Problems and Solutions in INTRODUCTORY MECHANICS

1 DAVID MORINP roblems and Solutions inINTRODUCTORYMECHANICSP roblems and SolutionsinINTRODUCTORY MECHANICSD avid MorinHarvard University David Morin 2014 All rights reservedISBN-10: 1482086921 ISBN-13: 978-1482086928 Printed by CreateSpaceCover image: iStock photograph by Vernon WileyAdditional resources located problem -solving Basic strategies .. Solving Problems symbolically .. Checking units/dimensions .. Checking limiting/special cases .. Taylor series .. List of strategies .. Getting started .. Solving the problem .. Troubleshooting .. Finishing up .. Looking ahead .. How to use this book .. Multiple-choice questions.

2 Problems .. Multiple-choice answers .. problem Solutions .. 202 Kinematics in Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers .. problem Solutions .. 363 Kinematics in 2-D (and 3-D) Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers .. problem Solutions .. 524 F= Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers .. problem Solutions .. 87iiiivCONTENTS5 Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers .. problem Solutions .. 1186 Introduction .. Multiple-choice questions.

3 Problems .. Multiple-choice answers .. problem Solutions .. 1587 Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers .. problem Solutions .. 1938 Angular Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers .. problem Solutions .. 2319 Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers .. problem Solutions .. 25610 Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers .. problem Solutions .. 27211 Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers.

4 problem Solutions .. 29712 Fictitious Introduction .. Multiple-choice questions .. Problems .. Multiple-choice answers .. problem Solutions .. 325 CONTENTSv13 Appendix A: Vectors .. Basics .. Cartesian coordinates .. Polar coordinates .. Adding and subtracting vectors .. Using components .. Dot product .. Cross product .. Appendix B: Taylor series .. Basics .. How many terms to keep? .. Dimensionless quantities .. Appendix C: Limiting cases, scientific method .. Appendix D: Problems requiring calculus .. 344 PrefaceThis problem book grew out of a freshman physics MECHANICS course taught at HarvardUniversity during the past decade and a half.

5 Most of the Problems are from exams or problemsets, although I have added others to round out the distribution of topics. Some of the problemsare standard ones, but many are offthe beaten path. In the end, there is a finite number of prin-ciples in INTRODUCTORY MECHANICS , so the Problems inevitably start looking familiar after a topics from the course that aren t included in this book are relativity and damped/drivenoscillatory motion. Perhaps these will appear in a future edition, along with other topics such asfluids and precessional angular book will be helpful to both high-school students and college students taking courses inintroductory physics (just MECHANICS , not electricity and magnetism).

6 Calculus is used through-out the book, although it turns out that only a sixth of the Problems actually require it. Thissubset of Problems is listed in Appendix D. If you haven t studied calculus yet, just steer clear ofthose Problems , and you can view this book as an algebra-based one. The Problems are gener-ally on the level of the one-star or two-star Problems in myIntroduction to Classical Mechanicstextbook,1which covers a number of more advanced topics such as Lagrangians, normal modes,gyroscopic motion, etc. I will occasionally refer you to that book if you are interested in delvingfurther into various is important to note that this bookshould not be thought of as a is an introduction to each chapter where the basics are presented, this introduction is is no substitute for the text in a chapter in a standard INTRODUCTORY textbook.

7 This book istherefore designed to be used in tandem with a normal textbook. You can think of this book assupplementing a textbook by providing a stockpile of additional Problems . Or you can think ofa textbook as supplementing this book by providing additional most chapters the first few Problems are foundational ones. These Problems cover basicresults and theorems that you can use when solving other Problems . When a basic result is statedin the introduction to each chapter, you will generally be referred to a foundational problem forthe proof. The book is self contained, in that we derive everything we need. It s just that manyof the derivations are shifted to the set of multiple-choice questions precedes the Problems in each chapter.

8 These questionsare usually conceptual ones that you can do in your head. In the rare case where they require acalculation, it is a very minor one. The book contains about 150 multiple-choice questions, inaddition to nearly 250 free-response on how you use this book, it can be an invaluable resource or a complete wasteof time. So here is some critical advice on using the Solutions to the Problems : If you are havingtrouble solving a problem , it is imperative that you don t look at the solution too soon. Broodover it for a while. If you do finally look at the solution,don tjust read it through. Instead, coverit up with a piece of paper and read one line at a time until you get a hint to get started.

9 Thenset the book aside and work out the problem for real. Repeat this process as necessary. Activelysolving the problem is the only way it will sink in. This piece of advice on how to use this bookis so important that I m going to repeat it and display it prominently in a box:1 Introduction to Classical MECHANICS , With Problems and Solutions , David Morin, Cambridge University Press,2008. This will be referred to as Morin (2008). viiviiiCONTENTSIf you need to look at the solution to a problem to get a hint (after having thought about itfor a while), cover it up with a piece of paper and read one line at a time until you can getstarted. Then set the book aside and work things out for real.

10 You will learn a great deal thisway. If you instead read a solution straight through without having first solved the problem ,you will learn very only scenario in which you should ever read a solution straight through is where you vealready solved the problem . However, even in this case you should be careful. If I ve given analternative solution, then you should again just read one line at a time until you can get startedand solve it that way belabor the point, it is quite astonishing how unhelpful it is to simply read a solutioninstead of solving a problem . You dthinkit would do some good, but in fact it is completelyineffective in raising your understanding to the next level.