Book description
Mechanics meets the requirement for an ideal text on Mechanics for undergraduate students. The book gives the readers a better understanding of topics like Rectilinear Motion, Conservation of Energy and Equation of Motion, provides a good number of examples with good use of real-time illustrations and exercises for practice and challenge. The book comprehensively covers topics like 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.
Table of contents
- Cover
- Title Page
- Contents
- Dedication
- Preface
- 1 ■ Introduction
-
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, T and X, Trelations 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
-
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
- 3.15 Multiplication of Three Vectors
- 3.16 Worked Out Examples III
- ■ Summary
- ■ Exercises
-
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
- 4.6 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
-
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
- 5.6 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
- 5.10 Worked Out Problems. Set III
- 5.11 Dynamics of a Spring Mass System
- 5.12 Worked Out Problems. Set IV
- 5.13 Simple Harmonic Motion in Two Perpendicular Directions, Lissajous Figures
- 5.14 The Second Law Applied to a System of Varying Mass
- 5.15 Worked Out Problems. Set V
- 5.16 Motion Under Electromagnetic Forces
- 5.17 Worked Out Problems. Set VI
- 5.18 The Second Law Applied to Uniform Circular Motion
- 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
- 5.22 Simple Pendulum
- ■ Summary
- ■ Exercises
-
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
- 6.3 Kepler’s Struggle with Mars
- 6.4 Kepler’s Third Law - Key to Inverse Square
- 6.5 The Law of Universal Gravitation
- Part II: Gravitational Field
- 6.6 The Gravitational Force Between Two Extended Objects
- 6.7 Gravitational Field
- 6.8 Direct Computation of the Gravitational Field
- 6.9 Satellites in Circular Orbits
- 6.10 Free Fall and Tidal Acceleration
- 6.11 Summary
- 6.12 Worked Out Problems
- 6.13 Appendix 6A: Explaining the Null Field Inside a Spherical Shell
- ■ Exercises
- 7 ■ Newton’s Third Law of Motion
-
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)
- 8.14 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
-
9 ■ Motion Under Central Forces
- 9.1 Plane Polar Co-ordinate System
- 9.2 Velocity and Acceleration of a Particle in the Polar System
- 9.3 Orbital Angular Momentum
- 9.4 Equations of Motion in the Polar Coordinate System
- 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
- 9.9 The Parabolic Trajectory of a Projectile is Part of an Elliptical Orbit
- 9.10 Motion Under an Inverse-Square-Law Repulsive Force
- 9.11 Appendix 9A: Conic Sections – Ellipse, Parabola, Hyperbola
- 9.12 Summary
- 9.13 Worked Out Problems
- ■ Exercises
-
10 ■ Work and Energy in 3-Dimensional Motion
- 10.1 Normal and Tangential Accelerations
- 10.2 Effect of Force Acting Over a Displacement – General Case
- 10.3 Evaluation of the Line Integral
- 10.4 Example of Evaluation of W – Work Done by the Force of Gravity
- 10.5 Example of Evaluation of W – Work Done by the Induced Electric Force
- 10.6 Relationship of Work to Kinetic Energy
- 10.7 Potential Energy of a Particle in a Conservative Field
- 10.8 Total Energy of a Particle in a Conservative Field
- 10.9 How Energy Determines the Forces of Constraint
- 10.10 The Example of a Betatron
- 10.11 Appendix 10A: How to Calculate the Radius of Curvature
- 10.12 Summary of Important Formulas
- 10.13 Worked Out Problems
- ■ Exercises
- 11 ■ Ideal Fluid at Rest and in Motion
-
12 ■ Motion of a System of Particles. Rigid Body Rotating about a Fixed Axis
- 12.1 Linear Bulk Motion of a System of Particles – Conservation of Momentum
- 12.2 Rotational Motion of a System of Particles – Conservation of Angular Momentum
- 12.3 Examples of Centre of Mass. Worked Out examples I
- 12.4 Worked Out Examples II
- 12.5 Breaking Up Dynamical Variables With a Component in the CM Frame
- 12.6 Rotation of a Rigid Body About a Fixed Axis
- 12.7 Simplest Examples of Rigid Body Dynamics
- 12.8 Angular Momentum is a Vector Quantity
- 12.9 The Amazing Gyroscope, the Spinning Top
- 12.10 The 2-Body Problem
- 12.11 Collision of Two Particles
- ■ Summary
- ■ Exercises
- 13 ■ Accelerating and Rotating Frames of Reference
- 14 ■ Relativistic Mechanics
- Appendix A ■ Beam Bending and Deflection Formulas
-
Appendix B ■ Instructions for Gnuplot
- B.1 To Start With
- B.2 Example 1: The Parabolic Trajectory of a Projectile
- B.3 Example 2: Gun Intercepting a Bomb
- B.4 Example 3: Displacement, Velocity and Acceleration of a Piston Driven by a Crank Wheel
- B.5 Example 4: Plotting Polar Equations of Conic Sections
- B.6 Example 5: Processing Ellipse
- B.7 Example 6: Plotting the G-Path of Mars
- B.8 Example 7: Lissajous Figures
- Notes
- Bibliography
- Acknowledgements
- Copyright
Product information
- Title: Mechanics
- Author(s):
- Release date: June 2012
- Publisher(s): Pearson India
- ISBN: 9788131773734
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