10.3 THE FORCED HARMONIC OSCILLATOR 421
The Undamped Forced Oscillator, 421; Resonance, 423; The Forced Damped Harmonic Oscillator, 424; Resonance in a Lightly Damped System: The Quality Factor Q, 426.
10.4 RESPONSE IN TIME VERSUS RESPONSE IN FREQUENCY 432 Note 10.1 SOLUTION OF THE EQUATION OF MOTION FOR THE UNDRIVEN DAMPED OSCILLATOR 433
The Use of Complex Variables, 433; The Damped Oscillator, 435.
Note 10.2 SOLUTION OF THE EQUATION OF MOTION FOR THE FORCED OSCILLATOR 437 PROBLEMS 438
11.1 THE NEED FOR A NEW MODE OF THOUGHT 442
11.2 THE MICHELSON-MORLEY EXPERIMENT 445
11.3 THE POSTULATES OF SPECIAL RELATIVITY 450
The Universal Velocity, 451; The Principle of Relativity, 451; The Postulates of Special Relativity, 452.
11.4 THE GALILEAN TRANSFORMATIONS 453
11.5 THE LORENTZ TRANSFORMATIONS 455 PROBLEMS 459
12.1 INTRODUCTION 462
12.2 SIMULTANEITY AND THE ORDER OF EVENTS 463
12.3 THE LORENTZ CONTRACTION AND TIME DILATION 466 The Lorentz Contraction, 466; Time Dilation, 468.
12.4 THE RELATIVISTIC TRANSFORMATION OF VELOCITY 472
12.5 THE DOPPLER EFFECT 475
The Doppler Shift in Sound, 475; Relaiivistic Doppler Effect, 477; The Doppler Effect for an Observer off the Line of Motion, 478.
12.6 THE TWIN PARADOX 480 PROBLEMS 484
13.1 MOMENTUM 490
13.2 ENERGY 493
13.3 MASSLESS PARTICLES 500
13.4 DOES LIGHT TRAVEL AT THE VELOCITY OF LIGHT? 508 PROBLEMS 512
14.1 INTRODUCTION 516
14.2 VECTORS AND TRANSFORMATIONS 516
Rotation about the z Axis, 517; Invariants of a Transformation, 520; The Transformation Properties of Physical Laws, 520; Scalar Invariants, 521.
14.3 MINIKOWSKI SPACE AND FOUR-VECTORS 521
14.4 THE MOMENTUM-ENERGY FOUR-VECTOR 527
14.5 CONCLUDING REMARKS 534 PROBLEMS 536
LIST OF EXAMPLES, CHAPTER 1 1.1 Law of Cosines, 5; 1.2 Work and the Dot Product, 5; 1.3 : Examples of the Vector Product in Physics, 7; 1.4 Area as a Vector, 7.
EXAMPLES 1.5 Vector Algebra, 9; 1.6 Construction of a Perpendicular Vector, 10. 1.7 Finding v from r, 16; 1.8 Uniform Circular Motion, 17. 1.9 Finding Velocity from Acceleration, 20; 1.10 Motion in a Uniform Gravi-
1 VECTORS AND KINEMATICS —A FEW MATHEMATICAL PRELIMINARIES tational Field, 21; 1.11 Nonuniform Acceleration—The Effect of a Radio Wave on an Ionospheric Electron, 22. §§ 1.12 Circular Motion and Rotating Vectors, 25. Ц 1.13 Circular Motion and Straight Line Motion in Polar Coordinates, 34; 1.14 Velocity of a Bead on a Spoke, 35; 1.15 Off-center Circle, 35; 1.16 Acceleration of a Bead on a Spoke, 37; 1.17 Radial Motion without Acceleration, 38. Щ
2 NEWTON’S LAWS—THE FOUNDATIONS OF NEWTONIAN MECHANICS EXAMPLES, CHAPTER 2 Ш 2.1 Astronauts in Space—Inertial Systems and Fictitious Force, 60. 2.2 The Astronauts' Tug-of-v,ar, 70; 2.3 Freight Tpiin, 72; 2.4 Constraints, 74; 2.5 Block on String 1, 75; 2.6 Block on String, 76; 2.7 The Whirling Block, 76; 2.8 The Conical Pendulum, 77. * 2.9 Turtle in an Elevator, 84; 2.10 Block and String 3, 87; 2.11 Dangling Rope, 88; 2,12 Whirling Rope, 89; 2.13 Pulleys, 90;"2.14 Block and Wedge with Friction, 93; 2.15 The Spinning Terror, 94; 2.16 'Tree Motion in a Viscous Medium, 96; 2.17 Spring and Block—The Equating- for Simple Harmonic Motion, 98; 2.18 The Spring Gun—An Example Illustrating Initial Conditions, 99. ;
3 MOMENTUM EXAMPLES, CHAPTER 3 3.1 The Boia, 115; 3.2 Drum Major’s Baton, 117; 3.3 Center of Mass of a Nonuniform Rod, 119; 3.4 Center of Mass of a Triangular Sheet, 120; 3.5 Center of Mass Motion, 122. 3.6 Spring Gun Recoil, 123; 3.7 Earth, Moon, and Sun—A Three Body System, 125; 3.8 The Push Ме-Pull You, 128. 3.9 Rubber Ball Rebound, 131; 3.10 How to Avoid Broken Ankles, 132. 3.11 Mass Flow and Momentum, 134; 3.12 Freight Car and Hopper, 135; 3.13 Leaky Freight Car, 136; 3.14 Rocket in Free Space, 138; 3.15 Rocket in a Gravitational Field, 139. 3.16 Momentum Transport to a Surface, 141; 3.17 A Dike at the Bend of a River, 143; 3.18 Pressure of a Gas, 144.
