-time, Velocity-time and Acceleration-time Graphs
- Motion in a Straight Line - Position-time Graph
- Relations for Uniformly Accelerated Motion (Graphical Treatment)
- Introduction

##### Laws of Motion

- Aristotle’s Fallacy
- The Law of Inertia
- Newton's First Law of Motion
- Newton’s Second Law of Motion
- Newton's Third Law of Motion
- Conservation of Momentum
- Equilibrium of a Particle
- Common Forces in Mechanics
- Circular Motion and Its Characteristics
- Solving Problems in Mechanics
- Static and Kinetic Friction
- Laws of Friction
- Inertia
- Intuitive Concept of Force
- Dynamics of Uniform Circular Motion - Centripetal Force
- Examples of Circular Motion (Vehicle on a Level Circular Road, Vehicle on a Banked Road)
- Lubrication - (Laws of Motion)
- Law of Conservation of Linear Momentum and Its Applications
- Rolling Friction
- Introduction

##### Work, Energy and Power

- Introduction of Work, Energy and Power
- Notions of Work and Kinetic Energy: the Work-Energy Theorem
- Kinetic Energy
- Work Done by a Constant Force and a Variable Force
- Concept of Work
- The Concept of Potential Energy
- The Conservation of Mechanical Energy
- Potential Energy of a Spring
- Various Forms of Energy : the Law of Conservation of Energy
- Power
- Collisions
- Non - Conservative Forces - Motion in a Vertical Circle

##### Motion of System of Particles and Rigid Body

##### System of Particles and Rotational Motion

- Motion - Rigid Body
- Centre of Mass
- Motion of Centre of Mass
- Linear Momentum of a System of Particles
- Vector Product of Two Vectors
- Angular Velocity and Its Relation with Linear Velocity
- Torque and Angular Momentum
- Equilibrium of Rigid Bodies
- Moment of Inertia
- Theorems of Perpendicular and Parallel Axes
- Kinematics of Rotational Motion About a Fixed Axis
- Dynamics of Rotational Motion About a Fixed Axis
- Angular Momentum in Case of Rotation About a Fixed Axis
- Rolling Motion
- Momentum Conservation and Centre of Mass Motion
- Centre of Mass of a Rigid Body
- Centre of Mass of a Uniform Rod
- Rigid Body Rotation
- Equations of Rotational Motion
- Comparison of Linear and Rotational Motions
- Values of Moments of Inertia for Simple Geometrical Objects (No Derivation)

##### Gravitation

- Kepler’s Laws
- Newton’s Universal Law of Gravitation
- The Gravitational Constant
- Acceleration Due to Gravity of the Earth
- Acceleration Due to Gravity Below and Above the Surface of Earth
- Acceleration Due to Gravity and Its Variation with Altitude and Depth
- Gravitational Potential Energy
- Escape Speed
- Earth Satellites
- Energy of an Orbiting Satellite
- Geostationary and Polar Satellites
- Weightlessness
- Escape Velocity
- Orbital Velocity of a Satellite

##### Properties of Bulk Matter

##### Mechanical Properties of Fluids

- Thrust and Pressure
- Transmission of Pressure in Liquids: Pascal’s Law
- Variation of Pressure with Depth
- Atmospheric Pressure and Gauge Pressure
- Hydraulic Machines
- STREAMLINE FLOW
- Applications of Bernoulli’s Equation
- Viscous Force Or Viscosity
- Reynolds Number
- Surface Tension
- Effect of Gravity on Fluid Pressure
- Terminal Velocity
- Critical Velocity
- Excess of Pressure Across a Curved Surface
- Introduction to Fluid Machanics
- Archimedes' Principle
- Stokes' Law
- Equation of Continuity
- Torricelli'S Law

##### Thermal Properties of Matter

- Heat and Temperature
- Measurement of Temperature
- Ideal-gas Equation and Absolute Temperature
- Thermal Expansion
- Specific Heat Capacity
- Calorimetry
- Change of State - Latent Heat Capacity
- Conduction
- Convection
- Radiation
- Newton’s Law of Cooling
- Qualitative Ideas of Blackbody Radiation
- Wein'S Displacement Law
- Stefan's Law
- Anomalous Expansion of Water
- Liquids and Gases
- Thermal Expansion of Solids
- Green House Effect

