Introduction to Classical Mechanics With Problems and ...

1 MORIN: FM 2007/10/9 19:08 pagei #1 Introduction to Classical MechanicsWith Problems and SolutionsThis textbook covers all the standard introductory topics in Classical Mechanics ,including Newton s laws, oscillations, energy, momentum, angular momentum,planetary motion, and special relativity. It also explores more advanced topics,such as normal modes, the Lagrangian method, gyroscopic motion, fictitiousforces, 4-vectors, and general contains more than 250 Problems with detailed solutions so students caneasily check their understanding of the topic. There are also over 350 unworkedexercises, which are ideal for homework assignments.

2 Password-protectedsolutions are available to instructors at vast number of Problems alone makes it an ideal supplementary book forall levels of undergraduate physics courses in Classical Mechanics . The text alsoincludes many additional remarks which discuss issues that are often glossedover in other textbooks, and it is thoroughly illustrated with more than 600figures to help demonstrate key a Lecturer in Physics at Harvard University. He received in theoretical particle physics from Harvard in 1996. When not writingphysics limericks or thinking of new Problems whose answers involveeor thegolden ratio, he can be found running along the Charles River or hiking in theWhite Mountains of New : FM 2007/10/9 19:08 page ii #2 MORIN: FM 2007/10/9 19:08 page iii #3 Introduction to ClassicalMechanicsWith Problems and SolutionsDavid MorinHarvard UniversityMORIN: FM 2007/10/9 19.

3 08 page iv #4 Cambridge University PressCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S o PauloCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UKPublished in the United States of America by Cambridge University Press, New on this title: D. Morin 2007 This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University published 2008 Printed in the United Kingdom at the University Press, CambridgeA catalog record for this publication is available from the British LibraryISBN 978-0-521-87622-3 hardbackCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication.

4 And does not guarantee that any content on suchwebsites is, or will remain, accurate or : FM 2007/10/9 19:08 pagev #5To Allen Gerry and Neil Tame,who took the timeto give a group of kidssome really cool problemsMORIN: FM 2007/10/9 19:08 page vi #6 There once was a Classical theory,Of which quantum disciples were said, Why spend so longOn a theory that s wrong? Well, it works for your everyday query!MORIN: FM 2007/10/9 19:08 page vii #7 ContentsPrefacepagexiii1 Strategies for solving General Units, dimensional Approximations, limiting Solving differential equations Solutions182 Balancing Balancing Solutions393 UsingF= Newton s Free-body Solving differential Projectile Motion in a plane, polar Solutions844 Linear differential Simple harmonic motion105viiMORIN: FM 2007/10/9 19.

5 08 page viii # Damped harmonic Driven (and damped) harmonic Coupled Solutions1275 Conservation of energy and Conservation of energy in one Small Conservation of energy in three The center of mass Inherently inelastic Solutions1946 The Lagrangian The Euler Lagrange The principle of stationary Forces of Change of Conservation Noether s Small Other Solutions2557 Central Conservation of angular The effective Solving the equations of Gravity, Kepler s Solutions300 MORIN: FM 2007/10/9 19.

6 08 page ix #9 Contentsix8 Angular momentum, Part I (Constant L) Pancake object Nonplanar Calculating moments of Angular Solutions3499 Angular momentum, Part II (General L) Preliminaries concerning The inertia Principal Two basic types of Euler s Free symmetric Heavy symmetric Solutions42810 Accelerating frames of Relating the The fictitious Solutions48611 Relativity (Kinematics) The The fundamental The Lorentz Velocity The invariant Minkowski The Doppler Relativity withoutc546 MORIN: FM 2007/10/9 19.

7 08 pagex # Solutions56512 Relativity (Dynamics) Energy and Transformations Collisions and Particle-physics Rocket Relativistic Solutions61913 Definition of Examples of Properties of Energy, Force and The form of physical Solutions64614 General The Equivalence Time Uniformly accelerating Maximal-proper-time Twin paradox Solutions666 Appendix A Useful formulas675 Appendix B Multivariable, vector calculus679 Appendix C F = ma vs. F = dp/dt690 Appendix D Existence of principal axes693 Appendix E Diagonalizing matrices696 Appendix F Qualitative relativity questions698 MORIN: FM 2007/10/9 19:08 page xi #11 ContentsxiAppendix G Derivations of the Lv/c2result704 Appendix H Resolutions to the twin paradox706 Appendix I Lorentz transformations708 Appendix J Physical constants and data711 References713 Index716 MORIN: FM 2007/10/9 19:08 page xii #12 MORIN: FM 2007/10/9 19.

8 08 page xiii #13 PrefaceThis book grew out of Harvard University s honors freshman Mechanics is essentially two books in one. Roughly half of each chapter follows the form ofa normal textbook, consisting of text, along with exercises suitable for homeworkassignments. The other half takes the form of a problem book, with all sortsof Problems (and solutions ) of varying degrees of difficulty. I ve always thoughtthat doing Problems is the best way to learn, so if you ve been searching for asupply to puzzle over, I think this will keep you busy for a book is somewhat of a quirky one, so let me say right at the start how Iimagine it being used: As the primary text for honors freshman Mechanics courses.

9 My original motivationfor writing it was the fact that there didn t exist a suitable book for Harvard s freshmancourse. So after nine years of using updated versions in the class, here is the finishedproduct. As a supplementary text for standard freshman courses for physics majors. Althoughthis book starts at the beginning of Mechanics and is self contained, it doesn t spendas much time on the introductory material as other freshman books do. I thereforedon t recommend using this as the only text for a standard freshman Mechanics , it will make an extremely useful supplement, both as a problem book for allstudents, and as a more advanced textbook for students who want to dive further intocertain topics.

10 As a supplementary text for upper-level Mechanics courses, or as the primary text whichis supplemented with another book for additional topics often covered in upper-levelcourses, such as Hamilton s equations, fluids, chaos, Fourier analysis, electricity andmagnetism applications, etc. With all of the worked examples and in-depth discussions,you really can t go wrong in pairing up this book with another one. As a problem book for anyone who likes solving physics Problems . This audienceranges from advanced high-school students, who I think will have a ball with it, toundergraduate and graduate students who want some amusing Problems to ponder, toprofessors who are looking for a new supply of Problems to use in their classes, andfinally to anyone with a desire to learn about physics by doing Problems .