Why Cats Land on Their Feet

Mark Levi is professor of mathematics at Pennsylvania State University. He is the author of The Mathematical Mechanic: Using Physical Reasoning to Solve Problems.

• Chapter 1 Fun with Physical Paradoxes, Puzzles, and Problems 1 1.1 Introduction 1 1.2 Background 3 1.3 Sources 3 Chapter 2 Outer Space Paradoxes 5 2.1 A Helium Balloon in a Space Shuttle 5 2.2 Space Navigation without Jets 9 2.3 A Paradox with a Comet 13 2.4 Speeding Up Causes a Slowdown 14 Chapter 3 Paradoxes with Spinning Water 17 3.1 A Puzzle with a Floating Cork 17 3.2 Parabolic Mirrors and Two Kitchen Puzzles 19 3.3 A Cold Parabolic Dish 21 3.4 Boating on a Slope 23 3.5 Navigating with No Engine or Sails 24 3.6 The Icebergs 25 Chapter 4 Floating and Diving Paradoxes 28 4.1 A Bathtub on Wheels 28 4.2 The Tub Problem--In More Depth 30 4.3 How to Lose Weight in a Fraction of a Second 32 4.4 An Underwater Balloon 33 4.5 A Scuba Puzzle 35 4.6 A Weight Puzzle 36 Chapter 5 Flows and Jets 39 5.1 Bernoulli's Law and Water Guns 39 5.2 Sucking on a Straw and the Irreversibility of Time 42 5.3 Bernoulli's Law and Moving Around in a Space Shuttle 44 5.4 A Sprinker Puzzle 45 5.5 Ejecting Water Fast but with Zero Speed? 48 5.6 A Pouring Water Puzzle 49 5.7 A Stirring Paradox 51 5.8 An Inkjet Printer Question 54 5.9 A Vorticity Paradox 55 Chapter 6 Moving Experiences: Bikes, Gymnastics, Rockets 57 6.1 How Do Swings Work? 57 6.2 The Rising Energy Cost 58 6.3 A Gymnast Doing Giants and a Hamster in a Wheel 60 6.4 Controlling a Car on Ice 63 6.5 How Does a Biker Turn? 64 6.6 Speeding Up by Leaning 65 6.7 Can One Gain Speed on a Bike by Body Motion Only? 66 6.8 Gaining Weight on a Motorbike 68 6.9 Feeling the Square in mv2 2 Through the Bike Pedals 69 6.10 A Paradox with Rockets 70 6.11 A Coffee Rocket 72 6.12 Throwing a Ball from a Moving Car 74 Chapter 7 Paradoxes with the Coriolis Force 77 7.1 What Is the Coriolis Force? 77 7.2 Feeling Coriolis in a Boeing 747 79 7.3 Down the Drain with Coriolis 80 7.4 High Pressure and Good Weather 80 7.5 What Causes Trade Winds? 82 Chapter 8 Centrifugal Paradoxes 84 8.1 What's Cheaper: Flying West or East? 84 8.2 A Coriolis Paradox 85 8.3 An Amazing Inverted Pendulum: What Holds It Up? 87 8.4 Antigravity Molasses 91 8.5 The "Proof" That the Sling Cannot Work 92 8.6 A David-Goliath Problem 93 8.7 Water in a Pipe 97 8.8 Which Tension Is Greater? 98 8.9 Slithering Ropes in Weightlessness 100 Chapter 9 Gyroscopic Paradoxes 104 9.1 How Does the Spinning Top Defy Gravity? 104 9.2 Gyroscopes in Bikes 108 9.3 A Rolling Coin 109 9.4 Staying on a Slippery Dome 111 9.5 Finding North with a Gyroscope 113 Chapter 10 Some Hot Stuff and Cool Things 117 10.1 Can Heat Pass from a Colder to a Hotter Object? 117 10.2 A Bike Pump and Molecular Ping-Pong 121 10.3 A Bike Pump as a Heat Pump 122 10.4 Heating a Room in Winter 124 10.5 Freezing Things with a Bike Tire 125 Chapter 11 Two Perpetual Motion Machines 127 11.1 Perpetual Motion by Capillarity 128 11.2 An Elliptical Mirror Perpetuum Mobile 129 Chapter 12 Sailing and Gliding 132 12.1 Shooting Cherry Pits and Sailing 133 12.2 Sailing Straight into the Wind 135 12.3 Biking against the Wind 136 12.4 Soaring without Updrafts 138 12.5 Danger of the Horizontal Shear Wind 141 Chapter 13 The Flipping Cat and the Spinning Earth 142 13.1 How Do Cats Flip to Land on Their Feet? 142 13.2 Can Trade Winds Slow Earth's Rotation? 144 Chapter 14 Miscellaneous 146 14.1 How to Open a Wine Bottle with a Book 146 14.2 :"t's Alive!" 149 14.3 Falling Faster Than g: A Falling Chain "Sucked in" by the Floor 150 14.4 A Man in a Boat with Drag 151 14.5 A "Phantom" Boat: No Wake and No Drag 154 14.6 A Constant-G Roller Coaster 156 14.7 Shooting at a Cart 158 14.8 Computing 2 with a Shoe 159 Appendix 161 A.1 Newton's Laws 161 A.2 Kinetic Energy, Potential Energy, Work 163 A.2.1 Work 163 A.2.2 Kinetic Energy 165 A.2.3 Potential Energy 166 A.2.4 Conservation of Energy 168 A.3 Center of Mass 169 A.4 Linear Momentum 171 A.5 The Torque 174 A.6 Angular Momentum 175 A.7 Angular Velocity, Centripetal Acceleration 178 A.8 Centrifugal and Centripetal Forces 181 A.9 Coriolis, Centrifugal, and Complex Exponentials 181 A.10 The Fundamental Theorem of Calculus 184 Bibliography 187 Index 189

