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  • Physics
    • The world around you!
    • Mechanics
      • Preface
      • Units, Vectors and Mathematical Physics
        • Units, Standards & Dimension analysis
        • Measurement
        • Scalars and Vectors
        • Multiplication of Two Vectors
        • Mathematical Physics
      • Kinematics
        • Speed, Velocity and Acceleration
        • Motion in 1-D and free fall
        • Motion in 2-D and Projectile motion
        • Relative velocity
      • Newton's Laws of Motion
        • Force and laws of motion
        • Friction
        • Simple Machines
      • Work, Energy and Power
        • Work and Kinetic energy
        • Potential energy and Energy conservation
        • Power
      • Linear Momentum
        • Momentum and Impulse
        • CM & CG
        • Collisions
      • Circular motion
        • Uniform circular motion
        • Vertical circular motion
      • Rotational Motion
        • Rotational kinematics
        • Moment of inertia
        • Dynamics of rotational motion
        • Angular momentum
        • Rolling Motion
      • Oscillations
        • Simple Harmonic Motion
        • Simple pendulum
      • Gravitation
        • Newton's universal law of gravitation
        • Gravitational potential energy
        • Kepler's Laws
      • Fluid Mechanics
        • Fluid density and pressure
        • Pascal's principle
        • Buoyancy and Archimedes' principle
        • Bernoulli's principle
      • Mechanical Properties of Matter
        • Elasticity
        • Surface tension
        • Viscosity in fluids
        • Stokes' law
    • Thermal Physics
      • Preface
      • Heat & Temperature
        • Internal energy & temperature
        • Sources of heat
      • Calorimetry
        • Specific heat
        • Change of State
        • Calorimeter
      • Thermal Expansion
        • Expansion of solids
        • Expansion of liquids and gases
        • Anomalous expansion of water
      • Heat Transfer
        • Conduction and Convection
        • Radiation
        • Applications of heat transfer
      • Kinetic Theory
        • Kinetic theory of gases
        • Ideal Gas Equations
      • Thermodynamics
        • First law of thermodynamics
        • Specific heat capacities of gases
        • Entropy and second law of thermodynamics
      • Heat Engines
        • Carnot cycle
        • Heat pumps
    • Waves and Optics
      • Preface
      • Wave Motion
        • Transverse and longitudinal waves
        • Wave characteristics
        • Reflection and interference of waves
        • Standing waves
      • Sound Waves
        • Properties of Sound Wave
        • Vibrations of air column
        • Interference of sound waves
        • Doppler effect
        • Musical Sounds
      • Nature of Light
        • Properties of light
        • Shadows and Eclipses
      • Reflection
        • Laws of reflection
        • Image formation in plane mirrors
        • Concave and convex mirrors
      • Refraction
        • Laws of refraction
        • Total internal reflection
        • Prisms and rainbows
        • Lenses
      • Interference and Diffraction
        • Wave nature of light
        • Interference
        • Diffraction
        • Polarization
      • Optical Instruments
        • Human Eye
        • Microscopes & Telescopes
        • Eyepieces & Cameras
    • Electricity
      • Preface
      • Electric Charge and Electric Field
        • Coulomb's law
        • Electric field
      • Electric Potential
        • Electric potentia and potential energy
        • Relation between field and potential
        • Electric dipole
      • Gauss's law
        • Gauss law
        • Spherical charge distribution
        • Linear charge distribution
        • Planar charge distribution
      • Capacitors and Dielectrics
        • Capacitors and Capacitance
        • Types of capacitors
        • Energy stored in a capacitor
        • Dielectric types
      • Current Electricity
        • Current, Resistance and ohm's law
        • Cells, EMF and Internal Resistance
        • Kirchoff's laws and electric circuits
        • Wheatstone bridge and potentiometer
        • Ammeter and Voltmeter
        • RC circuits in DC voltage
      • Thermal and Chemical effects of current
        • Joule's law of heating
        • Seebeck and Peltier effect
        • Thomson's effect
        • Faraday's laws of electrolysis
    • Electromagnetism
      • Preface
      • Magnetism
        • Magnets and magnetic fields
        • Magnetic materials and properties
        • Earth's magnetic field
        • Magnetometers
      • Magnetic Forces
        • Lorentz force
        • Magnetic force on a current carrying conductor
        • Torque on a current carrying loop
      • Magnetic field due to current
        • Biot-Savart's law
        • Ampere's law
      • EM Induction
        • Faraday's and Lenz's law
        • Self and Mutual induction
        • LC/LR circuits
      • A.C. Circuits
