Introductory Physics : Summaries, Examples, and Practice Problems

Physics describes how motion works in everyday life. Clothes washers and rolling pins are undergoing rotational motion. A flying bird uses forces. Tossing a set of keys involves equations that describe motion (kinematics). Two people bumping into each other while cooking in a kitchen involves linear momentum. This textbook covers topics related to units, kinematics, forces, energy, momentum, circular and rotational motion, Newton’s general equation for gravity, and simple harmonic motion (things that go back and forth). A math review is also included, with a focus on algebra and trigonometry. The goal of this textbook is to present a clear introduction to these topics, in small pieces, with examples that readers can relate to. Each topic comes with a short summary, a fully solved example, and practice problems. Full solutions are included for over 400 problems. This book is a very useful study guide for students in introductory physics courses, including high school and college students in an algebra-based introductory physics course and even students in an introductory calculus-level course. It can also be used as a standalone textbook in courses where derivations are not emphasized. This book is a very useful study guide for students in introductory physics courses, particularly high school and college students in an algebra-based introductory physics course, and even students in an introductory calculus-level course. Cover 1 Half Title 2 Title Page 4 Copyright Page 5 Table of Contents 6 Acknowledgements 18 Chapter 1 Units and Significant Figures 22 1.1 Introduction: Units Help Tell Us How Much 22 1.2 Unit Conversions 22 1.3 Power of 10 Conversions 26 1.4 Significant Figures 28 1.5 Chapter 1 Summary 29 Practice Problems 30 Section 1.2 30 Section 1.3 31 Section 1.4 33 Chapter 2 Motion in a Straight Line 36 2.1 Introduction: Describing Motion in the World 36 2.2 Motion Quantities 36 2.3 Displacement, Position, and Coordinate Systems 37 2.4 Average and Instantaneous Velocity 38 2.5 Average and Instantaneous Acceleration 39 2.6 Motion on a Line with Constant Acceleration 40 2.7 Free Fall 44 2.8 What If Acceleration Is Not Constant? 49 2.9 Chapter 2 Summary 49 Practice Problems 50 Section 2.4 50 Section 2.5 51 Section 2.6 53 Section 2.7 61 Chapter 3 Motion in Two and Three Dimensions 68 3.1 Introduction: Three Dimensions Are More Realistic Than One 68 3.2 Dimensions Behave Separately 68 3.3 Vector Math: Components and Magnitude and Direction 70 3.4 Doing Basic Math with Vectors: Adding Vectors, Multiplication by a Scalar 74 3.5 Two-Dimensional Constant Acceleration Problems 75 3.6 Projectile Motion 78 3.7 Motion in Three Dimensions 85 3.8 Chapter 3 Summary 85 Practice Problems 87 Section 3.3 87 Section 3.4 90 Section 3.5 93 Section 3.6 98 Chapter 4 Introduction to Forces 116 4.1 Introduction: Forces Cause Motion 116 4.2 Newton’s Second Law 116 4.3 Newton’s First and Third Laws 120 4.4 Chapter 4 Summary 121 Practice Problems 122 Section 4.2 122 Chapter 5 Specific Types of Forces, and Force Problems 128 5.1 Introduction: There are Different Types of Forces 128 5.2 Free Body Diagrams 128 5.3 What Forces Are on My Object? 130 5.4 Gravity (near Earth) 130 5.5 Kinetic Friction 133 5.6 Static Friction 136 5.7 Spring Forces 139 5.8 Common Force Problems, Type 1: Ramp Problems 141 5.9 Common Force Problems, Type 2: Problems with Elevators 146 5.10 Common Force Problems, Type 3: Problems With a Rope and Pulley 147 5.11 Common Force Problems, Type 4: Combining Force and Kinematics Problems 151 5.12 Chapter 5 Summary 154 Practice Problems: 156 Section 5.4 (Gravity near Earth) 156 Section 5.5 (Kinetic friction) 160 Section 5.6 (Static Friction) 165 Section 5.7 (Spring Forces) 169 Section 5.8 (Ramp Problems) 171 Section 5.9 (Problems with Elevators) 175 Section 5.10 (Problems with a Rope and a Pulley) 177 Section 5.11 (Combining Force and Kinematics Problems) 183 Chapter 6 Energy, and Work 190 6.1 Introduction: Motion Has Energy 190 6.2 Work by a Constant Force 190 6.3 Work Done by Springs, Where Force Changes with Position 192 6.4 Net Work 193 6.5 Kinetic Energy 195 6.6 The Work-Kinetic Energy Theorem 196 6.7 Potential Energy 197 6.8 Mechanical Energy 199 6.9 Conservation of