Wang J., Widjaja B.R. Competitive Physics. Mechanics and Waves

Singapore: World Scientific Publishing Co Pte Ltd, 2019. — 831 p.Competitive Physics grew out of a Physics Olympiad course taught by Wang Jinhui at Hwa Chong Institution — intended to prepare students for the annual Physics Olympiads and to imbue deeper knowledge in physics beyond the typical high school syllabus. It quickly became a collaboration with his former trainer in the Singapore Physics Olympiad national training team, Bernard Ricardo.
Competitive Physics is meant to be a theory-cum-problem book. The first half of each chapter explores physical theories with illustrations of how they can be creatively applied to problems. The latter half of each chapter revolves around puzzles that we hope will intrigue readers, as we believe that problem-solving is a crucial process in grasping the subtleties of the contents. Therefore, we have included a multitude of problems which are ranked by increasing difficulty from one to four stars. Some problems are original; some are taken from the various Physics Olympiads while the others are instructive classics that have withstood the test of time.
This book is the first part of a two-volume series which will discuss general problem-solving methods and delve into mechanics and waves — setting a firm foundation for other topics that will be presented in the second volume. We envision problem-solving to be a fun process — from the initial excite ment of approaching an unfamiliar problem, to the joy of pitting all of one’s knowledge against it and finally, the satisfaction earned from solving it after numerous failed attempts. In light of this, our goal is to spread the passion of problem-solving — an infectious hobby. It is difficult to quantify the factors that make a problem interesting or elegant but the following have been our guiding principles in writing Competitive Physics: 1. Physical Significance. Quintessentially, physics is about modeling the world around us. Therefore, it is gratifying to be able to analyze everyday phenomena and to leverage on this knowledge to improve such processes.For example, a problem in Chapter 3 asks: how should we run towards a shelter to minimize how wet we get in the rain? Meanwhile, Chapter 6 elucidates the reason behind why two colliding billiard balls leave at right angles relative to each other.2. Intuition. There are many overarching themes in physics — symmetry, the equivalence of different observational frames of reference, reversibility of processes and many more. Not only are these useful as sleights-of-hand in problem-solving, they reveal crucial aspects of the common structure of physical theories. Developing a strong hunch for them — a gut feeling that constantly bugs you to search for ways to exploit them — may prove to be beneficial in one’s future physics journey. As such, we have devoted the entire first chapter, Minimalistic Arguments, to honing this physical intuition.3. Insight. Sometimes, a seemingly complex problem can be vastly simplified by making an astute observation — whether mathematical or physical. Perhaps, it is to express the solution in terms of vectors or perhaps it is to observe that two different scenarios “feel” the same to a certain entity and thus conclude that the entity will respond in the same manner in both cases. Maybe it is to draw enlightening analogies between two problems that appear to be completely disparate on the surface. Ultimately, such problems which require perceptive thought do not have cookie-cutter approaches and require the reader to invent an appropriate technique on the spot. They hence implore the reader to really think and are very rewarding to solve.4. Fundamentals. The objectives above would not be possible without first mastering the fundamentals of a theory — the situations that it can be validly applied to, its assumptions and its ramifications. As such, we have also included many classic problems to reinforce understanding of the basics. To this end, we are extremely grateful to Dr. David J. Morin for allowing us to use some problems from his exemplary textbook: Introduction to Classical Mechanics.
In summary, our guiding principles are “PIIF”, as in the onomatopoeia “pffft” when, having read this book, you scoff at a future problem after swiftly spotting its trick. Jokes aside, it is paramount for the reader to first attempt the problems before peeking at the solutions. Even when perusing the solution to a problem, the reader should inspect it line by line until he or she reaches an inspiration that sets him or her back on track in attempt ing the problem again. Only by experiencing the process of problem-solving yourself can you internalize the clues in a problem that hint at a certain approach, understand why certain approaches are incorrect or desirable and ultimately, improve. There is no short-cut to developing an intuition for problem-solving besides trudging through an arduous but fulfilling journey of enigmas.
Despite our best efforts; the probability of this book being error-free is, unfortunately, akin to the odds of observing a car plate that reads “PHY51C.” Therefore, if the reader does spot any mistakes or dubious points in our discussions, we would appreciate if they are highlighted to us via the email competitivephysicsguide@gmail.com.Minimalistic Arguments
Dimensional Analysis
Limitations
Limiting Cases
Physical Principles
Scaling Arguments
Symmetry
Equivalent Frames
ReversibilitySolutions
Infinitesimal Elements
One-Dimensional Elements
Two-Dimensional Elements
Three-Dimensional ElementsSolutions
Kinematics
Vectors
Vector Algebra
Kinematic Quantities
Constant Acceleration
Projectile Motion with Drag
Polar Coordinates
Uniform Circular Motion
Circular Motion with Tangential Acceleration
Kinematics of a Rigid Body
Angular Speed and Velocity
Rolling
Constrained Motion
Univariate Differential Equations
Separable Differential Equations
Making Equations SeparableSolutions
Translational Dynamics
Linear Momentum
Newton's Three Laws
The First Law and Inertial Frames
The Second Law
The Third Law
Net External Force on a System of Particles
Center of Mass
Equations of Motion in Different Coordinates
Cartesian Coordinate System
Polar Coordinate System
Typical Forces in Mechanics
Normal Force
Friction
Spring Force
Tension
Gravitational Force
Types of Problems
Free-Body Diagrams
No Constraints
Conservation of String
Remaining on an Inclined Plane
Polar Coordinates
Rigid Body Constraint
Systems with Variable Amounts of Moving MassSolutions
Rotational Dynamics
Angular Momentum and Torque
Rigid Body about Stationary Axis
Rigid Body about General Axis
Collisions
Elastic Collisions
Inelastic Collisions
Collisions with a Rigid Body
Varying Amounts of Moving MassSolutions
Statics
Equilibrium
Connected Components
Friction
Strings under Distributed Force
Statically Indeterminate Situations
Virtual Work
The Principle of Virtual Work
Potential Energy
Stability of EquilibriumSolutions
Orbital Mechanics
Newton's Law of Gravitation
Conserved Quantities in Planetary Motion
Trajectory under Gravity
Conic Sections