        • Current, Voltage and RMS value
        • RLC circuits
        • Resonance and power in AC circuits
        • Machines and Devices
      • Electromagnetic Waves
        • Maxwell's equations
        • Light as EM Wave
        • Properties of EM Waves
    • Modern Physics
      • Preface
      • Bohr's atomic model
        • Rutherford's atomic model
        • Bohr's atomic model
      • Quantum theory
        • Photons and Photoelectric effect
        • Wave Nature of Particles
        • Quantum model of atom
        • X-rays
      • Nucleus
        • Properties of nucleus
        • Isotopes, isobars and isotones
        • Mass defect and binding energy
      • Radioactivity
        • Alpha, beta and gamma rays
        • Laws of radio-activity
        • Applications of radioactivity
      • Nuclear Reactions
        • Nuclear fission
        • Nuclear fusion
        • Radiation hazards
      • Semiconductor Electronics
        • Energy bands in solids
        • Semiconductor diodes
        • Half-wave and Full-wave rectifiers
        • BJTs and FETs
        • Applications of transistors
        • Digital Electronics
      • Communication Systems
        • Electromagnetic Waves
        • Modulation
  • Chemistry
    • Matter is everything!
    • Structure of Matter
      • Preface
      • Elements, Compounds and Mixtures
        • Elements
        • Compounds
        • Mixtures
        • Separation and Purification
      • Properties of Matter
        • Fundamental units
        • Derived units
        • Chemical properties
      • Measurement and Experimental techniques
        • Units and Conversions
        • Measurement and Evaluation
        • Physical constants
      • Atomic Structure
        • Atoms, Molecules and Ions
        • Dalton's atomic theory
        • Electrons, Protons and Neutrons
        • Atomic Models
        • Structure of an atom
        • Isotopes
      • Quantum Theory
        • The nature of light
        • Atomic spectrum
        • Wave Nature of Particle
        • Photoelectric Effect
        • Quantum mechanical model
      • Development of Periodic Table
        • Electronic configuration
        • Genesis of classification
        • Modern Periodic table
      • Periodic Properties
        • Atomic & Ionic radii
        • Ionization energies
        • Electron affinities
        • Electronegativity
      • Chemical Bonding
        • Octet and Fajans' rule
        • Valency
        • Ionic Bonding
        • Chemical Properties
        • Lewis dot structures
        • Resonance Structures
        • Covalent and Metallic Bonding
        • Valence Bond Theory
        • Molecular orbital theory
        • Hybridization of atomic orbitals
        • Molecular Geometry
      • Nuclear Chemistry
        • Alpha, Beta and Gamma radiation
        • Radioactive Transformations
        • Rate of Radioactive Decay
        • Effects of Radiation
        • Applications of radioisotopes
        • Nuclear Fission
        • Nuclear Fusion
    • States of Matter
      • Preface
      • Kinetic particle theory
        • Solids, Liquids and Gases
        • Change in states
        • Latent heat
      • Forces of Attraction
        • Intramolecular forces
        • Dipole forces
        • Intermolecular forces
        • Hydrogen bonding
      • Gases
        • Pressure of gas
        • Gas laws
        • Ideal gas equation
        • Molar mass and density
        • Dalton's law of partial pressure
        • Kinetic molecular theory
        • Effusion & Diffusion
        • Real and Ideal gases
      • Liquids
        • Surface tension
        • Viscosity
        • Evaporation
        • Boiling point
      • Solids
        • Crystalline solids
        • Structure of Solids
        • Properties of Solids
        • Elasticity and Hooke's law
        • Lattice Energy
      • Solutions
        • Types of Solutions
        • Colloids
        • Solubility
        • Concentration
        • Volumetric analysis
        • Enthalpy of Solutions
        • Raoult's Law
        • Colligative properties
        • Phase Diagrams
      • Atmosphere and Environment
        • Spheres of Earth
        • Atmosphere
        • Biogeochemical Cycles
      • Air, Water & Soil
        • Composition of air
        • Air pollution
        • Greenhouse effect
        • Water and its sources
        • Properties of Water
        • Water - treatment and pollution
        • Soil - pollution and control
        • Green chemistry
    • Chemical Reactions
      • Preface
      • Chemical Equations
        • Chemical Changes
        • Types of chemical reactions
        • Characteristics of chemical reactions
        • Balancing chemical equations
      • Chemical Calculations
        • Stoichiometry
        • The Mole
        • Mass Spectrometer
        • Molecular formulae
      • Acids, Bases and Salts
        • Acids
        • Bases
        • Salts
        • Acid-base Theories
        • Acid-base Classification
        • Nomenclature of acids, bases & salts
        • pH Scale and Buffer Solution
