Mechanics.
Datta, Somnath.
Mechanics. - 0 - 1 online resource (649 pages)
Cover -- Contents -- Preface -- Chapter 1: Introduction -- 1.1 Mechanics, the Science of Motion -- 1.2 Time Evolution of Coordinates -- 1.3 Galileo's Law of Inertia, Newton's First Law of Motion -- 1.4 Experimental Verification of the First Law -- 1.5 Inertial Frame of Reference -- 1.6 In Search of Conservation Laws -- 1.7 Measure of Inertia, Inertial Mass -- Chapter 2: Velocity and Acceleration in Rectilinear Motion -- 2.1 Displacement-Time Graph -- 2.2 Velocity of a Particle -- 2.3 Acceleration -- 2.4 Simple Harmonic Motion -- 2.5 Worked out Examples I -- 2.6 Obtaining V,T and X,T Relations from Areas of A-T and V-T Graphs -- 2.7 Standard Kinematical Relations for Constant Acceleration -- 2.8 Velocity and Displacement for a Harmonically Varying Acceleration -- 2.9 Worked Out Examples II -- Summary -- Exercises -- Chapter 3: Vectors in Physics. Velocity and Acceleration as Vectors -- 3.1 Knowing Vectors by their Properties -- 3.2 Is Vector Just a Directed Straight line? -- 3.3 Mathematical Representation of Vectors -- 3.4 The Displacement Vector -- 3.5 Magnitude of a Vector -- 3.6 Radius Vector as a Function of Time -- 3.7 The Velocity Vector -- 3.8 Infinitesimal Displacement, Line Element, Speed -- 3.9 Acceleration -- 3.10 Worked Out Examples I -- 3.11 Centripetal Acceleration in Uniform Circular Motion -- 3.12 Combination of Normal and Tangential Accelerations in Non-Uniform Circular Motion -- 3.13 Worked Out Examples II -- 3.14 Multiplication of Two Vectors -- 3.14.1 Component of a Vector in a Given Direction -- Scalar Product -- 3.14.2 Vector Product is an Axial Vector -- 3.14.3 Area as a Cross Product -- 3.15 Multiplication of three Vectors -- 3.15.1 Volume as a Triple Product -- 3.15.2 Determinant of a Cross Product and of a Scalar Triple Product -- 3.15.3 Vector Triple Product -- 3.16 Worked Out Examples III -- Summary -- Exercises. Chapter 4: Conservation of Momentum -- 4.1 Galilean Transformation -- 4.2 Momentum in One Dimension. Definition of Mass -- 4.3 Conservation of Linear Momentum -- 4.4 Invariance of Momentum Conservation Under Galilean Transformation -- 4.5 Illustrative Examples of Momentum Conservation -- 4.5.1 Example 1: Velocity of a Large Block After Being Hit by Bullets -- 4.5.2 Example 2: Recoil Velocity of a Cannon -- 4.6 Propulsion of a Rocket -- 4.7 Worked Out Examples. Set I -- 4.8 When there is a Flow of Momentum -- 4.9 Momentum Conservation from a Comoving Frame of Reference -- Summary -- Exercises -- Chapter 5: Newton's Second Law of Motion -- 5.1 How a Force Alters the Momentum of a Particle -- 5.2 Equations of Motion, and how to Solve them -- 5.3 Can the Second Law be Applicable to Extended Objects? -- 5.4 Forces of Nature we Shall Reckon with -- 5.5 Motion Under Gravity Near the Surface of the Earth -- 5.5.1 Velocity-independent Nature of the Force of Gravity -- 5.5.2 Stone Thrown from the Top of a Tower -- 5.5.3 Motion of a Projectile -- 5.5.4 Equation of a Parabola -- 5.6 Worked Out Examples. Set I -- 5.7 Motion Against Resistive Forces, Dry Friction -- 5.8 Worked Out Problems. Set II -- 5.9 Motion Against Resistive Forces, Fluid Friction -- 5.9.1 Aerodynamic Drag, Terminal Velocity -- 5.9.2 Example of Terminal Velocity - Millikan's Experiment to Find Electronic Charge -- 5.10 Worked Out Problems. Set III -- 5.11 Dynamics of a Spring Mass System -- 5.11.1 Motion Under a Pure Spring Force -- 5.11.2 Spring Force in Combination with Gravity -- 5.11.3 Vertical Oscillation of a Ship -- 5.12 Worked Out Problems. Set IV -- 5.13 Simple Harmonic Motion in Two Perpendicular Directions, Lissajous Figures -- 5.14 The Second Lawapplied to a System of Varying Mass -- 5.14.1 The Equation of Motion -- 5.14.2 Horizontal Propulsion of a Jet Plane. 