Description
Book SynopsisTable of ContentsChapter 1 Background and Roadmap 1
1.1 Newton’s Laws 2
1.2 How You’ll Be Approaching Dynamics 3
1.3 Units 5
1.4 Symbols, Notation, and Conventions 7
1.5 Gravitation 13
1.6 A Comprehensive Dynamics Application 14
Chapter 2 Motion of Translating Bodies 17
2.1 Straight-Line Motion 18
Example 2.1 Velocity Determination Via Integration 25
Example 2.2 Deceleration Limit Determination 26
Example 2.3 Constant Acceleration/Speed/Distance Relationship 27
Example 2.4 Position-Dependent Acceleration 28
Example 2.5 Velocity-Dependent Acceleration (A) 30
Example 2.6 Velocity-Dependent Acceleration (B) 31
Exercises 2.1 32
2.2 Cartesian Coordinates 36
Example 2.7 Coordinate Transformation (A) 42
Example 2.8 Coordinate Transformation (B) 43
Example 2.9 Rectilinear Trajectory Determination (A) 44
Example 2.10 Rectilinear Trajectory Determination (B) 46
Exercises 2.2 48
2.3 Polar and Cylindrical Coordinates 52
Example 2.11 Velocity—Polar Coordinates 58
Example 2.12 Acceleration—Polar Coordinates (A) 60
Example 2.13 Acceleration—Polar Coordinates (B) 61
Example 2.14 Velocity And Acceleration—Cylindrical Coordinates 62
Exercises 2.3 64
2.4 Path Coordinates 69
Example 2.15 Analytical Determination of Radius of Curvature 72
Example 2.16 Acceleration—Path Coordinates 74
Example 2.17 Speed Along A Curve 76
Exercises 2.4 78
2.5 Relative Motion and Constraints 82
Example 2.18 One Body Moving on Another 89
Example 2.19 Two Bodies Moving Independently (A) 90
Example 2.20 Two Bodies Moving Independently (B) 91
Example 2.21 Simple Pulley 92
Example 2.22 Double Pulley 93
Exercises 2.5 95
2.6 Just the Facts 101
System Analysis (SA) Exercises 104
Chapter 3 Inertial Response of Translating Bodies 107
3.1 Cartesian Coordinates 108
Example 3.1 Analysis of A Spaceship 110
Example 3.2 Forces Acting on An Airplane 111
Example 3.3 Sliding Ming Bowl 112
Example 3.4 Response of An Underwater Probe 114
Example 3.5 Particle in an Enclosure 116
Exercises 3.1 118
3.2 Polar Coordinates 128
Example 3.6 Ming Bowl on A Moving Slope 129
Example 3.7 Ming Bowl in Motion 130
Example 3.8 Ming Bowl on A Moving Slope With Friction 132
Example 3.9 No-Slip In A Rotating Arm 134
Example 3.10 Forces Acting on A Payload 136
Exercises 3.2 138
3.3 Path Coordinates 144
Example 3.11 Forces Acting on My Car 145
Example 3.12 Finding A Rocket’s Radius of Curvature 146
Example 3.13 Force and Acceleration for A Sliding Pebble 148
Example 3.14 Determining Slip Point in A Turn 150
Exercises 3.3 151
3.4 Linear Momentum and Linear Impulse 155
Example 3.15 Changing the Space Shuttle’s Orbit 156
Example 3.16 Block on A Sanding Belt 158
Example 3.17 Two-Car Collision 159
Exercises 3.4 160
3.5 Angular Momentum and Angular Impulse 166
Example 3.18 Change In Speed of A Model Plane 169
Example 3.19 Angular Momentum of A Bumper 170
Example 3.20 Angular Momentum of A Tetherball 172
Exercises 3.5 174
3.6 Orbital Mechanics 175
Example 3.21 Analysis of an Elliptical Orbit 188
Example 3.22 Determining Closest Approach Distance 189
Exercises 3.6 190
3.7 Impact 196
Example 3.23 Dynamics of Two Pool Balls 200
Example 3.24 More Pool Ball Dynamics 202
Exercises 3.7 202
3.8 Oblique Impact 205
Example 3.25 Oblique Billiard Ball Collision 207
Example 3.26 Another Oblique Collision 209
Exercises 3.8 212
3.9 Just The Facts 215
System Analysis (SA) Exercises 218
Chapter 4 Energetics of Translating Bodies 221
4.1 Kinetic Energy 222
Example 4.1 Speed of an Arrow 224
Example 4.2 Change in Speed Due to an Applied Force 225
Example 4.3 Change in Speed Due to Slipping 226