        • Acid-base titration
      • Thermo Chemistry
        • Energy changes
        • System, Surroundings and Types
        • Energy, heat and work
        • First law of thermodynamics
        • Enthalpy and Hess' law
        • Second law of thermodynamics
        • Gibbs free energy
      • Chemical Kinetics
        • Rate (speed) of reaction
        • Integrated Rate laws
        • Order of reaction
        • Catalyst
      • Chemical Equilibrium
        • Reversible and Irreversible reactions
        • Law of mass action
        • Equilibrium constants
        • Le Chatelier Principle
      • Oxidation and Reduction
        • Redox reactions
        • Oxidizing and reducing agents
        • Oxidation number
        • Balancing of reactions
        • Everyday examples
      • Electrochemistry
        • Conductors and Semiconductors
        • Ohm's Law
        • Electrolysis
        • Corrosion
        • Faraday's laws
        • Voltaic or Galvanic cell
        • Electromotive Force (EMF)
        • Cells or batteries
    • Metals and Non-metals
      • Preface
      • Overview
        • Properties of metals
        • Uses of metals
        • Properties of non-metals
        • Uses of non-metals
      • Hydrogen
        • Properties of Hydrogen
        • Preparation and Uses of Hydrogen
        • Water
        • Heavy water
        • Hydrogen peroxide
      • Alkali & Alkaline Earth Metals
        • s-Block elements
        • Properties of s-Block elements
        • Sodium and its compounds
        • Potassium and its compounds
        • Magnesium and its compounds
        • Calcium and its compounds
      • Boron Family
        • Properties of IIIA Elements
        • Boron and its compounds
        • Aluminum and its compounds
      • Carbon Family
        • Extraction and Uses of IV A elements
        • Physical Properties of IVA elements
        • Physical Properties of Carbon
        • Chemical Properties of Carbon
        • Silicon and its compounds
      • Nitrogen Family
        • Properties of VA elements
        • Compounds of VA elements
        • Nitrogen and its compounds
        • Ammonia
        • Phosphorus and its compounds
      • Oxygen Family
        • Properties of VIA elements
        • Oxygen and its compounds
        • Sulfur and its compounds
      • Halogens
        • Production of Halogens
        • Properties of Halogens
        • Compounds of Halogens
        • Uses of Halogens
      • Noble Gases
        • Discovery and Isolation of noble gases
        • Properties of noble gases
        • Xenon and its Compounds
      • Transition Metals
        • Physical Properties of d-Block elements
        • Chemical Properties of d-Block elements
        • Metal Oxoanions Salts
        • Iron
        • Copper
      • Inner transition Metals
        • Lanthanides
        • Actinides
      • Metallurgy & Alloys
        • Concentration of Ores
        • Extraction of Metals
        • Corrosion of Metals
        • Alloys of Metals
      • Coordination Compounds
        • Metal complexes
        • Ligands
        • Bonding Theories
        • Properties of Coordination Compounds
        • Stereo and Structural isomerism
        • Applications of compounds
    • Organic Chemistry
      • Preface
      • Overview
        • Organic compounds
        • Carbon and its allotropes
        • Classification of organic compounds
        • Nomenclature of organic compounds
        • Homologous series
        • Isomerism
      • Hydrocarbons
        • Alkanes
        • Alkenes
        • Alkynes
        • Aromatic hydrocarbons
      • Alcohols, Phenols & Ethers
        • Alcohols
        • Phenols
        • Ethers
      • Halogen derivatives
        • Aryl and Alkyl halides
        • Chloroform
        • Iodoform and Perflourides
      • Aldehydes and Ketones
        • Carbonyl Compounds
        • Preparation of aldehydes and ketones
        • Properties of aldehydes and ketones
      • Carboxylic Acids
        • Structure and Acidity
        • Acetic acid
        • Carboxylic acid derivatives
        • Soaps and Detergents
      • Nitrogen Derivatives
        • Amines
        • Cyanides and Cyanates
        • Nitro compounds
      • Reaction Mechanisms
        • Components of reaction
        • Electronic Displacement
        • Structure and Acidity
        • Classification of Reactions
        • Substitution Reactions
        • Elimination reactions
        • Organic Synthesis
      • Polymers
        • Macromolecules and Polymers
        • Classification of polymers
        • Commercial polymers
        • Biodegradable polymers
      • Biochemistry
        • Carbohydrates
        • Glucose and Fructose
        • Sucrose
        • Starch
        • Proteins
        • Vitamins
        • Lipids
        • Enzymes
        • Nucleic acids
      • Organic Chemistry Today
        • Analgesics
        • Antacids
        • Antimicrobials
        • Antivirals
        • Antiseptics
        • Sweetening Agents
  • Biology
    • Wonders of the inner world!
