Competitive Physics: Mechanics And Waves

by Jinhui Wang, Bernard Ricardo Widjaja

Overview

Written by a former Olympiad student, Wang Jinhui, and a Physics Olympiad national trainer, Bernard Ricardo, Competitive Physics delves into the art of solving challenging physics puzzles. This book not only expounds a multitude of physics topics from the basics but also illustrates how these theories can be applied to problems, often in an elegant fashion. With worked examples that depict various problem-solving sleights of hand and interesting exercises to enhance the mastery of such techniques, readers will hopefully be able to develop their own insights and be better prepared for physics competitions. Ultimately, problem-solving is a craft that requires much intuition. Yet, this intuition can only be honed by mentally trudging through an arduous but fulfilling journey of enigmas.Mechanics and Waves is the first of a two-part series which will discuss general problem-solving methods, such as exploiting the symmetries of a system, to set a firm foundation for other topics.

Product Details

ISBN-13:	9789813233942
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	10/09/2018
Pages:	832
Product dimensions:	6.69(w) x 9.61(h) x 1.75(d)

About the Author

Wang Jinhui was a Physics Olympiad trainer at his alma mater, Hwa Chong Institution, from 2016 to 2017. An enthusiastic solver of challenging problems of which life is only a part, he placed first in the 2016 Princeton University Online Physics Competition and was awarded Bronze in the Singapore Physics Olympiad in 2014. Jinhui is currently pursuing his undergraduate studies at Stanford University.

Bernard Ricardo is a Physics Consultant and a seasoned national trainer of Singapore's Physics Olympiad team (since 2005). He received his GraDip in Mathematics from the University of London (2013), M. Sc. in Applied Physics from the National University of Singapore (2010) and B. Eng. in Electrical and Electronic Engineering from the Nanyang Technological University (2008). A passionate educator who received the Outstanding Physics Teacher Award from the Institute of Physics Singapore for his contributions to the Singapore team, Bernard is currently researching physics education for high-performing students at the National Institute of Education for his Ph.D. As a former contestant himself, Bernard was awarded Silver in the 34th International Physics Olympaid (2003), as well as Gold and the 'Best in Experiment' Award in the 4th Asian Physics Olympiad in the same year.

Table of Contents

Dedication v

Preface vii

1 Minimalistic Arguments 1

1.1 Dimensional Analysis 1

1.2 Limiting Cases 5

1.3 Physical Principles 6

Problems 11

Solutions 15

2 Infinitesimal Elements 25

2.1 One-Dimensional Elements 25

2.2 Two-Dimensional Elements 31

2.3 Three-Dimensional Elements 38

Problems 41

Solutions 43

3 Kinematics 51

3.1 Vectors 51

3.2 Kinematic Quantities 60

3.3 Constant Acceleration 65

3.4 Polar Coordinates 72

3.5 Kinematics of a Rigid Body 79

3.6 Univariate Differential Equations 99

Problems 106

Solutions 113

4 Translational Dynamics 137

4.1 Linear Momentum 137

4.2 Newton's Three Laws 137

4.3 Net External Force on a System of Particles 139

4.4 Equations of Motion in Different Coordinates 148

4.5 Typical Forces in Mechanics 149

4.6 Types of Problems 153

4.7 Systems with Variable Amounts of Moving Mass 174

Problems 182

Solutions 192

5 Rotational Dynamics 219

5.1 Angular Momentum and Torque 219

5.2 Moment of Inertia 228

5.3 Applying τ = $$$ 239

Problems 247

Solutions 253

6 Energy and Momentum 275

6.1 Linear Momentum 275

6.2 Angular Momentum 276

6.3 Work and Energy 280

6.4 Deriving the Equation of Motion from Energy 297

6.5 Galilean Transformations and Center of Mass Frame 299

6.6 Collisions 303

6.7 Varying Amounts of Moving Mass 315

Problems 321

Solutions 329

7 Statics 363

7.1 Equilibrium 363

7.2 Connected Components 373

7.3 Friction 377

7.4 Strings under Distributed Force 385

7.5 Statically Indeterminate Situations 389

7.6 Virtual Work 393

Problems 406

Solutions 413

8 Orbital Mechanics 431

8.1 Newton's Law of Gravitation 431

8.2 Trajectory under Gravity 434

8.3 Conic Sections 437

8.4 Kepler's Three Laws 446

8.5 Two-Body Problem 448

8.6 Mass Distributions 451

Problems 456

Solutions 459

9 Fluids 469

9.1 Properties of a Fluid 469

9.2 Fluid Statics 471

9.3 Surface Tension 475

9.4 Fluid Dynamics 494

Problems 499

Solutions 505

10 Oscillations 521

10.1 Simple Harmonic Motion 521

10.2 Deriving Angular Frequency from Potential Energy 529

10.3 Damped Oscillations 532

10.4 Coupled Oscillations 542

Problems 552

Solutions 557

11 Non-Inertial Frames 577

11.1 Purely Accelerating Frame 577

11.2 Accelerating and Rotating Frame 586

11.3 Centrifugal Force 589

11.4 Coriolis Force 596

Problems 606

Solutions 610

12 Lagrangian Mechanics 623

12.1 Action and Hamilton's Principle 623

12.2 Calculus of Variations 624

12.3 Equations of Motion 627

12.4 Systems with Constraints 634

12.5 Conserved Quantities and Symmetry* 642

Problems 650

Solutions 656

13 Waves 681

13.1 Introduction 681

13.2 The Wave Equation 687

13.3 One-Dimensional Waves at, a Boundary 703

13.4 Other Effects 716

Problems 723

Solutions 728

14 Interference 745

14.1 The Principle of Superposition 745

14.2 Standing Waves 782

14.3 Beats 792

Problems 794

Solutions 798

Bibliography 811

Index 813