5.14.3 Vertical Propulsion of a Rocket -- 5.14.4 A Raindrop Falling through the Atmosphere -- 5.15 Worked Out Problems. Set V -- 5.16 Motion Under Electromagnetic Forces -- 5.16.1 Charged Particle in a Uniform Electric Field -- 5.17 Worked Out Problems. Set VI -- 5.18 The Second Lawapplied to Uniform Circular Motion -- 5.18.1 Example 1: Banking of Road Surface for Fast Moving Vehicles -- 5.18.2 Example 2: Conical Pendulum -- 5.18.3 Example 3: A Satellite in a Circular Orbit -- 5.18.4 Example 4: Calculation of Bohr Radius -- 5.19 Worked Out Examples. Set VII -- 5.20 Geometrical Structure of the Second Law Exemplified by Force Perpendicular to Velocity -- 5.21 Motion of a Charged Particle Moving in a Uniform Magnetic Field -- 5.21.1 Cyclotron Frequency -- 5.21.2 General Solution: Helical Motion -- 5.22 Simple Pendulum -- 5.22.1 Complete Equations of Motion -- 5.22.2 Simplified Solution. 1st-Order Approximation -- 5.22.3 T, ac, at in the Simplified Solution -- 5.22.4 Exact Expressions for T, ac , at -- 5.22.5 2nd-Order Approximation -- Summary -- Exercises -- Chapter 6: The Law of Universal Gravitation -- Part I : A Brief History of Gravitation -- 6.1 Newton and the Apple and the Moon -- 6.2 Heliocentric Model of Copernicus -- 6.2.1 Motion of Planets as Seen from Earth - Geocentric View of the Greek School -- 6.2.2 Motion of Planets as Seen from Earth - Heliocentric Explanation of Copernicus -- 6.2.3 Geocentric Path of Venus from the Copernican model -- 6.2.4 Geocentric Path of Mars from the Copernican Model -- 6.2.5 Calculation of the Periods of the Planets by Copernicus -- 6.2.6 Calculation of the Orbital Radii of the Planets by Copernicus -- 6.3 Kepler's Struggle with Mars -- 6.4 Kepler's Third Law - Key to Inverse Square -- 6.4.1 Kepler's Laws of Planetary Motion -- 6.5 The Law of Universal Gravitation -- Part II : Gravitational Field. 6.6 The Gravitational Force between Two Extended Objects -- 6.6.1 The Force of Gravitation between Two Point Objects in Vector Notation -- 6.6.2 Principle of Superposition -- 6.7 Gravitational Field -- 6.7.1 A Source and a Test Particle -- 6.7.2 Gravitational Field Lines -- 6.8 Direct Computation of the Gravitational Field -- 6.8.1 Finding the Field by Volume and Surface Integration -- 6.8.2 An Elementary Introduction to the Spherical Coordinate System -- 6.8.3 Field Due to a Spherical Shell of Uniform Surface Mass Density -- 6.8.4 Field Due to a Spherically Symmetrical Distribution of Matter -- 6.8.5 Force of Interaction between Two Spherically Symmetric Mass Distributions -- 6.9 Satellites in Circular Orbits -- 6.9.1 Relationship between Orbital Radius and the Period of Revolution -- 6.9.2 Geostationary Satellites -- 6.10 Free Fall and Tidal Acceleration -- 6.10.1 Examples of Free Fall -- 6.10.2 Tidal Deformation -- 6.10.3 Tidal Force -- 6.10.4 Tidal Forces on a Sphere -- 6.11 Summary -- 6.12 Worked Out Problems -- 6.13 Appendix 6A: Explaining the Null Field Inside a Spherical Shell -- Exercises -- Chapter 7: Newton's Third Law of Motion -- 7.1 A Slide Show on Newton's Third Law of Motion -- 7.2 Free Body Diagrams -- 7.2.1 What is a Freebody Diagram? -- 7.2.2 The Golden Rules for Understanding Newton's Laws of Motion -- 7.3 Further Examples of FBDS -- 7.4 Every Real Force Has a Parent -- 7.5 Worked Out Problems -- Exercises -- Chapter 8: Work and Energy in One Dimensional Motion -- 8.1 Work and Kinetic Energy -- 8.2 Example of Work-Work Done by the Uniform Force of Gravity - Near the Earth's Surface -- 8.3 Example of Work-Work Done by the Inverse Square Force of Gravity -- 8.4 Power - the Rate of Doing Work -- 8.5 Example of Work - the Spring Mass System -- 8.6 Example of Work - Work Done by Electrostatic Forces. 8.7 Conservative and Non-Conservative Forces -- 8.8 The Concept of Potential Energy - Example Spring -- 8.9 Potential Energy in General -- 8.10 Total Energy of a Particle in a Conservative Field -- 8.11 Energy Conservation in a Spring Mass System -- 8.12 Concept of a Potential Well -- 8.13 Energy Conservation of a Particle Freely Falling Under the Gravitational Pull of the Earth (or the Sun) -- 8.13.1 Example 1. An Object Thrown Upward with Velocity v0 -- 8.13.2 Example 2. Velocity of a Particle Falling Vertically from a Height h Above the Surface of the Earth -- 8.14 Energy Conservation of a Charged Particle Moving in an Electrostatic Field -- 8.15 Work and Energy in Rocket Propulsion -- 8.16 Summary of Important Formulas -- 8.17 Worked Out Problems -- Exercises -- Chapter 9: Motion Under Central Forces -- 9.1 Plane Polar Co-Ordinate System -- 9.2 Velocity and Acceleration of a Particle in the Polar System -- 9.2.1 The Velocity v(r, (Sk(B) -- 9.2.2 Line Element, Square of Velocity -- 9.2.3 Derivatives of the Base Vectors -- 9.2.4 Acceleration a(r, (Sk(B) -- 9.2.5 Simple Examples -- 9.3 Orbital Angular Momentum -- 9.3.1 Orbital Angular Momentum, an Axial Vector -- 9.3.2 Equation of Motion for the Orbital Angular Momentum -- 9.3.3 Conservation of Orbital Angular Momentum under Central Forces -- 9.3.4 Kepler's 2nd Law: Conservation of Areal Velocity -- 9.4 Equations of Motion in the Polar Coordinate System -- 9.4.1 Radial and Transverse Components of the Equation of Motion -- 9.4.2 Motion Under a Central Force - the First Integrals of the Equation of Motion -- 9.4.3 Second Integrals of the Equation of Motion -- Effective Potential for Radial Motion -- 9.5 Motion Under an Inverse-Square-Law Attractive Force -- 9.6 Classification of Trajectories in an Inverse-Square-Law Field-Kepler's 1st Law of Planetary Orbit -- 9.7 Kepler's Third Law of Planetary Orbits. 9.8 A Closer Look at Planetary (Satellite) Orbits.
Mechanics meets the requirement for an ideal text on Mechanics for undergraduate students. The book gives the readers a better understanding of topics like Rectiline Motion, Conservation of Energy and Equation of Motion. Provides a good number of examples with good use real time illustration and exercises for practice and challenge. The book comprehensively covers of Newton's Law of Motion, Conservation Laws of momentum, energy and Law of gravitation and includes 180 worked out examples and 185 end of chapter exercises.
9788131798805
Electronic books.