    • Biochemistry
      • Preface
      • Introduction
        • Chemical basis of life
        • Milestones in Biochemistry
        • Applications
      • Structure of matter
        • Matter
        • Elements
        • Isotopes
      • Chemical Bonding
        • Introduction
        • Covalent Bond
        • Ionic Bond
        • Molecular Shape and Function
        • Chemical reactions
      • Water
        • Universal solvent
        • Polarity of Water
        • Properties of water
        • Dissociation of water molecules
      • Carbon
        • Nature of carbon
        • Molecular Diversity
      • Molecules of Life
        • Biological molecules
        • Polymers
        • Carbohydrates
        • Lipids
        • Proteins
        • Enzymes
        • Nucleic acids
    • Cell Biology
      • Preface
      • Basic Unit of Life
        • Cell diversity
        • Cell theory
        • Cell shapes
        • Prokaryotic cells
        • Eukaryotic cells
      • Cell Structure
        • Cell membrane
        • Transport in cells
        • Parts of cell
        • Cell Organelles
        • Summary
      • Cellular Energetics
        • Metabolic activities
        • Coupled Reactions
        • Bioenergetics
        • Enzymes
      • Cellular Respiration
        • Introduction
        • Catabolic Pathways
        • Respiratory Substrates
        • Respiratory Quotient
        • Redox Reactions
        • Stages of Respiration
        • Fermentation
      • Photosynthesis
        • Discovery of photosynthesis
        • Process of photosynthesis
        • Products of photosynthesis
        • Photophosphorylation
        • Calvin Cycle
        • C4 Pathway (Hatch-Slack Cycle)
        • CAM Plants
      • Cell Communication
        • Introduction
        • Cell Signaling
        • Stages of cell signaling
        • Transduction Pathways
        • Response
      • Cell Division
        • Role of cell division
        • Mitosis
        • Cytokinesis
        • Binary Fission
        • Evolution of Mitosis
        • Cell Cycle Control
    • Genetics
      • Preface
      • Heredity
        • Introduction
        • Reproduction
        • Meiosis
        • Mitosis and Meiosis
      • Mendelian Genetics
        • Mendel's experiment
        • Mendel's Laws of Inheritance
        • Inherited disorders
        • Genetic testing and counseling
      • Chromosomal Basis of Inheritance
        • Introduction
        • Chromosomes
        • Linkage and crossing over
        • Sex-linked inheritance
        • Abnormalities
        • Genetic basis of development
      • Molecular Genetics
        • Introduction
        • The search for genetic material
        • DNA and Replication
        • Gene regulation and expression
        • Genetic Code
        • Protein synthesis
        • DNA packaging
        • DNA mutations
        • Molecular basis of cancer
        • Genetics of Viruses and Bacteria
        • Operons
      • DNA Technology and Applications
        • Recombinant DNA technology
        • Restriction Fragment Analysis
        • DNA Cloning
        • DNA Libraries
        • Genome mapping
        • Genomics
        • Practical applications
    • Evolutionary Biology
      • Preface
      • Exploring Life
        • What is life
        • Origin of life
        • Evolution of Life
        • Unity and Diversity
        • Evolution
      • Understanding Evolution
        • Diversity of life
        • Evidence of Evolution
        • Basic principles of evolution
        • Evolutionary Applications
      • Modern Evolutionary Synthesis
        • Theories of evolution
        • Mechanisms of Change
        • Outcomes of Evolution
        • Sources of Variation in a population
        • Hardy- Weinberg Equilibrium
      • Diversity of Organisms
        • Origin and diversity of life
        • Chemical evolution
        • RNA World
        • Systematics
        • Binomial Nomenclature
      • Monera & Protista
        • Kingdom Monera
        • Bacteria-Reproduction
        • Pathogenic and Useful Bacteria
        • Eubacteria
        • Importance of Prokaryotes
        • Kingdom Protista
        • Classification of Protista
      • Kingdom Fungi
        • Fungus
