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Why Cats Land on Their Feet and 76 Other Physical Paradoxes and Puzzles

Mark Levi
Princeton University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Mark Bollman
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The subtitle of this book is “And 76 Other Physical Paradoxes And Puzzles”, and the title tells it like it is. There are a number of classical physics paradoxes and some new ones here, all broken down and carefully explained. One challenge of a more mathematical nature crops up as the last puzzle in the book: how to compute the square root of 2 with only a stopwatch and a sneaker.

There are evidently a lot of paradoxes about water out there — fully three chapters (of fourteen) deal with unexpected behavior from moving liquids, including both printer ink and molasses, along with water itself. On that list is the eminently practical “How to open a wine bottle with a book” (p. 146). In addressing the scenario posed in the title, the author notes that this is not because the cats spin their tails when falling and notes that “As an experimental fact, tailless cats are just as good as the tailed ones in flipping over.” I assume that this experiment was vetted by an institutional review board, and cannot help but wonder what that proposal must have looked like. (A theoretical argument against tail-spinning makes a much less risky case for why a different mechanism must be at work.)

Each problem is posed and then solved, with full and appropriate attention to the physical laws involved. From a mathematician’s perspective, the derivations are appropriately rigorous: while the requisite sums and integrals are usually to be found in the appendices, they are nonetheless in the book. As a source of carefully-applied mathematics, this book is a fine addition to popular science writing.

And if you’re thinking about sneakers and the square root of 2, I have one final word: “pendulum”.

Mark Bollman ( is associate professor of mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry; his interest in physics stems from four years as the physics instructor at a previous employer. His claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.

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 v2 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