Background and Roadmap 1

1.1 Newton’s Laws 2

1.2 How You’ll Be Approaching Dynamics 2

1.3 Units and Symbols 6

1.4 Gravitation 10

1.5 The Pieces of the Puzzle 11

Chapter 2

Motion of Translating Bodies 16

2.1 Straight-Line Motion 17

Examples 23

Exercises 2.1 28

2.2 Cartesian Coordinates 33

Examples 38

Exercises 2.2 43

2.3 Polar and Cylindrical Coordinates 47

Examples 54

Exercises 2.3 58

2.4 Path Coordinates 64

Examples 67

Exercises 2.4 71

2.5 Relative Motion and Constraints 76

Examples 82

Exercises 2.5 87

2.6 Just the Facts 93

System Analysis 97

Chapter 3

Inertial Response of Translating Bodies 99

3.1 Cartesian Coordinates 100

Examples 102

Exercises 3.1 108

3.2 Polar Coordinates 119

Examples 120

Exercises 3.2 127

3.3 Path Coordinates 133

Examples 134

Exercises 3.3 139

3.4 Linear Momentum and Linear Impulse 143

Examples 145

Exercises 3.4 147

3.5 Angular Momentum and Angular Impulse 155

Examples 158

Exercises 3.5 161

3.6 Orbital Mechanics 163

Examples 176

Exercises 3.6 178

3.7 Impact 183

Examples 189

Exercises 3.7 191

3.8 Oblique Impact 193

Examples 196

Exercises 3.8 200

3.9 Just the Facts 203

System Analysis 206

Chapter 4

Energetics of Translating Bodies 209

4.1 Kinetic Energy 210

Examples 212

Exercises 4.1 215

4.2 Potential Energies and Conservative Forces 220

Examples 225

Exercises 4.2 231

4.3 Power and Efficiency 243

Examples 247

Exercises 4.3 250

4.4 Just the Facts 255

System Analysis 257

Chapter 5

Multibody Systems 258

5.1 Force Balance and Linear Momentum 259

Examples 263

Exercises 5.1 268

5.2 Angular Momentum 273

Examples 277

Exercises 5.2 279

5.3 Work and Energy 282

Examples 284

Exercises 5.3 287

5.4 Stationary Enclosures with Mass Inflow and Outflow 288

Examples 291

Exercises 5.4 293

5.5 Nonconstant Mass Systems 299

Examples 303

Exercises 5.5 305

5.6 Just the Facts 310

System Analysis 313

Chapter 6

Kinematics of Rigid Bodies Undergoing Planar Motion 314

6.1 Relative Velocities on a Rigid Body 315

Examples 320

Exercises 6.1 325

6.2 Instantaneous Center of Rotation (icr) 333

Examples 335

Exercises 6.2 341

6.3 Rotating Reference Frames and Rigid-Body Accelerations 346

Examples 350

Exercises 6.3 356

6.4 Relative Motion on a Rigid Body 361

Examples 365

Exercises 6.4 371

6.5 Just the Facts 378

System Analysis 380

Chapter 7

Kinetics of Rigid Bodies Undergoing Two-dimensional Motion 382

7.1 Curvilinear Translation 384

Examples 385

Exercises 7.1 392

7.2 Rotation about a Fixed Point 396

Examples 401

Exercises 7.2 411

7.4 Linear/Angular Momentum of Two-Dimensional Rigid Bodies 457

Examples 460

Exercises 7.4 462

7.5 Work/Energy of Two-Dimensional Rigid Bodies 468

Examples 471

Exercises 7.5 475

7.6 Just the Facts 482

System Analysis 484

Chapter 8

Kinematics and Kinetics of Rigid Bodies in Three-dimensional Motion 487

8.1 Spherical Coordinates 488

8.2 Angular Velocity of Rigid Bodies in Three-Dimensional Motion 489

Examples 493

8.3 Angular Acceleration of Rigid Bodies in Three-Dimensional Motion 495

Examples 496

8.4 General Motion of and on Three-Dimensional Bodies 497

Examples 498

Exercises 8.4 502

8.5 Moments and Products of Inertia for a Three-Dimensional Body 506

8.6 Parallel Axis Expressions for Inertias 508

Examples 510

Exercises 8.6 511

8.7 Angular Momentum 513

Examples 517

Exercises 8.7 520

8.8 Equations of Motion for a Three-Dimensional Body 521

Examples 524

Exercises 8.8 526

8.9 Energy of Three-Dimensional Bodies 532

Examples 534

Exercises 8.9 536

8.10 Just the Facts 537

System Analysis 541

7.3 General Motion 422

Examples 425

Exercises 7.3 444

Chapter 9

Vibratory Motions 542

9.1 Undamped, Free Response for Single-Degree-of-Freedom Systems 543

Examples 546

Exercises 9.1 549

9.2 Undamped, Sinusoidally Forced Response for Single-Degree-of- Freedom Systems 555

Examples 558

Exercises 9.2 560

9.3 Damped, Free Response for Single-Degree-of-Freedom Systems 563

Examples 567

Exercises 9.3 568

9.4 Damped, Sinusoidally Forced Response for Single-Degree-of- Freedom Systems 569

Examples 572

Exercises 9.4 575

9.5 Just the Facts 576

System Analysis 579

 Appendix A

Numerical Integration Light 580

 Appendix B

Properties of Plane and Solid Bodies 588

 Appendix C

Some Useful Mathematical Facts 592

 Appendix D

Material Densities 595

Bibliography 597

Index 598