        • Nutrition and Fungal Lifestyles
        • Classification of Fungi
        • Fungi Impact on Ecosystem
        • Useful Fungi
      • Kingdom Plantae
        • Introduction
        • Thallophyta
        • Bryophyta
        • Pteridophyta
        • Gymnosperms
        • Angiosperms
        • Plants and Human Welfare
      • Kingdom Animalia
        • Evolution of Animals
        • Basis of Classification
        • Animal Development
        • Classifying Animals
        • Human Evolution
        • Microbes in human welfare
      • Ecology and Biosphere
        • Scope of ecology
        • Subfields of Ecology
        • Ecology and Evolutionary Biology
        • Ecosystem
        • Biomes
      • Animal Behavior
        • Introduction
        • The Diversity of Behavior
        • Animal communication
        • Learning and evolution of behavior
      • Community & Population Ecology
        • Community interactions
        • Trophic structure
        • Biological magnification
        • Biomes
        • Biogeochemical cycles
        • Humans and the biosphere
        • The study of Population Ecology
        • Population viability analysis
        • Population cycles
      • Conservation & Restoration Ecology
        • Introduction
        • Conservation of biodiversity
        • Natural resources
        • Air
        • Water
        • Soil
        • Management of Natural Resources
        • Coal and Petroleum
    • Plant Form and Function
      • Preface
      • Plant Structure
        • Basic plant structure
        • Root System
        • Shoot system
        • Leaf and Flower
        • Seed
      • Growth & Development
        • Plant growth and development
        • Primary Growth
        • Secondary Growth
        • Morphogenesis
      • Transport in Plants
        • Introduction
        • Absorption through roots
        • Active transport
        • Ascent of Sap
        • Transpiration
        • Cohesion and Adhesion
        • Transport of Minerals, Food
      • Nutrition in Plants
        • Nutrition - plant growth
        • Modes of Nutrition
        • Minerals and Essential nutrients
        • Photosynthesis for plant nutrition
        • Nutritional Adaptations
      • Plant Reproduction
        • Introduction
        • Asexual reproduction
        • Sexual Reproduction
        • Pollination and Fertilization
        • Seeds
        • Apomixis and Polyembryony
      • Plant Responses
        • Plant response to stimuli
        • Phytohormones (Plant Hormones)
        • Tropisms and Nasties
        • Circadian Rhythms
        • Response to stress
        • Defensive Mechanisms
        • Apoptosis and Senescence
      • Crop and Medicinal Plants
        • Agriculture
        • Plant Breeding
        • Medicinal plants
        • Plant Biotechnology
    • Animal Form and Function
      • Preface
      • Basic Principles
        • Nature of animals
        • Tissues and Organs
        • Homeostasis and Thermoregulation
        • Metabolism
      • Life Processes
        • Circulation
        • Respiration
        • Digestion
        • Vision and Sense
        • Immune Mechanism
        • Endocrine and Nervous system
      • Nutrition
        • Need of nutrition
        • Nutrition in Animals
        • Nutrition in Humans
      • Animal Physiology
        • Introduction
        • Physiology of Annelida
        • Physiology of Arthropoda
        • Physiology of Amphibia
        • Physiology of Chordata
      • Reproduction and Development
        • Asexual Reproduction
        • Sexual Reproduction
        • Morphogenesis
        • Mammalian Development
      • Animal Husbandry
        • Farming practices
        • Cattle Farming
        • Poultry Farming
        • Fish Production
        • Aquaculture
        • Bee Keeping
        • Sericulture
    • Human Physiology
      • Preface
      • Introduction to Human Body
        • Physiology
        • Transport system
        • Communication
        • Intake of raw materials and elimination of waste
        • Protection
        • Reproduction
        • Diseases and illness
      • Human cells & Tissues
        • Human Cells
        • Tissues
        • General Principles
        • Movement of substances with in body fluids