Mechanical Energy 201 6.10 Power 206 6.11 Chapter 6 Summary 207 Practice Problems 209 Section 6.2 (Work Done by Constant Forces), Section 6.3 (Work Done by Springs) and Section 6.4 (Net Work) 209 Section 6.5 (Kinetic Energy) 213 Section 6.6 (Work-Kinetic Energy Theorem) 213 Section 6.7 (Potential Energy) 216 Section 6.8 (Mechanical Energy) 217 Section 6.9 (Conservation of Mechanical Energy) 219 Section 6.10 (Power) 225 Chapter 7 Linear Momentum and Collisions 228 7.1 Introduction: Collisions and Momentum 228 7.2 Linear Momentum 228 7.3 Linear Momentum Problems Without Collisions 229 7.4 Collisions and Linear Momentum 230 7.5 Collisions, Problem Type 1: Perfectly Inelastic Collisions with One Dimension 231 7.6 Collisions, Problem Type 2: Elastic Collisions with One Dimension 232 7.7 Perfectly Inelastic Collisions with Two Dimensions 236 7.8 How Much Force Happened? 240 7.9 Extra Topic: Center of Mass and Linear Momentum Conservation 241 7.10 Chapter 7 Summary 243 Practice Problems 245 Section 7.3 (Linear Momentum Problems without Collisions) 245 Section 7.5 (Perfectly Inelastic Collisions with One Dimension) 246 Section 7.6 (Elastic Collisions with One Dimension) 250 Section 7.7 (Perfectly Inelastic Collisions with Two Dimensions) 254 Section 7.8 (How Much Force Happened) 260 Section 7.9 (Center of Mass) 261 Chapter 8 Uniform Circular Motion (Moving in a Circle at Constant Speed) 264 8.1 Introduction: Sometimes Things Move in a Circle 264 8.2 Centripetal and Tangential Directions 264 8.3 Centripetal Acceleration 265 8.4 Net Force in the Centripetal Direction (Also Called Centripetal Force) 266 8.5 Chapter 8 Summary 269 Practice Problems 269 Section 8.3 (Centripetal Acceleration) 269 Section 8.4 (Net Force in the Centripetal Direction; Also Called Centripetal Force) 271 Chapter 9 Rotation Motion and Forces 276 9.1 Introduction: Rotational Motion is Like Linear Motion 276 9.2 Units for Angle: Radians and Revolutions 276 9.3 Rotation Equivalents of Position, Velocity, and Acceleration 277 9.4 Motion with Constant Angular Acceleration 278 9.5 Moment of Inertia (Rotation Equivalent of Mass) 281 9.6 Torque (Rotation Equivalent of Force) 283 9.7 Newton’s Second Law (Rotation Equivalent) 285 9.8 Relating Angular Displacement, Angular Velocity, and Angular Acceleration to Linear Displacement, Linear Velocity, and Linear Acceleration 288 9.9 Extra Topic: Torque is a Vector; Calculating Its Components 290 9.10 Chapter 9 Summary 292 Practice Problems 294 Section 9.2 (Units for Angle) 294 Section 9.4 (Motion with Constant Angular Acceleration) 297 Section 9.5 (Moment of Inertia) 299 Section 9.6 (Torque) 301 Section 9.7 (Newton’s Second Law) 303 Section 9.8 (Relating Angular Displacement, Angular Velocity, and Angular Acceleration to Linear Displacement, Linear Velocity, and Linear Acceleration) 305 Section 9.9 (Extra Topic: Torque Vector Components) 309 Chapter 10 Rotation: Energy, Momentum, and Rolling 312 10.1 Introduction: Energy and Momentum for Rotation 312 10.2 Rotation and Kinetic Energy 312 10.3 Rolling (Without Slipping) 314 10.4 Rotation Equivalent of Work 317 10.5 Rotation Equivalent of Power 318 10.6 Angular Momentum 319 10.7 Conservation of Angular Momentum 321 10.8 Chapter 10 Summary 325 Practice Problems 326 Section 10.2 (Rotation and Kinetic Energy) 326 Section 10.3 (Rolling, without Slipping) 328 Section 10.4 (Rotation and Work) 331 Section 10.5 (Rotation and Power) 332 Section 10.6 (Angular Momentum) 334 Section 10.7 (Conservation of Angular Momentum and Rotation Collisions) 335 Chapter 11 Newton’s More General Law of Gravity 340 11.1 Introduction: Gravity Is Different Away from The Ground 340 11.2 Newton’s Law of Gravity 340 11.3 Connecting m∙g with Newton’s Law of Gravity 342 11.4 Potential Energy from Gravity Using Newton’s Law of Gravity 343 11.5 Newton’s Law of Gravity with Conservation of Mechanical Energy 345 11.6 Newton’s Law of Gravity with Circular Motion 349 11.7 Chapter 11 Summary 351 Practice Problems 352 Section 11.2 (Newton’s Law of Gravity) 352 Section 11.4 (Potential Energy from Gravity Using Newton’s Law of Gravity) 353 Section 11.5 (Newton’s Law of Gravity with Conservation of Mechanical Energy) 355 Section 11.6 (Newton’s Law of Gravity with Circular Motion) 359 Chapter 12 Simple Harmonic Motion 362 12.1 