This book of problems and solutions in classical mechanics is dedicated to junior or senior undergraduate students in physics, engineering, applied mathematics, astronomy, or chemistry who may want to improve their problems solving skills, or to freshman graduate students who may be seeking a refresh of the material.
The book is structured in ten chapters, starting with Newtons laws, motion with air resistance, conservation laws, oscillations, and the Lagrangian and Hamiltonian Formalisms. The last two chapters introduce some ideas in nonlinear dynamics, chaos, and special relativity. Each chapter starts with a brief theoretical outline, and continues with problems and detailed solutions. A concise presentation of differential equations can be found in the appendix. A variety of problems are presented, from the standard classical mechanics problems, to context-rich problems and more challenging problems.
Key features:
Presents a theoretical outline for each chapter.
Motivates the students with standard mechanics problems with step-by-step explanations.
Challenges the students with more complex problems with detailed solutions.
| Preface |
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xi | |
| Acknowledgments |
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xiii | |
| About the Authors |
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xv | |
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1 | (42) |
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1 | (6) |
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1 | (1) |
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1 | (1) |
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1.1.1.2 Position, Velocity, and Acceleration |
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1 | (1) |
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1.1.1.3 Seal ar (Dot) and Vector (Cross) Product |
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1 | (1) |
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2 | (1) |
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2 | (1) |
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2 | (1) |
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3 | (1) |
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3 | (1) |
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3 | (1) |
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1.1.2.1 Cartesian Coordinates |
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3 | (1) |
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1.1.2.2 Cylindrical Polar Coordinates |
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4 | (1) |
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1.1.2.3 Spherical Polar Coordinates |
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4 | (1) |
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5 | (1) |
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1.1.3.1 Newton's First Law - The Law of Inertia |
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5 | (1) |
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1.1.3.2 Newton's Second Law |
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5 | (1) |
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1.1.3.3 Newton's Third Law (Action-Reaction) |
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6 | (1) |
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1.2 Problems and Solutions |
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7 | (36) |
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Chapter 2 Motion with Air Resistance |
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43 | (26) |
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43 | (1) |
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2.1.1 Drag Force of Air Resistance |
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43 | (1) |
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2.2 Problems and Solutions |
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44 | (25) |
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Chapter 3 Momentum and Angular Momentum |
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69 | (22) |
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69 | (2) |
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69 | (1) |
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69 | (1) |
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69 | (1) |
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70 | (1) |
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3.1.5 Principle of Conservation of Angular Momentum |
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70 | (1) |
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3.1.6 Principle of Conservation of the Angular Momentum for a System of N Particles |
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71 | (1) |
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3.2 Problems and Solutions |
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71 | (20) |
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91 | (24) |
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91 | (2) |
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4.1.1 Work Kinetic Energy Theorem |
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91 | (1) |
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4.1.2 Conservative Forces |
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91 | (1) |
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4.1.3 Obtaining the Equation of the Motion from the Conservation of the Energy |
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92 | (1) |
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4.2 Problems and Solutions |
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93 | (22) |
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115 | (28) |
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115 | (3) |
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115 | (1) |
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5.1.2 Simple Harmonic Motion |
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115 | (1) |
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116 | (1) |
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5.1.4 Particular Types of Oscillations and the Differential Equations Associated with Them |
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116 | (1) |
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5.1.4.1 Damped Oscillations |
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116 | (1) |
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5.1.4.2 Weak Damping β < ω0 |
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117 | (1) |
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5.1.4.3 Critical Damping β = ω0 |
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117 | (1) |
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5.1.4.4 Strong Damping β > ω0 |
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117 | (1) |
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5.1.4.5 Driven Damped Oscillations |
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117 | (1) |
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5.2 Problems and Solutions |
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118 | (25) |
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Chapter 6 Lagrangian Formalism |
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143 | (24) |
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143 | (1) |
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143 | (1) |
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6.1.2 Hamilton's Principle |
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143 | (1) |
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6.2 Problems and Solutions |
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144 | (23) |
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Chapter 7 Hamiltonian Formalism |
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167 | (30) |
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167 | (1) |
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167 | (1) |
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7.1.2 Example - One-Dimensional Systems |
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167 | (1) |
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7.2 Problems and Solutions |
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168 | (29) |
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Chapter 8 Coupled Oscillators and Normal Modes |
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197 | (24) |
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197 | (1) |
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8.2 Problems and Solutions |
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198 | (23) |
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Chapter 9 Nonlinear Dynamics and Chaos |
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221 | (20) |
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221 | (1) |
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9.2 Problems and Solutions |
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221 | (20) |
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Chapter 10 Special Relativity |
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241 | (14) |
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241 | (6) |
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10.1.1 Galileo's Transformations |
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241 | (1) |
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10.1.2 Postulates of the Theory of Relativity |
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242 | (1) |
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10.1.3 Lorentz Transformations |
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242 | (1) |
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10.1.4 Length Contraction, Time Dilation |
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243 | (1) |
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10.1.5 Composing Velocities |
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244 | (2) |
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10.1.6 Relativistic Dynamics |
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246 | (1) |
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247 | (1) |
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247 | (1) |
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247 | (1) |
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10.2 Problems and Solutions |
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247 | (8) |
| Appendix: Differential Equations |
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255 | (4) |
| Bibliography |
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259 | (2) |
| Index |
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261 | |
Carolina C. Ilie is a Sigma Xi Fellow, Full Professor with tenure at State University of New York at Oswego. She taught Classical Mechanics for more than ten years and she designed various problems for her students. Dr. Ilie obtained the Ph.D. in Physics and Astronomy at University of Nebraska at Lincoln, a M.Sc. in Physics at the Ohio State University and at University of Bucharest, Romania. She received the Presidents Award for Teaching Excellence in 2016 and the Provost Award for Mentoring in Scholarly and Creative Activity in 2013. Her research is focused on condensed matter physics: dynamics at surfaces, capillary condensation, perovskites photovoltaics. She lives in Central New York with her spouse, also a physicist, and their two sons. Her hobbies are classical music and languages.
Zachariah S. Schrecengost is a State University of New York alumnus. He graduated summa cum laude with a BS degree having completed majors in Physics, Software Engineering, and Applied Mathematics. He took the Advanced Mechanics course with Dr. Ilie and loved to be involved in this project. He brings to the project the experience of writing other two books of problems, but also the fresh perspective of the student taking classical mechanics and the enthusiasm and talent of an alumnus who is a physics and upper-level mathematics aficionado. Mr. Schrecengost works as software engineer in Syracuse while working towards his PhD in Physics at Syracuse University.
Elina M. van Kempen graduated summa cum laude from the State University of New York at Oswego, with a double major in Physics and Applied Mathematics, and a minor in Computer Science. She is now working on her PhD in Computer Science at the University of California, Irvine, with a focus on Security and Privacy. At SUNY Oswego, she had the great opportunity to take several courses taught by Dr. Carolina Ilie, including her course on Advanced Mechanics. Elina M. van Kempen also tutored SUNY Oswego, in Physics, Mathematics, and Computer Science, and enjoyed helping students succeed in their classes. She loves traveling, cooking, and swimming.
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