University Physics I - Classical Mechanics, 2019

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CONTENTS ix 8.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 9 Rotational dynamics 191 9.1 Rotational kinetic energy, and moment of inertia . . . . . . . . . . . . . . . . . . . . 191 9.2 Angular momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 9.3 The cross product and rotational quantities . . . . . . . . . . . . . . . . . . . . . . . 197 9.4 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.5 Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 9.6 Rolling motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 9.7 In summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 9.8 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 9.8.1 Torques and forces on the wheels of an accelerating bicycle . . . . . . . . . . 213 9.8.2 Blocks connected by rope over a pulley with non-zero mass . . . . . . . . . . 214 9.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 10 Gravity 221 10.1 The inverse-square law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 10.1.1 Gravitational potential energy . . . . . . . . . . . . . . . . . . . . . . . . . . 224 10.1.2 Types of orbits under an inverse-square force . . . . . . . . . . . . . . . . . . 227 10.1.3 Kepler’s laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 10.2 Weight, acceleration, and the equivalence principle . . . . . . . . . . . . . . . . . . . 236 10.3 In summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
x CONTENTS 10.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 10.4.1 Orbital dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 10.4.2 Orbital data from observations: Halley’s comet . . . . . . . . . . . . . . . . . 245 10.5 Advanced Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 10.5.1 Tidal Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 10.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 11 Simple harmonic motion 253 11.1 Introduction: the physics of oscillations . . . . . . . . . . . . . . . . . . . . . . . . . 253 11.2 Simple harmonic motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 11.2.1 Energy in simple harmonic motion . . . . . . . . . . . . . . . . . . . . . . . . 259 11.2.2 Harmonic oscillator subject to an external, constant force . . . . . . . . . . . 260 11.3 Pendulums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.3.1 The simple pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.3.2 The “physical pendulum” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.4 In summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 11.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 11.5.1 Oscillator in a box (a basic accelerometer!) . . . . . . . . . . . . . . . . . . . 268 11.5.2 Meter stick as a physical pendulum . . . . . . . . . . . . . . . . . . . . . . . . 270 11.6 Advanced Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272 11.6.1 Mass on a spring damped by friction with a surface . . . . . . . . . . . . . . 272
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Page 5 and 6: ii
Page 7 and 8: iv CONTENTS 1.6 Problems . . . . .
Page 9 and 10: vi CONTENTS 5.1 Conservative intera
Page 11: viii CONTENTS 7.7 Examples . . . .
Page 15 and 16: xii CONTENTS 13.2.1 Temperature and
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Page 19 and 20: Chapter 1 Reference frames, displac
Page 21 and 22: 1.2. POSITION, DISPLACEMENT, VELOCI
Page 33 and 34: 1.3. REFERENCE FRAME CHANGES AND RE
Page 35 and 36: 1.3. REFERENCE FRAME CHANGES AND RE
Page 37 and 38: 1.4. IN SUMMARY 19 with a velocity
Page 39 and 40: 1.5. EXAMPLES 21 1.5 Examples 1.5.1
Page 41 and 42: 1.5. EXAMPLES 23 (twice what it was
Page 43 and 44: 1.5. EXAMPLES 25 Note that I have d
Page 45 and 46: 1.6. PROBLEMS 27 1.6 Problems Probl
Page 47 and 48: 1.6. PROBLEMS 29 Problem 5 You are
Page 49 and 50: Chapter 2 Acceleration 2.1 The law
Page 51 and 52: 2.1. THE LAW OF INERTIA 33 This is
Page 53 and 54: 2.2. ACCELERATION 35 2.2 Accelerati
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Page 57 and 58: 2.2. ACCELERATION 39 2.2.2 Motion w
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Page 61 and 62: 2.3. FREE FALL 43 proportional to t
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2.4. IN SUMMARY 45 4. Changes in ve
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2.5. EXAMPLES 47 which the rocket r
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2.6. PROBLEMS 49 (a) How far did yo
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Chapter 3 Momentum and Inertia 3.1
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3.1. INERTIA 53 reliable, repeatabl
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3.1. INERTIA 55 3.1.2 Inertial mass
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3.2. MOMENTUM 57 the system is p i
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3.3. EXTENDED SYSTEMS AND CENTER OF
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3.4. IN SUMMARY 61 3.3.2 Recoil and
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3.5. EXAMPLES 63 3.5 Examples 3.5.1
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3.5. EXAMPLES 65 3.5.2 Collision in
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3.6. PROBLEMS 67 3.6 Problems Probl
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Chapter 4 Kinetic Energy 4.1 Kineti
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4.1. KINETIC ENERGY 71 v 2i =0,v 1f
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4.1. KINETIC ENERGY 73 special case
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4.1. KINETIC ENERGY 75 This immedia
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4.2. “CONVERTIBLE” AND “TRANS
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4.2. “CONVERTIBLE” AND “TRANS
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4.3. IN SUMMARY 81 7. Besides the c
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4.4. EXAMPLES 83 On the other hand,
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4.4. EXAMPLES 85 K cm ′ = 1 2 (m
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4.5. PROBLEMS 87 (a) What is the in
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Chapter 5 Interactions and energy 5
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5.1. CONSERVATIVE INTERACTIONS 91 T
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5.1. CONSERVATIVE INTERACTIONS 93 A
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5.1. CONSERVATIVE INTERACTIONS 95 d
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5.2. DISSIPATION OF ENERGY AND THER
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5.4. CONSERVATION OF ENERGY 99 leve
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5.5. IN SUMMARY 101 gravitational p
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5.6. EXAMPLES 103 5.6 Examples 5.6.