620.1
Mechanics. - 0 - 1 online resource (649 pages)
Cover -- Contents -- Preface -- Chapter 1: Introduction -- 1.1 Mechanics, the Science of Motion -- 1.2 Time Evolution of Coordinates -- 1.3 Galileo's Law of Inertia, Newton's First Law of Motion -- 1.4 Experimental Verification of the First Law -- 1.5 Inertial Frame of Reference -- 1.6 In Search of Conservation Laws -- 1.7 Measure of Inertia, Inertial Mass -- Chapter 2: Velocity and Acceleration in Rectilinear Motion -- 2.1 Displacement-Time Graph -- 2.2 Velocity of a Particle -- 2.3 Acceleration -- 2.4 Simple Harmonic Motion -- 2.5 Worked out Examples I -- 2.6 Obtaining V,T and X,T Relations from Areas of A-T and V-T Graphs -- 2.7 Standard Kinematical Relations for Constant Acceleration -- 2.8 Velocity and Displacement for a Harmonically Varying Acceleration -- 2.9 Worked Out Examples II -- Summary -- Exercises -- Chapter 3: Vectors in Physics. Velocity and Acceleration as Vectors -- 3.1 Knowing Vectors by their Properties -- 3.2 Is Vector Just a Directed Straight line? -- 3.3 Mathematical Representation of Vectors -- 3.4 The Displacement Vector -- 3.5 Magnitude of a Vector -- 3.6 Radius Vector as a Function of Time -- 3.7 The Velocity Vector -- 3.8 Infinitesimal Displacement, Line Element, Speed -- 3.9 Acceleration -- 3.10 Worked Out Examples I -- 3.11 Centripetal Acceleration in Uniform Circular Motion -- 3.12 Combination of Normal and Tangential Accelerations in Non-Uniform Circular Motion -- 3.13 Worked Out Examples II -- 3.14 Multiplication of Two Vectors -- 3.14.1 Component of a Vector in a Given Direction -- Scalar Product -- 3.14.2 Vector Product is an Axial Vector -- 3.14.3 Area as a Cross Product -- 3.15 Multiplication of three Vectors -- 3.15.1 Volume as a Triple Product -- 3.15.2 Determinant of a Cross Product and of a Scalar Triple Product -- 3.15.3 Vector Triple Product -- 3.16 Worked Out Examples III -- Summary -- Exercises. Chapter 4: Conservation of Momentum -- 4.1 Galilean Transformation -- 4.2 Momentum in One Dimension. Definition of Mass -- 4.3 Conservation of Linear Momentum -- 4.4 Invariance of Momentum Conservation Under Galilean Transformation -- 4.5 Illustrative Examples of Momentum Conservation -- 4.5.1 Example 1: Velocity of a Large Block After Being Hit by Bullets -- 4.5.2 Example 2: Recoil Velocity of a Cannon -- 4.6 Propulsion of a Rocket -- 4.7 Worked Out Examples. Set I -- 4.8 When there is a Flow of Momentum -- 4.9 Momentum Conservation from a Comoving Frame of Reference -- Summary -- Exercises -- Chapter 5: Newton's Second Law of Motion -- 5.1 How a Force Alters the Momentum of a Particle -- 5.2 Equations of Motion, and how to Solve them -- 5.3 Can the Second Law be Applicable to Extended Objects? -- 5.4 Forces of Nature we Shall Reckon with -- 5.5 Motion Under Gravity Near the Surface of the Earth -- 5.5.1 Velocity-independent Nature of the Force of Gravity -- 5.5.2 Stone Thrown from the Top of a Tower -- 5.5.3 Motion of a Projectile -- 5.5.4 Equation of a Parabola -- 5.6 Worked Out Examples. Set I -- 5.7 Motion Against Resistive Forces, Dry Friction -- 5.8 Worked Out Problems. Set II -- 5.9 Motion Against Resistive Forces, Fluid Friction -- 5.9.1 Aerodynamic Drag, Terminal Velocity -- 5.9.2 Example of Terminal Velocity - Millikan's Experiment to Find Electronic Charge -- 5.10 Worked Out Problems. Set III -- 5.11 Dynamics of a Spring Mass System -- 5.11.1 Motion Under a Pure Spring Force -- 5.11.2 Spring Force in Combination with Gravity -- 5.11.3 Vertical Oscillation of a Ship -- 5.12 Worked Out Problems. Set IV -- 5.13 Simple Harmonic Motion in Two Perpendicular Directions, Lissajous Figures -- 5.14 The Second Lawapplied to a System of Varying Mass -- 5.14.1 The Equation of Motion -- 5.14.2 Horizontal Propulsion of a Jet Plane. 