4 WORK AND ENERGY EXAMPLES, CHAPTER 4 4.1 Mass Thrown Upward in a Uniform Gravitational Field, 154; 4.2 Solving the Equation of Simple Harmonic Motion, 154. 4.3 Vertical Motion in an Inverse Square Field, 156. 4.4 The Conical Pendulum, 161; 4.5 Escape Velocity—The General Case, 162. 4.6 The Inverted Pendulum, 164; 4.7 Work Done by a Uniform Force, 165; 4.8 Work Done by a Central Force, 167; 4.9 A Path-dependent Line Integral, 167; 4.10 Parametric Evaluation of a Line Integral, 168.
4.11 Potential Energy of a Uniform Force Field, 170; 4.12 Potential Energy of an Inverse Square Force, 171; 4.13 Bead, Hoop, and Spring, 172.
4.14 Energy and Stability—The Teeter Toy, 175.
4.15 Molecular Vibrations, 179; 4.16 Small Oscillations, 181.
4.17 Block Sliding down Inclined Plane, 183.
4.18 Elastic Collision of Two Balls, 190; 4.19 Limitations on Laboratory Scattering Angle, 193.
5 SOME EXAMPLES, CHAPTER 5
MATHEMATICAL 5.1 Partial Derivatives, 203; 5.2 Applications of the Partial Derivative, 205. ASPECTS 5.3 Gravitational Attraction by a Particle, 208; 5.4 Uniform Gravitational
OF FORCE Field, 209; 5.5 Gravitational Attraction by Two Point Masses, 209.
AND 5.6 Energy Contours for a Binary Star System, 212.
ENERGY 5.7 The Curl of the Gravitational Force, 219; 5.8 A Nonconservative Force, 220; 5.9 A Most Unusual Force Field, 221; 5.10 Construction of the Potential Energy Function, 222; 5.11 How the Curl Got Its Name, 224.
5.12 Using Stokes'Theorem, 227.
6 ANGULAR EXAMPLES, CHAPTER 6
MOMENTUM 6.1 Angular Momentum of a Sliding Block, 236 ; 6.2 Angular Momentum AND FIXED AXIS of the Conical Pendulum, 237.
ROTATION 6.3 Central Force Motion and the Law of Equal Areas, 240; 6.4 Capture Cross Section of a Planet, 241; 6.5 Torque on a Sliding Block, 244; 6.6 Torque on the Conical Pendulum, 245; 6.7 Torque due to Gravity, 247.
6.8 Moments of Inertia of Some Simple Objects, 250; 6.9 The Parallel Axis Theorem, 252.
6.10 Atwood's Machine with a Massive Pulley, 254.
6.11 Grandfather's Clock, 256; 6.12 Kater’s Pendulum, 258; 6.13 The Doorstep, 259.
6.14 Angular Momentum of a Rolling Wheel, 262; 6.15 Disk on Ice, 26 ,
6.16 Drum Rolling down a Plane, 265; 6.17 Drum Rolling down a Plane: Energy Method, 268; 6.18 The Falling Stick, 269.
7 RIGID BODY EXAMPLES, CHAPTER 7
MOTION 7.1 Rotations through Finite Angles, 289; 7.2 Rotation in the xy Plane, 29 ,
AND THE 7.3 Vector Nature of Angular Velocity, 291; 7.4 Angular Momentum of a
CONSERVATION Rotating Skew Rod, 292; 7.5 Torque on the Rotating Skew Rod, 293, 7.6 OF Torque on the Rotating Skew Rod (Geometric Method), 294.
