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.
Author(s): Jinhui Wang, Bernard Ricardo Widjaja
Publisher: World Scientific Publishing
Year: 2019
Language: English
Pages: 831
City: Singapore
Tags: Competitive Physics
Intro
Contents
Dedication
Preface
1 Minimalistic Arguments
1.1 Dimensional Analysis
1.1.1 Limitations
1.2 Limiting Cases
1.3 Physical Principles
1.3.1 Scaling Arguments
1.3.2 Symmetry
1.3.3 Equivalent Frames
1.3.4 Reversibility
Problems
Solutions
2 Infinitesimal Elements
2.1 One-Dimensional Elements
2.2 Two-Dimensional Elements
2.3 Three-Dimensional Elements
Problems
Solutions
3 Kinematics
3.1 Vectors
3.1.1 Vector Algebra
3.2 Kinematic Quantities
3.3 Constant Acceleration
3.3.1 Projectile Motion with Drag
3.4 Polar Coordinates
3.4.1 Uniform Circular Motion. 3.4.2 Circular Motion with Tangential Acceleration3.5 Kinematics of a Rigid Body
3.5.1 Angular Speed and Velocity
3.5.2 Rolling
3.5.3 Constrained Motion
3.6 Univariate Differential Equations
3.6.1 Separable Differential Equations
3.6.2 Making Equations Separable
Problems
Solutions
4 Translational Dynamics
4.1 Linear Momentum
4.2 Newton's Three Laws
4.2.1 The First Law and Inertial Frames
4.2.2 The Second Law
4.2.3 The Third Law
4.3 Net External Force on a System of Particles
4.3.1 Center of Mass
4.4 Equations of Motion in Different Coordinates. 4.4.1 Cartesian Coordinate System4.4.2 Polar Coordinate System
4.5 Typical Forces in Mechanics
4.5.1 Normal Force
4.5.2 Friction
4.5.3 Spring Force
4.5.4 Tension
4.5.5 Gravitational Force
4.6 Types of Problems
4.6.1 Free-Body Diagrams
4.6.2 No Constraints
4.6.3 Conservation of String
4.6.4 Remaining on an Inclined Plane
4.6.5 Polar Coordinates
4.6.6 Rigid Body Constraint
4.7 Systems with Variable Amounts of Moving Mass
Problems
Solutions
5 Rotational Dynamics
5.1 Angular Momentum and Torque
5.1.1 Rigid Body about Stationary Axis
5.1.2 Rigid Body about General Axis. 6.6 Collisions6.6.1 Elastic Collisions
6.6.2 Inelastic Collisions
6.6.3 Collisions with a Rigid Body
6.7 Varying Amounts of Moving Mass
Problems
Solutions
7 Statics
7.1 Equilibrium
7.2 Connected Components
7.3 Friction
7.4 Strings under Distributed Force
7.5 Statically Indeterminate Situations
7.6 Virtual Work
7.6.1 The Principle of Virtual Work
7.6.2 Potential Energy
7.6.3 Stability of Equilibrium
Problems
Solutions
8 Orbital Mechanics
8.1 Newton's Law of Gravitation
8.1.1 Conserved Quantities in Planetary Motion
8.2 Trajectory under Gravity
8.3 Conic Sections.