        • Cell division
      • Nervous System
        • Introduction
        • Neurons
        • Nerves
        • Types of Nervous System
        • Brain
        • Reflex Action and Arcs
        • Diseases and Disorders
      • Sensory System
        • Eye
        • Ear
        • Nose
        • Taste buds
      • Endocrine & Reproductive System
        • Hormones
        • Hormonal Signaling
        • Adrenal glands
        • Thyroid & Parathyroid glands
        • Pituitary gland & Hypothalamus
        • Pancreas
        • Other hormones
        • Hormones from Non-endocrine tissues
        • Reproductive system
        • Female Reproductive Anatomy
        • Male Reproductive Anatomy
        • Fertilization
        • Embryonic Development and Birth
      • Digestive System
        • Nutrition
        • Organs of digestive system
        • Digestion & Absorption
        • Disorders
      • Cardiovascular System
        • Heart
        • Blood Vessels - Intricate networks
        • Heart Diseases
        • Tests for Diagnosis
        • Cholesterol test
        • Radionuclide imaging
      • Respiratory System
        • Lungs
        • Respiratory Cycle
        • Breathing Control
        • Aerobic and Anaerobic respiration
        • Lung Diseases
      • Muscular System
        • Introduction
        • Skeletal system
        • Skull
        • Thoracic cage
        • Appendicular Skeleton
        • Types of muscle fibers
      • Immune System
        • Defense Mechanisms
        • Innate Immunity
        • Leukocytes
        • Adaptive Immunity
        • Humoral and cell-mediated Immunity
        • Summary
      • Lymphatic System
        • Introduction
        • Basic Anatomy
        • Importance of Lymphatic System
        • Lymphatic disorders
      • Urinary System
        • Structure of urinary system
        • Kidney
        • Osmoregulation & Excretion
        • Disorders
        • Diagnosis and treatment
      • Health & Diseases
        • Health
        • Types of Disease
        • Spread of Infectious Diseases
        • Symptoms of Disease
        • Diseases caused by bacteria
        • Diseases Caused by Protozoa
        • Other diseases
      • Common Health Problems
        • Anemia
        • Hypertension
        • Cholesterol
        • Hypothermia
        • Obesity
        • Diabetes
        • Hypoglycemia
        • Systemic lupus erythematosus
        • Tests
      • Medical Diagnostics
        • Diagnosis
        • Creatinine Test
        • Blood Urea Nitrogen Test
        • Sodium in blood
        • Blood sugar test
        • Musculoskeletal Tests
        • Chest x-ray
        • Tuberculin skin test
        • UGI Endoscopy
        • Liver and thyroid tests
        • Mammogram
        • Electro encephalogram
        • Other Blood tests
        • Cancer markers
  • Math
    • The language of science!
    • Arithmetic
      • Preface
      • Number Systems
        • Decimal Number System
        • Types of Numbers
        • HCF & LCM
        • Binary Number System
        • Surds
      • Fractions and Divisibility
        • Fractions
        • Decimals
        • Tests of Divisibility
      • Squares and Cubes
        • Squares and Square Roots
        • Cubes and Cube Roots
      • Ratio and Proportions
        • Ratios
        • Proportions
        • Rate & Speed
      • Commercial Arithmetic
        • Percentage
        • Profit, Loss & Discount
        • Simple & Compound Interest
        • Commercial Applications
    • Algebra
      • Preface
      • Basic Algebra
        • Exponents
        • Expressions and Polynomials
        • Expansions
        • Factorization
      • Higher Algebra
        • Linear equations & inequations
        • Quadratic Equations
        • Theory of equations
        • Partial Fractions
        • Complex Numbers
        • Logarithms
      • Progressions
        • Arithmetic Progressions
        • Geometric Progressions
        • Harmonic Progressions
        • Mathematical Induction
        • Exp. and log series
      • Matrices
        • Types of Matrices
        • Operations on Matrices
        • Determinant of a Square Matrix
        • Inverse of a Square Matrix
        • Solving System of Linear Equations
