#### 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
- 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
- Concept of 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
- 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

- Concept of Pressure
- Pascal's Law
- Variation of Pressure with Depth
- Atmospheric Pressure and Gauge Pressure
- Hydraulic Machines
- STREAMLINE FLOW
- Bernoulli’S Principle
- 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

- Temperature and Heat
- 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 Processes
- 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
- Behaviour of Gases
- Equation of State of a Perfect Gas
- Work Done in Compressing a Gas
- Introduction of Kinetic Theory of an Ideal Gas
- Kinetic Interpretation of Temperature
- 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
- 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

#### notes

## Vector Addition- Analytical Method

Adding two or more vectors is called vector addition. What is a vector? Any quantity which has magnitude along with direction is a vector. Some of the examples for vector quantities are displacement, velocity, acceleration, force, pressure etc. Mathematical operations can be performed between two or more vectors. In this article, we will learn about the vector addition of two quantities using the analytical methods.

**What is vector addition?**The process of adding two or more vectors is called vector addition. Depending on the direction of the vector, vector addition is categorised into two types. They are –

**Parallelogram law of vector addition**

**Triangular law of vector addition.**

Consider a vector `bar A and bar B`

**Parallelogram law of vector addition**If two vectors are arranged head to head or tail to tail then, the parallelogram law of vector addition is carried out.

**Statement“If two vectors are considered to be the adjacent sides of a parallelogram, then the resultant of two vectors is given by the vector that is a diagonal passing through the point of contact of two vectors.”**

**Method**Step-wise vector addition of two vectors using Parallelogram law of vector addition is given below-

**Step 1:**Consider two vectors; `bar A and bar B`

**Step 2:**Bring the tail of `bar A` to the tail of `bar B`. Here the direction of vectors is not changed.

**Step 3:**Draw a lines parallel to `bar A` and `bar B` with the same magnitude, in a way to complete parallelogram.

**Step 4:**Join the point o and r by a straight line with an arrow pointing towards the r. This is diagonal to the parallelogram.

And this is the resultant vector `bar R, bar A + bar B = bar R`

**Triangular law of vector addition.**

If two vectors are arranged head to tail the traingular law of vector addition is carried out.

**Statement:**

**“When two vectors are represented by two sides of a triangle in magnitude and direction were taken in the same order then the third side of that triangle represents in magnitude and direction the resultant of the vectors.”**

**Method:**Step-wise vector addition of two vectors using Triangular law of vector addition is given below-

**Step 1:**Consider two vectors, `bar A and bar B`

**Step 2:**Bring the head of `bar A` to the tail of `bar B`. Here the direction of vectors is not changed.

**Step 3:**Join the tail of `bar A`to the head of `bar B`by a straight line with an arrow pointing towards the head of `bar B`

This new vector is the resultant vector `bar C, bar A + bar B = bar C`

**Why vector addition is important?**In physics, vector quantities like force interact with each other and produce a resultant effect on the objects upon which they are applied. Since the impact of all these forces is taken into consideration when finding the nature of motion of the system, so, in order to find the resultant of these forces, operations such as addition, subtraction and multiplication are required to be performed on these forces.