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Newtonian Dynamics
An Introduction



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ISBN 9781032046624
December 20, 2021 Forthcoming by CRC Press
280 Pages 133 B/W Illustrations

 
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Book Description

This textbook provides a comprehensive review of Newtonian dynamics at a level suitable for undergraduate physics students. It demonstrates that Newton’s three laws of motion, combined with a few simple force laws, can not only describe the motions of everyday objects observed on the surface of the Earth, but can also account for the motions of celestial objects seen in the sky. It helps bridge the problematic transition between elementary physics courses and upper-division physics course. The book will start off at a level suitable for undergraduate (freshman) physics students and will very gradually increase, until, towards the end, it will approach (but not quite reach) a level characteristic of a graduate (senior) physics course.

Each chapter of the book will end with a large number of numerical and analytical exercises and, in all appropriate cases, the final answers to the exercises will be specified. The large number of exercises will allow students to accurately test their understanding of the material presented in the book, ideal for students who are self-studying or are taking classes remotely.

Key features:

  • Provides a brief and accessible introduction to a complex topic.
  • Contains a thorough treatment of the motions of heavenly bodies than conventional elementary mechanics texts.
  • Provides a wealth of end-of-chapter exercises to test understanding.

Table of Contents

Preface 
Acknowledgements 

Measurement and Units
Mks Units 
Standard Prefixes 
Other Units.
Dimensional Analysis  
Experimental Errors 
Exercises 

Motion in One Dimension
Introduction 
Displacement 
Velocity 
Acceleration 
Motion with Constant Velocity 
Motion with Constant Acceleration 
Useful Results 
Free-Fall Under Gravity 
Exercises 

Motion in Three Dimensions
Introduction 
Vector Mathematics 
Scalars and Vectors 
Vector Algebra
Cartesian Components of a Vector 
Coordinate Transformations 
Scalar Product 
Vector Product 
Vector Displacement, Velocity, and Acceleration
Motion with Constant Velocity 
Motion with Constant Acceleration
Projectile Motion 
Relative Velocity 
Exercises

Newton's Laws of Motion
Introduction 
Newton's First Law of Motion 
Newton's Second Law of Motion 
Measurement of Force 
Newton's Third Law of Motion 
Mass, Weight, and Reaction
Block Resting on Earth's Surface 
Block in an Elevator 
Suspended Masses 
Block Suspended by a Single Cable 
Block Suspended by Three Cables
Two Blocks Suspended by Five Cables 
Many Blocks Suspended by Many Cables 
Catenary 
Suspension Bridge 
Cable-Pulley Systems 
Simple Pulley 
Compound Pulley 
Table Pulley 
Atwood Machine 
Velocity-Dependent Forces
Friction 
Inclined Planes 
Smooth Planes 
Rough Planes 
Frames of Reference 
Exercises 

Conservation of Energy
Introduction 
Energy Conservation During Free-Fall 
Work 
Conservative and Non-Conservative Force-Fields 
Potential Energy 
Hooke's Law 
Motion in a General One-Dimensional Potential 
Power 
Exercises 

Conservation of Momentum
Introduction 
Two-Component Systems 
Hot-Air Balloon 
Cannon and Cannonball 
Multi-Component Systems 
Explosion of Krypton 
Rocket Science 
Impulses 
Bouncing Ball 
One-Dimensional Collisions 
Elastic Collisions 
Totally Inelastic Collisions 
Inelastic Collisions 
Two-Dimensional Collisions 
Exercises 

Circular Motion 
Introduction 
Uniform Circular Motion
Centripetal Acceleration 
Rotating Weight on the End of a Cable 
Banked Curve 
Conical Pendulum 
Non-Uniform Circular Motion 
Vertical Pendulum 
Motion on Curved Surfaces 
Fairground Ride 
Skier on a Hemispherical Mountain 
Exercises 

Rotational Motion
Introduction
Rigid Body Rotation 
Is Rotation a Vector? 
Center of Mass 
Centroid of Regular Pyramid 
Moment of Inertia 
Perpendicular Axis Theorem 
Parallel Axis Theorem 
Moment of Inertia of a Circular Disk
Standard Moments of Inertia 
Torque 
Power and Work 
Translational Motion Versus Rotational Motion 
Unwinding Pulley 
Physics of Baseball Bats
Combined Translational and Rotational Motion 
Cylinder Rolling Down a Rough Incline
Exercises

Angular Momentum
Introduction 
Angular Momentum of a Point Particle 
Angular Momentum of an Extended Object 
Angular Momentum of a Multi-Component System 
Conservation of Angular Momentum 
Two Movable Weights on a Rotating Rod 
Figure Skater 
Bullet Striking a Pivoted Rod 
Spinning Top
Exercises 

Statics
Introduction 
Principles of Statics 
Equilibrium of a Laminar Object 
Rods and Cables 
Horizontal Rod Suspended from Two Cables 
Pivoting Horizontal Rod Supported by a Cable
Ladders and Walls 
Jointed Rods 
Tipping or Sliding?
Exercises

Oscillatory Motion 
Introduction 
Simple Harmonic Motion 
Torsion Pendulum 
Simple Pendulum 
Compound Pendulum 
Exercises 

Rotating Reference Frames
Introduction 
Rotating Reference Frames 
Centrifugal Acceleration 
Coriolis Force
Foucault Pendulum 
Exercises 

Newtonian Gravity 
Introduction 
Universal Gravity 
Surface Gravity 
Gravitational Potential Energy 
Escape Velocity 
Circular Orbits 
Lunar Orbital Period 
Geostationary Satellites 
Exercises 

Orbital Motion
Introduction 
Kepler's Laws 
Planetary Equations of Motion 
Conic Sections 
Kepler's Second Law 
Kepler's First Law 
Kepler's Third Law 
Orbital Parameters 
Orbital Energies 
Transfer Orbits 
Low-Eccentricity Orbits 
Two-Body Dynamics 
Binary Star Systems 
Exercises

Gravitational Potential Theory
Introduction
Gravitational Potential
Axially-Symmetric Mass Distributions 
Gravitational Potential due to a Uniform Sphere 
Gravitational Potential Outside a Uniform Spheroid 
Rotational Flattening 
Rotational Flattening of Earth 
Tidal Elongation 
Tidal Elongation of Earth due to Moon
Tidal Elongation of Earth due to Sun
Ocean Tides 
Luni-Solar Precession 
Exercises

Useful Mathematics 
Calculus 
Series Expansions 
Trigonometric Identities 
Hyperbolic Identities 
Complex Identities 
Vector Identities 

Bibliography
Index 

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Author(s)

Biography

Richard Fitzpatrick is a Professor of physics at the University of Texas at Austin, USA, where he has been a faculty member since 1994. He is a member of the Royal Astronomical Society, a fellow of the American Physical Society, and the author of several textbooks.