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5.6. EXAMPLES 105 problem involves
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5.7. ADVANCED TOPICS 107 where the
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5.8. PROBLEMS 109 5.8 Problems Prob
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5.8. PROBLEMS 111 here? Explain. (f
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Chapter 6 Interactions, part 2: For
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6.1. FORCE 115 however, somewhat mo
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6.2. FORCES AND POTENTIAL ENERGY 11
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6.2. FORCES AND POTENTIAL ENERGY 11
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6.3. FORCES NOT DERIVED FROM A POTE
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6.5. IN SUMMARY 127 F s,1 n a F s,1
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6.6. EXAMPLES 131 pushes on the bra
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6.6. EXAMPLES 133 This is a huge di
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6.7. PROBLEMS 135 Problem 6 Draw a
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Chapter 7 Impulse, Work and Power 7
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7.2. WORK ON A SINGLE PARTICLE 139
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7.3. THE “CENTER OF MASS WORK”
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7.4. WORK DONE ON A SYSTEM BY ALL T
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7.6. IN SUMMARY 151 which is equal
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7.7. EXAMPLES 155 To plot all this
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7.7. EXAMPLES 157 (a) The external
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7.8. PROBLEMS 159 Problem 5 A block
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Chapter 8 Motion in two dimensions
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8.1. DEALING WITH FORCES IN TWO DIM
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8.2. PROJECTILE MOTION 165 The over
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8.3. INCLINED PLANES 167 8.3 Inclin
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8.4. MOTION ON A CIRCLE (OR PART OF
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8.5. IN SUMMARY 175 As we shall see
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8.6. EXAMPLES 177 8.6 Examples You
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8.7. ADVANCED TOPICS 179 8.7 Advanc
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8.7. ADVANCED TOPICS 181 Now we jus
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8.7. ADVANCED TOPICS 183 Note that
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8.7. ADVANCED TOPICS 185 The cyan a
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8.8. PROBLEMS 187 (b) What is the w
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8.8. PROBLEMS 189 (e) The power is
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Chapter 9 Rotational dynamics Rotat
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9.2. ANGULAR MOMENTUM 193 9.2 Angul
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9.2. ANGULAR MOMENTUM 195 thing is
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9.3. THE CROSS PRODUCT AND ROTATION
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9.3. THE CROSS PRODUCT AND ROTATION
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9.4. TORQUE 201 momentum involves t
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9.4. TORQUE 203 wrenches). It is al
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9.5. STATICS 205 important in engin
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9.6. ROLLING MOTION 207 9.6 Rolling
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9.6. ROLLING MOTION 209 contact wit
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9.7. IN SUMMARY 211 (Note how I hav
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9.8. EXAMPLES 213 9.8 Examples This
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9.8. EXAMPLES 215 Solution The figu
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9.9. PROBLEMS 217 9.9 Problems Prob
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9.9. PROBLEMS 219 A 20-kg plank of
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Chapter 10 Gravity 10.1 The inverse
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10.1. THE INVERSE-SQUARE LAW 223 ne
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10.1. THE INVERSE-SQUARE LAW 225 it
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10.1. THE INVERSE-SQUARE LAW 227 in
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10.1. THE INVERSE-SQUARE LAW 229 an
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10.1. THE INVERSE-SQUARE LAW 231 el
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10.1. THE INVERSE-SQUARE LAW 233 10
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10.1. THE INVERSE-SQUARE LAW 235 Fr
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10.2. WEIGHT, ACCELERATION, AND THE
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10.2. WEIGHT, ACCELERATION, AND THE
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10.3. IN SUMMARY 241 shifted and/or
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10.4. EXAMPLES 243 10.4 Examples 10
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10.4. EXAMPLES 245 The diagram of t
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10.5. ADVANCED TOPICS 247 10.5 Adva
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10.6. PROBLEMS 249 10.6 Problems Pr
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10.6. PROBLEMS 251 an orbit around
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Chapter 11 Simple harmonic motion 1
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11.2. SIMPLE HARMONIC MOTION 255 is
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11.2. SIMPLE HARMONIC MOTION 257 Th
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11.2. SIMPLE HARMONIC MOTION 259 If
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11.2. SIMPLE HARMONIC MOTION 261 Th
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11.3. PENDULUMS 263 o θ l F t F G
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11.3. PENDULUMS 265 11.3.2 The “p
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11.4. IN SUMMARY 267 9. A simple pe
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11.5. EXAMPLES 269 (b) The amplitud
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11.5. EXAMPLES 271 AsshowninSection
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11.6. ADVANCED TOPICS 273 Figure 11
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11.6. ADVANCED TOPICS 275 the oscil
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11.7. PROBLEMS 277 (that is, with r
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Chapter 12 Waves in one dimension 1
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12.1. TRAVELING WAVES 281 Perhaps t
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12.1. TRAVELING WAVES 283 ξ 1 0.5
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12.1. TRAVELING WAVES 285 Comparing
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12.1. TRAVELING WAVES 287 waves, th
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12.2. STANDING WAVES AND RESONANCE
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12.2. STANDING WAVES AND RESONANCE
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12.3. CONCLUSION, AND FURTHER RESOU
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12.5. EXAMPLES 297 However, if you
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12.6. ADVANCED TOPICS 299 12.6 Adva
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12.6. ADVANCED TOPICS 301 In the lo
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Chapter 13 Thermodynamics 13.1 Intr
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13.2. INTRODUCING TEMPERATURE 305 a
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13.2. INTRODUCING TEMPERATURE 307 m
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13.3. HEAT AND THE FIRST LAW 309 th
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13.3. HEAT AND THE FIRST LAW 311 ca
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13.4. THE SECOND LAW AND ENTROPY 31
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13.5. IN SUMMARY 319 13.5 In summar
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13.7. PROBLEMS 323 13.7 Problems Pr
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