      • Sets and Relations
        • Types of Sets
        • Operations on Sets
        • Relations
      • Functions and Statements
        • Functions
        • Statements
      • Permutations and Combinations
        • Permutations
        • Combinations
        • Binomial Theorem
      • Vector Algebra
        • Operations on Vectors
        • Dot and Cross products
        • Multiplication of 3 or more vectors
    • Geometry
      • Preface
      • Lines and Angles
        • Points, Lines and Planes
        • Angles
        • Parallel Lines and Transversal
        • Perpendicular and angle bisectors
      • Triangles
        • Classification of Triangles
        • Terms Related to a Triangle
        • Congruency & Similarity
        • Construction of Triangles
      • Polygons
        • Polygon
        • Quadrilaterals
        • Parallelograms
        • Rectangles, Rhombuses & Squares
        • Trapezoids
      • Circles
        • Circumference & Area
        • Angles & Arcs
        • Tangents & Sectors
        • Equation of a Circle
        • System of circles
      • Mensuration
        • Mensuration of 2D figures
        • Mensuration of 3D figures
      • Co-ordinate Geometry
        • Locus
        • Transformation of axes
        • Straight Lines
        • Pair of Straight Lines
        • Polar Co-ordinates
      • Conic Sections
        • Parabola
        • Ellipse
        • Hyperbola
      • 3D Geometry
        • Co-ordinate Axes and Planes
        • Direction Cosines & Ratios
        • Equation of a Line in Space
        • Planes
        • Spheres
    • Trigonometry
      • Preface
      • Pythagorean Theorem
        • Right Triangles and Pythagorean Theorem
        • Applications of Pythagorean theorem
      • Trigonometric Ratios and Identities
        • Trigonometric Ratios
        • Trigonometric Identities
        • Properties of trigonometrical functions
      • Heights & Distances
        • Angle of Elevation
        • Angle of Depression
      • Trigonometric Equations
        • Principal Solution
        • General Solutions
        • Trigonometric Inequalities
      • Properties of Triangles
        • Law of Sines and Cosines
        • Area of a Triangle
        • Miscellaneous
      • Inverse Trigonometric & Hyperbolic Functions
        • Inverse Trigonometric Functions
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        • Inverse Hyperbolic Functions
    • Calculus
      • Preface
      • Limits and Continuity
        • Limits
        • L' Hospital's Rule
        • Continuity and differentiability
      • Differentiation
        • Rules for Differentiation
        • Derivatives of Trigonometric Functions
        • Derivatives of Special Functions
        • Higher Order Derivatives
      • Graphs of Functions and Derivatives
        • Maxima & Minima
        • Increasing and Decreasing Functions
        • Graphs & Mean Value Theorems
      • Applications of Derivatives
        • Rate of Change
        • Optimization Problems
        • Tangents & Normals
        • Errors & Approximations
      • Partial Differentiation
        • Partial Derivatives
        • Homogeneous Functions
      • Integration
        • Integration Rules
        • Integration by Substitution
        • Integration by Parts
        • Integration by Partial Fractions
        • Reduction Formulae
      • Definite Integrals
        • Evaluation of Definite Integrals
        • Reduction Formulae
        • Integration as limit of sum
      • Applications of Definite Integrals
        • Area Under a Curve
        • Volumes
        • Special Applications
      • Differential Equations
        • Formation of differential equations
        • Types of differential equations
        • Applications of differential equations
    • Statistics
      • Preface
      • Data Analysis
        • One-variable Data Analysis
        • Two-variable Data Analysis
      • Measures of center and dispersion
        • Median, mean, mode & range
        • Mean Deviation
        • Standard deviation
      • Probability
        • Probability of an event
        • Conditional probability
        • Random variables and distributions
  • Practice Tests
  • Model Tests
  • The world around you!