"A collection of physical puzzlers, often with counter intuitive manifestations, which, for all that, admit rigorous explanation supported by physical intuition... [H]ugely entertaining and provide hours of brainy activities."--Alexander Bogomolny, CTK Insights "This book seeks to nurture this physical intuition in readers by analyzing several paradoxes while keeping the math to a minimum. Through examining one puzzle or paradox after another, Levi emphasizes the underlying principles involved and helps foster an intuitive understanding of why things work the way they do. Readers will find themselves coaxed into learning because they want to satisfy their curiosity as they examine each puzzle... [A]n excellent resource for understanding some less-obvious principles of physics."--William Baer, Library Journal "Each chapter can be read in a few minutes time, say while you are drinking a cup of tea or coffee. It will give you a lot of inspiration to challenge or entertain your friends during a reception or another get-together with some different kind of beverages. Of course you will impress them only when they haven't read the book themselves already. Hence make sure that you are the first."--Adhemar Bultheel, European Mathematical Society "Mathematician Levi has assembled a fascinating collection of 77 puzzles, some clever new originals and some twists to old ones that challenge physical intuition... [A] pleasurable challenge."--Choice "Quite how a falling cat manages to land on its feet is a classic conundrum for undergraduate students of physics. Levi presents this and other puzzles, with a few clues to how to go about solving them using only high-school mathematics. He explains all the necessary physics concepts in the appendix too."--Nature Physics "Why Cats Land On Their Feet relies on a novel approach to problem solving that is not based on mathematics, but on models and physical intuition... By looking beyond formulas and equations, Levi's goal is to provide readers who have a familiarity with basic high-school math and physics with critical thinking skills that can be applied to a range of physics problems beyond the book."--Mechanical Engineering-CIME "Levi uses titillating puzzles and a humorous tone to truly infuse fun into the book. A must have for anyone that likes physics, or for that matter hates. Why Cats Land On Their Feet is a book that introduces the reader to the cool side of physics and then engages for hours."--Sarthak Shankar, Organiser "The book is written in an accessible style and presumes little mathematical knowledge: a couple of puzzles refer to some basic calculus, but most require only arithmetic. It is suitable for everyone from sixth form students upwards... Teachers and lecturers will particularly appreciate this text, finding in it numerous quirky thought-experiments, actual experiments and trivia to catch their students' attention."--Paul Taylor, Mathematics Today "This book will cultivate and challenge your physical intuition. Above all, it shows that physics and mathematics can be fun and useful at the same time."--Catherine A. Gorini, Mathematics Teacher "It is written with a lot of humor, and provides helpful insights without going into unnecessarily complicated physical or mathematical techniques. The style is informal and attractive, which makes the reading of the book a real pleasure."--Kiril Bankov, Mathematical Gazette