ANGULAR 7-7 Gyroscope Precession, 298; 7.8 Why a Gyroscope Precesses, 299. MOMENTUM 7.9 Precession of the Equinoxes, 300; 7.10 The Gyrocompass Effect, 30 ,
7.11 Gyrocompass Motion, 302; 7.12 The Stability of Rotating Objects, 304.
7.13 Rotating Dumbbell, 310; 7.14 The Tensor of Inertia for a Rotating Skew Rod, 312; 7.15 Why Flying Saucers Make Better Spacecraft than Do Flying
Cigars, 314. 1Q
7.16 Stability of Rotational Motion, 322; 7.17 The Rotating Rod, 323; 7. ° Fiilar'c Pnilaftrmc anrl Tnmup-frpe Precession. 324.
8 NONINERTIAL SYSTEMS AND FICTITIOUS FORCES EXAMPLES, CHAPTER 8 8.1 The Apparent Force of Gravity, 346; 8.2 Cylinder on an Accelerating Plank, 347; 8.3 Pendulum in an Accelerating Car, 347. 8.4 The Driving Force of the Tides, 350; 8.5 Equilibrium Height of the Tide, 352. 8.6 Surface of a Rotating Liquid, 362; 8.7 The Coriolis Force, 363; 8.8 Deflection of a Falling Mass, 364; 8.9 Motion on the Rotating Earth, 366; 8.10 Weather Systems, 366; 8.11 The Foucault Pendulum, 369.
9 CENTRAL FORCE MOTION EXAMPLES, CHAPTER 9 9.1 Noninteracting Particles, 384; 9.2 The Capture of Comets, 387; 9.3 Perturbed Circular Orbit, 388. ' 9.4 Hyperbolic Orbits, 393; 9.5 Satellite Orbit, 396; 9.6 Satellite Maneuver, 398. 9.7 The Law of Periods, 403.
10 THE HARMONIC OSCILLATOR EXAMPLES, CHAPTER 10 10.1 Initial Conditions and the Frictionless Harmonic Oscillator, 411. 10.2 The 0 of Two Simple Oscillators, 419; 10.3 Graphical Analysis of a Damped Oscillator, 420. 10.4 Forced Harmonic Oscillator Demonstration, 424; 10.5 Vibration Eliminator, 428.
11 THE SPECIAL THEORY OF RELATIVITY EXAMPLES, CHAPTER 11 11.1 The Galilean Transformations, 453; 11.2 A Light Pulse as Described by the Galilean Transformations, 455.
12 RELATIVISTIC KINEMATICS EXAMPLES, CHAPTER 12 12.1 Simultaneity, 463; 12.2 An Application of the Lorentz Transformations, 464; 12.3 The Order of Events: Timelike and Spacelike Intervals, 465. 12.4 The Orientation of a Moving Rod, 467; 12.5 Time Dilation and Meson Decay, 468; 12.6 The Role of Time Dilation in an Atomic Clock, 470. 12.7 The Speed of Light in a Moving Medium, 474. 12.8 Doppler Navigation, 479.
13 RELATIVISTIC MOMENTUM AND ENERGY EXAMPLES, CHAPTER 13 13.1 Velocity Dependence of the Electron's Mass, 492. 13.2 Relativistic Energy and Momentum in an Inelastic Collision, 496; 13.3 The Equivalence of Mass and Energy, 498. 13 Л Tkn ctt i cm. 11 r n -X , ,_LX pm.
13.6 The Compton Effect, 503; 13.7 Pair Production, 505; 13.8 The Photon Picture of the Doppler Effect, 507.
13.9 The Rest Mass of the Photon, 510; 13.10 Light from a Pulsar, 510.
EXAMPLES, CHAPTER 14
14.1 Transformation Properties of the Vector Product, 518; 14.2 A Nonvector, 519.
14.3 Time Dilation, 524; 14.4 Construction of a Four-vector: The Four-velocity, 525; 14.5 The Relativistic Addition of Velocities, 526.
14.6 The Doppler Effect, Once More, 530; 14.7 Relativistic Center of Mass Systems, 531; 14.8 Pair Production in Electron-electron Collisions, 533.