Exercises 4.1 228
4.2 Potential Energy 233
Example 4.4 Speed Due to A Drop 237
Example 4.5 Designing A Nutcracker 238
Example 4.6 Change in Speed Using Potential Energy 240
Example 4.7 Falling Enclosure 241
Example 4.8 Reexamination of an Orbital Problem 243
Exercises 4.2 244
4.3 Power 255
Example 4.9 Time Needed to Increase Speed 258
Example 4.10 0 to 60 Time at Constant Power 259
Example 4.11 Determining A Cyclist’s Energy Efficiency 260
Exercises 4.3 261
4.4 Just the Facts 265
System Analysis (SA) Exercises 268
Chapter 5 Multibody Systems 269
5.1 Force Balance and Linear Momentum 270
Example 5.1 Finding A Mass Center 274
Example 5.2 Finding A System’s Linear Momentum 275
Example 5.3 Motion of A Two-Particle System 276
Example 5.4 Finding Speed of A Bicyclist/Cart 277
Example 5.5 Momentum of A Three-Mass System 278
Exercises 5.1 279
5.2 Angular Momentum 285
Example 5.6 Angular Momentum of Three Particles 288
Example 5.7 Angular Momentum About A System’s Mass Center 289
Exercises 5.2 290
5.3 Work and Energy 293
Example 5.8 Kinetic Energy of A Modified Baton 295
Example 5.9 Kinetic Energy of A Translating Modified Baton 296
Example 5.10 Spring-Mass System 297
Exercises 5.3 299
5.4 Stationary Enclosures with Mass Inflow and Outflow 300
Example 5.11 Water Jet Impinging on Stationary Vane 303
Example 5.12 Force Due to A Stream of Mass Particles 304
Exercises 5.4 305
5.5 Nonconstant Mass Systems 311
Example 5.13 Motion of A Toy Rocket 315
Example 5.14 Helicopter Response to A Stream of Bullets 317
Exercises 5.5 318
5.6 Just the Facts 323
System Analysis (SA) Exercises 326
Chapter 6 Kinematics of Rigid Bodies Undergoing Planar Motion 327
6.1 Relative Velocities on A Rigid Body 328
Example 6.1 Velocity of A Pendulum 334
Example 6.2 Velocity of A Constrained Link 335
Example 6.3 Angular Speed of A Spinning Disk 336
Example 6.4 Velocity of Link-Constrained Body 337
Example 6.5 Relative Angular Velocity 338
Exercises 6.1 340
6.2 Instantaneous Center of Rotation (ICR) 347
Example 6.6 Angular Speed Determination Via ICR 348
Example 6.7 Velocity on A Constrained Body Via ICR 350
Example 6.8 Velocity of the Contact Point During Roll Without Slip 351
Example 6.9 Pedaling Cadence and Bicycle Speed 352
Example 6.10 Rotation Rate of An Unwinding Reel Via ICR 354
Exercises 6.2 355
6.3 Rotating Reference Frames and Rigid-Body Accelerations 360
Example 6.11 Acceleration of A Pedal Spindle 363
Example 6.12 Acceleration During Roll Without Slip 364
Example 6.13 Tip Acceleration of A Two-Link Manipulator 365
Example 6.14 Acceleration of A Point on A Cog of A Moving Bicycle 367
Example 6.15 Path of Point on Rolling Disk 369
Exercises 6.3 370
6.4 Relative Motion on A Rigid Body 375
Example 6.16 Absolute Velocity of A Specimen In A Centrifuge 379
Example 6.17 Velocity Constraints—Closing Scissors 380
Example 6.18 Velocity and Acceleration In A Tube 381
Example 6.19 Angular Acceleration of A Constrained Body 383
Example 6.20 Angular Acceleration 385
Exercises 6.4 386
6.5 Just the Facts 393
System Analysis (SA) Exercises 395
Chapter 7 Kinetics of Rigid Bodies Undergoing Two-Dimensional Motions 397
7.1 Curvilinear Translation 398
Example 7.1 Determining the Acceleration of A Translating Body 399
Example 7.2 Tension In Support Chains 400
Example 7.3 General Motion of A Swinging Sign 403
Example 7.4 Normal Forces on A Steep Hill 406
Exercises 7.1 408
7.2 Rotation About A Fixed Point 412
Example 7.5 Mass Moment of Inertia of A Rectangular Plate 417
Example 7.6 Mass Moment of Inertia of A Circular Sector 418