##### Mechanical Properties of Solids

##### Thermodynamics

- Thermal Equilibrium
- Zeroth Law of Thermodynamics
- Heat, Internal Energy and Work
- First Law of Thermodynamics
- Specific Heat Capacity
- Thermodynamic State Variables and Equation of State
- Thermodynamic Process
- Heat Engines
- Refrigerators and Heat Pumps
- Second Law of Thermodynamics
- Reversible and Irreversible Processes
- Carnot Engine
- Isothermal Processes
- Adiabatic Processes

##### Behaviour of Perfect Gases and Kinetic Theory of Gases

##### Kinetic Theory

- Molecular Nature of Matter
- Gases and Its Characteristics
- Equation of State of a Perfect Gas
- Work Done in Compressing a Gas
- Introduction of Kinetic Theory of an Ideal Gas
- Interpretation of Temperature in Kinetic Theory
- Law of Equipartition of Energy
- Specific Heat Capacities - Gases
- Mean Free Path
- Kinetic Theory of Gases - Concept of Pressure
- Kinetic Theory of Gases- Assumptions
- rms Speed of Gas Molecules
- Degrees of Freedom
- Avogadro's Number

##### Oscillations and Waves

##### Oscillations

- Periodic and Oscillatory Motions
- Simple Harmonic Motion (SHM)
- Simple Harmonic Motion and Uniform Circular Motion
- Velocity and Acceleration in Simple Harmonic Motion
- Force Law for Simple Harmonic Motion
- Energy in Simple Harmonic Motion
- Some Systems Executing Simple Harmonic Motion
- Damped Simple Harmonic Motion
- Forced Oscillations and Resonance
- Displacement as a Function of Time
- Periodic Functions
- Oscillations - Frequency

##### Waves

#### description

- Definition of Vector Product

#### notes

**Vector Product or Cross Product of two vectors:**

The vector product or cros product of two vectors `vec"A"` and `vec"B"` is another vector `vec"C"`, whose magnitude is equal to the product of the magnitudes of the two vectors and sine of the smaller angle between them.

If Θ is the smaller angle between `vec"A"` and `vec"B"`, then

`vec"A"xxvec"B" = vec"C" = "AB" sin theta hat"C"`

where `hatC` is a unit vector in the direction of `vecC`. The direction of `vecC` or `hatC`(i.e. vector product of two vectors) is perpendicular to the plane containing `vec"A"` and `vec"B"` and pointing in the direction of advance of a right handed screw when rotated from `vec"A"` to `vec"B"`.

Some important properties of cross products are as follows:

(a) For parallel as well as anti parallel vectors(i.e. when `theta` = 0° or 180°), the cross product is zero.

(b) the magnitude of cross product of two perpendicular vectors is equal to the product of the magnitudes of the given vectors.

(c) Vector product is anti-commutative i.e. `vec"A" xx vec"E" = -vec"B" xx vec"A"`

(d) Vector product is distributive i.e. `vec"A"xx(vec"B" +vec"C")=vec"A" xx vec"B" + vecA xx vec"C"`

(e)`vecA xx vecB` does not change sign under reflection i.e. `(-vecA)xx(-vecB)=vecA xx vecB`

(f) For unit orthogonal vectors, we have

`hatixxhati=hatjxxhatj=hatkxxhatk=0,hatixxhatj=hatk,hatjxxhatk=hati and hatkxxhati=hatj`

moreover `hatjxxhati=-hatk, hatkxxhatj=-hati and hatixxhatk=-hatj`

(g) In terms of components `vec"A"xxvec"B"= |(hati,hatj,hatk),(A_x,A_y,A_z),(B_x,B_y,B_z)|`

The angular velocity of a body or a particle is defined as the ratio of the angular dispacement of the body or the particle to the time interval during which this displacement occurs.

ω = `("d" theta)/"dt"`

The direction of angular velocity is along the axis of rotation. it is measured in radian/sec and its dimensional formula is [M°L°T^{-1}].

The relation betwennt angular velocity and linear velocity is given by

`vecv = vecomegaxxvecr`

The angular acceleration of a body is defined as the ratio of the change in the angular velocity to the time interval.

`"Angular acceleration" = "Change in angular velocity"/("Time taken")`

`vecalpha = ("d"vecomega)/"dt"`

The unit of angular acceleration is rad s^{-2} and dimensional formula is [M°L°L^{-2}]