  • Mechanics
    • Preface
    • Units, Vectors and Mathematical Physics
    • Kinematics
    • Newton's Laws of Motion
    • Work, Energy and Power
    • Linear Momentum
    • Circular motion
    • Rotational Motion
    • Oscillations
    • Gravitation
    • Fluid Mechanics
    • Mechanical Properties of Matter
  • Thermal Physics
    • Preface
    • Heat & Temperature
    • Calorimetry
    • Thermal Expansion
    • Heat Transfer
    • Kinetic Theory
    • Thermodynamics
    • Heat Engines
  • Waves and Optics
    • Preface
    • Wave Motion
    • Sound Waves
    • Nature of Light
    • Reflection
    • Refraction
    • Interference and Diffraction
    • Optical Instruments
  • Electricity
    • Preface
    • Electric Charge and Electric Field
    • Electric Potential
    • Gauss's law
    • Capacitors and Dielectrics
    • Current Electricity
    • Thermal and Chemical effects of current
  • Electromagnetism
    • Preface
    • Magnetism
    • Magnetic Forces
    • Magnetic field due to current
    • EM Induction
    • A.C. Circuits
    • Electromagnetic Waves
  • Modern Physics
    • Preface
    • Bohr's atomic model
    • Quantum theory
    • Nucleus
    • Radioactivity
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    • Semiconductor Electronics
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  • Physics
  • Mechanics
    • Kinematics
      • Speed, Velocity and Acceleration
      • Motion in 1-D and free fall
      • Motion in 2-D and Projectile motion
      • Relative velocity
  • Speed, Velocity and Acceleration
  • Summary
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Relative motion Relative motion The laws of physics which apply when you are at rest on the earth also apply in any reference frame moving at a constant velocity with respect to the earth. The bike racers here are in relative motion with respect to each other. Lets learn more about the concept of relative velocity as we run through this topic.

Learning Objectives

After completing the topic, the student will be able to:

  • Connect day–to–day experiences to linear motion.
  • Discriminate clearly between distance and displacement.
  • Define and distinguish between speed, average speed, instantaneous speed, velocity, acceleration and deceleration.
  • Differentiate between uniform and non–uniform motions.
  • Develop and apply equations of motion.
  • Understand the nature of acceleration due to gravity.
  • Develop and apply position and displacement vectors in two dimensions.
  • Apply equations of motion in X and Y directions.
  • Develop and apply equations of motion, time of flight and range of projectile for any projected object.
  • Apply changes to the equations of motion, time of flight, height reached by the projectile, range of projectile when a projectile is launched vertically upwards.
  • Understand and correlate the concept of relative velocity to daily life examples like moving boat in a river etc.,.
Tugboat Tugboat race The participants in the tugboat race maneuver to optimize their chances of winning. They do so by controlling the displacement, velocity and acceleration of their boats.
Introduction

Kinematics is the branch of mechanics that describes the motion of objects without considering the cause of motion. It provides a foundation that will help us in all areas of physics. It is most intimately connected with dynamics (another branch of mechanics): while kinematics describes motion, dynamics explains the cause for this motion.

It involves the relationships between the quantities displacement (d),velocity (v), acceleration (a), and time (t). We develop a mathematical formalism that allows us to represent the position, velocity, and acceleration of moving objects, and to express how these quantities are related to each other with time.

Note: We will restrict our study to speeds that are slow compared to the speed of light and also to objects which are generally large, compared to atoms or molecules.

Reference frame Reference frame When we talk about the motion of an object, we first determine a reference frame and then according to this reference frame we discuss the motion of the object. With respect to Earth, the Sun appears to move across the sky, but it is the Earth which is actually spinning and causing that apparent motion.
Study of Motion

The world, and everything in it, moves. We see cars and trains moving, a person walking on the street, birds flying in the sky, a leaf floating in the breeze. Even seemingly stationary things such as buildings move with Earth′s rotation. Earth orbiting around the Sun, the Sun's orbit around the center of the Milky Way galaxy and the galaxy′s migration relative to other galaxies are all examples of such movements. In fact, nothing in the entire universe is completely stationary.

Reference Frame: All motions are relative to some frame of reference. An object is said to be in motion if the position of the object changes with respect to some reference frame. If an object is said to be at rest, then it means that it is being described with respect to a reference frame that is moving together with the body. The reference frame is called the 'observer' and is arbitrarily chosen. The example below illustrates the concept of an observer.

Look at a person standing in a playground. His position relative to the ground, the trees and the buildings in the background does not change. So it appears as if he is at rest. But he is standing on the ground i.e. on the Earth, which rotates on its axis revolving around the Sun. If we have a facility to stand on the Sun, we will feel that the person is moving! That is the person is rotating as well as moving forward, along with the Earth. Thus, the person is at rest (or is not moving) relative to the ground, the trees and the buildings. But, on the other hand, the person, along with the ground, the trees and the buildings, is moving with respect to the Sun.

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EAMCET (ENGG) JEE (MAIN) JEE (ADV) NEET

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