Example 7.7 Mass Moment of Inertia of A Complex Disk 421
Example 7.8 Analysis of A Rotating Body 422
Example 7.9 Forces Acting at Pivot of Fireworks Display 425
Example 7.10 Determining A Wheel’s Imbalance Eccentricity 428
Exercises 7.2 429
7.3 General Motion 439
Example 7.11 Acceleration Response of an Unrestrained Body 442
Example 7.12 Response of A Falling Rod 446
Example 7.13 More Response of A Falling Rod 448
Example 7.14 Acceleration Response of A Driven Wheel 450
Example 7.15 Acceleration Response of A Driven Wheel—Take Two 452
Example 7.16 Falling Spool 455
Example 7.17 Tipping of A Ming Vase 456
Example 7.18 Equations of Motion for A Simple Car Model 459
Example 7.19 Analysis of A Simple Transmission 461
Exercises 7.3 463
7.4 Linear/Angular Momentum of Two-Dimensional Rigid Bodies 476
Example 7.20 Angular Impulse Applied to Space Station 478
Example 7.21 Impact Between A Pivoted Rod and A Moving Particle 479
Exercises 7.4 481
7.5 Work/Energy of Two-Dimensional Rigid Bodies 487
Example 7.22 Angular Speed of A Hinged Two-Dimensional Body 488
Example 7.23 Response of A Falling Rod Via Energy 490
Example 7.24 Design of A Spring-Controlled Drawbridge 491
Exercises 7.5 493
7.6 Just The Facts 500
System Analysis (SA) Exercises 502
Chapter 8 Kinematics and Kinetics of Rigid Bodies In Threedimensional Motion 505
8.1 Spherical Coordinates 506
8.2 Angular Velocity of Rigid Bodies in Three-Dimensional Motion 508
Example 8.1 Angular Velocity of A Simplified Gyroscope 512
Example 8.2 Angular Velocity of A Hinged Plate 513
8.3 Angular Acceleration of Rigid Bodies in Three-Dimensional Motion 514
Example 8.3 Angular Acceleration of A Simple Gyroscope 515
8.4 General Motion of and on Three-Dimensional Bodies 516
Example 8.4 Motion of A Disk Attached to A Bent Shaft 517
Example 8.5 Velocity and Acceleration of A Robotic Manipulator 520
Exercises 8.4 522
8.5 Moments and Products of Inertia for A Three-Dimensional Body 527
8.6 Parallel Axis Expressions For Inertias 530
Example 8.6 Inertial Properties of A Flat Plate 532
Exercises 8.6 533
8.7 Angular Momentum 535
Example 8.7 Angular Momentum of A Flat Plate 540
Example 8.8 Angular Momentum of A Simple Structure 540
Exercises 8.7 542
8.8 Equations of Motion For A Three-Dimensional Body 544
Example 8.9 Reaction Forces of A Constrained, Rotating Body 546
Exercises 8.8 548
8.9 Energy of Three-Dimensional Bodies 553
Example 8.10 Kinetic Energy of A Rotating Disk 555
Exercises 8.9 557
8.10 Just The Facts 559
System Analysis (SA) Exercises 563
Chapter 9 Vibratory Motions 565
9.1 Undamped, Free Response for Single-Degreeof-Freedom Systems 566
Example 9.1 Natural Frequency of A Cantilevered Balcony 569
Example 9.2 Displacement Response of A Single-Story Building 572
Exercises 9.1 573
9.2 Undamped, Sinusoidally Forced Response for Single-Degree-of-Freedom Systems 580
Example 9.3 Forced Response of A Spring-Mass System 582
Example 9.4 Time Response of an Undamped System 583
Exercises 9.2 584
9.3 Damped, Free Response for Single-Degree-ofFreedom Systems 588
Example 9.5 Vibration Response of A Golf Club 591
Exercises 9.3 592
9.4 Damped, Sinusoidally Forced Response for Single-Degree-of-Freedom Systems 593
Example 9.6 Response of A Simple Car Model on A Wavy Road 596
Example 9.7 Response of A Sinusoidally Forced, Spring-Mass Damper 598
Exercises 9.4 599
9.5 Just The Facts 600
System Analysis (SA) Exercises 603
Appendix A Numerical Integration Light 605
Appendix B Properties of Plane and Solid Bodies 613
Appendix C Some Useful Mathematical Facts 617
Appendix D Material Densities 621
Biblography 623
Index 625