Introduction: Motion Repeats 362 12.2 Repetitive Motion Quantities, and Simple Harmonic Motion 362 12.3 Position, Velocity and Acceleration 363 12.4 Simple Harmonic Motion and Objects on Springs 365 12.5 Simple Harmonic Motion: Simple Pendulum 368 12.6 Object Connected to a Spring and Mechanical Energy 369 12.7 Chapter 12 Summary 372 Practice Problems 373 Sections 12.2, 12.3, and 12.4 (Repetitive Motion Quantities; Position, Velocity, and Acceleration; Simple Harmonic Motion and Objects on Springs) 373 Section 12.5 (Simple Pendulum) 377 Section 12.6 (Object Connected to a Spring and Mechanical Energy) 378 Chapter 13 Math Review 382 13.1 Introduction: Physics Uses Math 382 13.2 Algebra Problems – Solving for a Variable 382 13.3 Exponential Numbers 383 13.4 Solving When Something is Squared, Part 1 384 13.5 Solving When Something is Squared, Part 2 386 13.6 Two Equations at Once 387 13.7 Trigonometry 390 13.8 Circle Geometry Review 392 13.9 Chapter 13 Summary 392 Practice Problems 393 Section 13.2 (Algebra Problems – Solving for a Variable) 393 Section 13.3 (Exponential Numbers) 395 Section 13.4 (Solving When Something is Squared, Part 1) 396 Section 13.5 (Solving When Something Is Squared, Part 2 – Quadratic Formula) 398 Section 13.6 (Two Equations at Once) 400 Section 13.7 (Trigonometry) 403 Index 406 Mechanics;,Calculus,101;,Introductory,Physics;,Physics,1;,Algebra,101;,Physics,101 Mechanics,Calculus 101,Introductory Physics,Physics 1,Algebra 101,Physics 101 Physics describes how motion works in everyday life. Clothes washers and rolling pins are undergoing rotational motion. A flying bird uses forces. Tossing a set of keys involves equations that describe motion (kinematics). Two people bumping into each other while cooking in a kitchen involves linear momentum.This textbook covers topics related to units, kinematics, forces, energy, momentum, circular and rotational motion, Newton's general equation for gravity, and simple harmonic motion (things that go back and forth). A math review is also included, with a focus on algebra and trigonometry. The goal of this textbook is to present a clear introduction to these topics, in small pieces, with examples that readers can relate to. Each topic comes with a short summary, a fully solved example, and practice problems. Full solutions are included for over 400 problems. This book is a very useful study guide for students in introductory physics courses, including high school and college students in an algebra-based introductory physics course and even students in an introductory calculus-level course. It can also be used as a standalone textbook in courses where derivations are not emphasized.Key features: Organizes a difficult subject into short and clearly written sections. Can be used alongside any introductory physics textbook. Presents clear examples for every problem type discussed in the textbook. Michael Antosh teaches physics at the University of Rhode Island, USA. He obtained a Ph.D. in physics from Brown University. "Physics describes how motion works in everyday life. Clothes washers and rolling pins are undergoing rotational motion. A flying bird uses forces. Tossing a set of keys involves equations that describe motion (kinematics). Two people bumping into each other while cooking in a kitchen involves linear momentum. The goal of this textbook is to have topics laid out clearly, in small pieces, with examples that readers can relate to. Each topic comes with a short summary, a fully solved example, and practice problems. Full solutions are included for many practice problems, including strategy and math in addition to the answer. This textbook covers topics related to units, kinematics, forces, energy, momentum, circular and rotational motion, Newton's general equation for gravity, and simple harmonic motion (things that go back and forth). A math review is also included, with a focus on algebra and trigonometry. This book is a very useful study guide for students in introductory physics courses, particularly high school and college students in an algebra-based introductory physics course, and even students in an introductory calculus-level course. It can also be used as a standalone textbook in courses where derivations are not emphasized"-- Provided by publisher