Mechanics
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 a...
| Other Authors: | |
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| Format: | eBook |
| Language: | Inglés |
| Published: |
[Place of publication not identified]
Pearson
2012
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| Edition: | 1st edition |
| Series: | Always learning.
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| Subjects: | |
| See on Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009627788106719 |
Table of Contents:
- 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, θ)
- 9.2.2 Line Element, Square of Velocity
- 9.2.3 Derivatives of the Base Vectors
- 9.2.4 Acceleration a(r, θ)
- 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.