5.14.3 Vertical Propulsion of a Rocket -- 5.14.4 A Raindrop Falling through the Atmosphere -- 5.15 Worked Out Problems. Set V -- 5.16 Motion Under Electromagnetic Forces -- 5.16.1 Charged Particle in a Uniform Electric Field -- 5.17 Worked Out Problems. Set VI -- 5.18 The Second Lawapplied to Uniform Circular Motion -- 5.18.1 Example 1: Banking of Road Surface for Fast Moving Vehicles -- 5.18.2 Example 2: Conical Pendulum -- 5.18.3 Example 3: A Satellite in a Circular Orbit -- 5.18.4 Example 4: Calculation of Bohr Radius -- 5.19 Worked Out Examples. Set VII -- 5.20 Geometrical Structure of the Second Law Exemplified by Force Perpendicular to Velocity -- 5.21 Motion of a Charged Particle Moving in a Uniform Magnetic Field -- 5.21.1 Cyclotron Frequency -- 5.21.2 General Solution: Helical Motion -- 5.22 Simple Pendulum -- 5.22.1 Complete Equations of Motion -- 5.22.2 Simplified Solution. 1st-Order Approximation -- 5.22.3 T, ac, at in the Simplified Solution -- 5.22.4 Exact Expressions for T, ac , at -- 5.22.5 2nd-Order Approximation -- Summary -- Exercises -- Chapter 6: The Law of Universal Gravitation -- Part I : A Brief History of Gravitation -- 6.1 Newton and the Apple and the Moon -- 6.2 Heliocentric Model of Copernicus -- 6.2.1 Motion of Planets as Seen from Earth - Geocentric View of the Greek School -- 6.2.2 Motion of Planets as Seen from Earth - Heliocentric Explanation of Copernicus -- 6.2.3 Geocentric Path of Venus from the Copernican model -- 6.2.4 Geocentric Path of Mars from the Copernican Model -- 6.2.5 Calculation of the Periods of the Planets by Copernicus -- 6.2.6 Calculation of the Orbital Radii of the Planets by Copernicus -- 6.3 Kepler's Struggle with Mars -- 6.4 Kepler's Third Law - Key to Inverse Square -- 6.4.1 Kepler's Laws of Planetary Motion -- 6.5 The Law of Universal Gravitation -- Part II : Gravitational Field. 6.6 The Gravitational Force between Two Extended Objects -- 6.6.1 The Force of Gravitation between Two Point Objects in Vector Notation -- 6.6.2 Principle of Superposition -- 6.7 Gravitational Field -- 6.7.1 A Source and a Test Particle -- 6.7.2 Gravitational Field Lines -- 6.8 Direct Computation of the Gravitational Field -- 6.8.1 Finding the Field by Volume and Surface Integration -- 6.8.2 An Elementary Introduction to the Spherical Coordinate System -- 6.8.3 Field Due to a Spherical Shell of Uniform Surface Mass Density -- 6.8.4 Field Due to a Spherically Symmetrical Distribution of Matter -- 6.8.5 Force of Interaction between Two Spherically Symmetric Mass Distributions -- 6.9 Satellites in Circular Orbits -- 6.9.1 Relationship between Orbital Radius and the Period of Revolution -- 6.9.2 Geostationary Satellites -- 6.10 Free Fall and Tidal Acceleration -- 6.10.1 Examples of Free Fall -- 6.10.2 Tidal Deformation -- 6.10.3 Tidal Force -- 6.10.4 Tidal Forces on a Sphere -- 6.11 Summary -- 6.12 Worked Out Problems -- 6.13 Appendix 6A: Explaining the Null Field Inside a Spherical Shell -- Exercises -- Chapter 7: Newton's Third Law of Motion -- 7.1 A Slide Show on Newton's Third Law of Motion -- 7.2 Free Body Diagrams -- 7.2.1 What is a Freebody Diagram? -- 7.2.2 The Golden Rules for Understanding Newton's Laws of Motion -- 7.3 Further Examples of FBDS -- 7.4 Every Real Force Has a Parent -- 7.5 Worked Out Problems -- Exercises -- Chapter 8: Work and Energy in One Dimensional Motion -- 8.1 Work and Kinetic Energy -- 8.2 Example of Work-Work Done by the Uniform Force of Gravity - Near the Earth's Surface -- 8.3 Example of Work-Work Done by the Inverse Square Force of Gravity -- 8.4 Power - the Rate of Doing Work -- 8.5 Example of Work - the Spring Mass System -- 8.6 Example of Work - Work Done by Electrostatic Forces. 8.7 Conservative and Non-Conservative Forces -- 8.8 The Concept of Potential Energy - Example Spring -- 8.9 Potential Energy in General -- 8.10 Total Energy of a Particle in a Conservative Field -- 8.11 Energy Conservation in a Spring Mass System -- 8.12 Concept of a Potential Well -- 8.13 Energy Conservation of a Particle Freely Falling Under the Gravitational Pull of the Earth (or the Sun) -- 8.13.1 Example 1. An Object Thrown Upward with Velocity v0 -- 8.13.2 Example 2. Velocity of a Particle Falling Vertically from a Height h Above the Surface of the Earth -- 8.14 Energy Conservation of a Charged Particle Moving in an Electrostatic Field -- 8.15 Work and Energy in Rocket Propulsion -- 8.16 Summary of Important Formulas -- 8.17 Worked Out Problems -- Exercises -- Chapter 9: Motion Under Central Forces -- 9.1 Plane Polar Co-Ordinate System -- 9.2 Velocity and Acceleration of a Particle in the Polar System -- 9.2.1 The Velocity v(r, (Sk(B) -- 9.2.2 Line Element, Square of Velocity -- 9.2.3 Derivatives of the Base Vectors -- 9.2.4 Acceleration a(r, (Sk(B) -- 9.2.5 Simple Examples -- 9.3 Orbital Angular Momentum -- 9.3.1 Orbital Angular Momentum, an Axial Vector -- 9.3.2 Equation of Motion for the Orbital Angular Momentum -- 9.3.3 Conservation of Orbital Angular Momentum under Central Forces -- 9.3.4 Kepler's 2nd Law: Conservation of Areal Velocity -- 9.4 Equations of Motion in the Polar Coordinate System -- 9.4.1 Radial and Transverse Components of the Equation of Motion -- 9.4.2 Motion Under a Central Force - the First Integrals of the Equation of Motion -- 9.4.3 Second Integrals of the Equation of Motion -- Effective Potential for Radial Motion -- 9.5 Motion Under an Inverse-Square-Law Attractive Force -- 9.6 Classification of Trajectories in an Inverse-Square-Law Field-Kepler's 1st Law of Planetary Orbit -- 9.7 Kepler's Third Law of Planetary Orbits. 9.8 A Closer Look at Planetary (Satellite) Orbits.
Mechanics meets the requirement for an ideal text on Mechanics for undergraduate students. The book gives the readers a better understanding of topics like Rectiline Motion, Conservation of Energy and Equation of Motion. Provides a good number of examples with good use real time illustration and exercises for practice and challenge. The book comprehensively covers of Newton's Law of Motion, Conservation Laws of momentum, energy and Law of gravitation and includes 180 worked out examples and 185 end of chapter exercises.
9788131798805
Electronic books.
620.1