Introductory Physics with Algebra as a Second Language: Mastering Problem-Solving

CHAPTER 1 THE BOTTOM LINE FOR SOLVING PHYSICS PROBLEMS 1

CHAPTER 2 LINEAR VELOCITY AND ACCELERATION 3

2.1 Linear Motion Equations 3

2.2 The Idea Behind How to Use Motion Equations 4

2.3 Constant/Average Speed or Velocity Problems 5

2.4 Constant/Average Speed or Velocity—Two Intervals, Same Direction 6

2.5 Constant/Average Speed or Velocity—Two Intervals, Direction Change 10

2.6 Constant/Average Speed or Velocity—Two Objects 13

2.7 How to Set Up Constant/Average Speed or Velocity Problems 15

2.8 Constant/Average Acceleration Problems 16

2.9 Constant/Average Acceleration—One Interval 17

2.10 Constant/Average Acceleration—Multiple Intervals 20

2.11 Constant/Average Acceleration—“Free-Fall” 22

2.12 Constant/Average Acceleration—Two Objects 27

2.13 How to Set Up Constant/Average Acceleration Problems 29

CHAPTER 3 VECTORS 31

3.1 Magnitude and Direction, and x- and y-Components 31

3.2 Vectors along One Axis 37

3.3 Vector Addition 38

3.4 How to Set Up Vector Problems 42

3.5 “Back Where You Started”—When Vectors Add to Zero 42

3.6 Subtracting Vectors, OR, When One of the Added Vectors Is Unknown 45

CHAPTER 4 PROJECTILE MOTION 49

4.1 Projectile Motion: Combining Three Basic Concepts 49

4.2 When Initial Velocity Is Horizontal 50

4.3 How to Set Up Projectile Motion Problems 55

4.4 When Final Velocity Is Horizontal (at Maximum Height) 56

4.5 When Initial and Final Heights Are Equal 61

4.6 When Both Initial and Final Velocities Are at Angles 62

CHAPTER 5 FORCE AND NEWTON’S LAWS OF MOTION 69

5.1 How to Draw a Free-Body Diagram (FBD) 70

5.2 Forces in 1D 72

5.3 How to Set Up Force Problems 75

5.4 Motion Intervals in Force Problems 76

5.5 Objects Connected by Strings, Ropes, and so on 80

5.6 Forces in 2D 83

5.7 Sliding—Kinetic Friction 86

5.8 “Just about to Slip”—Maximum Static Friction 90

5.9 Inclines or Ramps 93

5.10 Objects Pushing on Each Other 97

CHAPTER 6 CIRCULAR MOTION AND CENTRIPETAL FORCE 100

6.1 Tangential Speed and Centripetal Acceleration 100

6.2 Comparing Circular Motion at Two Different Radii 101

6.3 Comparing Circular Motion at Two Different Speeds 102

6.4 How to Set Up Circular Motion Comparison Problems 103

6.5 How to Think about Centripetal Force Problems 104

6.6 Circular Motion with a Horizontal String 105

6.7 How to Set Up Centripetal Force Problems 107

6.8 Circular Motion with a String at an Angle 107

6.9 Circular Motion on an Unbanked Road with Friction 111

6.10 Circular Motion on a Banked Road without Friction 113

6.11 Vertical Circular Motion—Lowest Point 117

6.12 Vertical Circular Motion—Highest Point, Upside-Down 118

6.13 Vertical Circular Motion—Highest Point, Right-Side-Up 121

CHAPTER 7 GRAVITATION AND ORBITS 123

7.1 Weight and g at a Planet’s Surface 123

7.2 Adding Gravitational Force Vectors 125

7.3 Circular Orbit Problems 129

7.4 Circular Orbit Equations 133

7.5 Comparing Orbits at Two Different Radii 134

CHAPTER 8 WORK AND ENERGY 136

8.1 Work Done by a Constant/Average Force 136

8.2 Work Problems—with Two or More Forces 137

8.3 Work Problems—when Forces Are Not Given 140

8.4 How to Set Up Work Problems 147

8.5 The Work-Energy Theorem—KE Only 148

8.6 How to Set Up Work-Energy Problems—KE only 153

8.7 Potential Energy, Conservative and Nonconservative Forces 154

8.8 The Work-Energy Theorem—KE and PE 155

8.9 How to Set Up Work-Energy Problems—KE and PE 161

8.10 Conservation of Energy—When W_nc = 0 162

8.11 How to Set Up Conservation of Energy Problems 166

8.12 How to Split Up a Difficult Problem 166

CHAPTER 9 IMPULSE, MOMENTUM, AND CENTER OF MASS 170

9.1 The Impulse-Momentum Theorem 170

9.2 1D Impulse and Momentum 172

9.3 2D Impulse and Momentum 174

9.4 How to Set Up Impulse and Momentum Problems 178

9.5 Conservation of Momentum 179

9.6 1D Collisions—Objects Coming Together 181

9.7 1D Explosions—Objects Pushing Apart 183

9.8 1D Elastic Collisions 185

9.9 2D Collisions 189

9.10 How to Set Up Conservation of Momentum Problems 195

9.11 Center of Mass 196

9.12 1D Center of Mass 196

9.13 2D Center of Mass 198

9.14 How to Set Up Center of Mass Problems 201

CHAPTER 10 ANGULAR VELOCITY AND ACCELERATION 202

10.1 How to Relate Angular and Tangential or Linear Quantities 202

10.2 Two-Object, Two-Circle Problems 204

10.3 How to Set up two-Object, Two-Circle Problems 208

10.4 Constant/Average Angular Velocity 209

10.5 How to Set Up Constant/Average Angular Velocity Problems 212

10.6 Constant/Average Angular Acceleration 212

10.7 Constant/Average Angular Acceleration—Multiple Intervals 215

10.8 Constant/Average Angular Acceleration—with Tangential or Linear Acceleration 218

10.9 Constant/Average Angular Acceleration—with Centripetal Acceleration 223

10.10 Summary of Angular Velocity and Acceleration Equations 226

10.11 How to Set Up Constant/Average Angular Acceleration Problems 227

CHAPTER 11 TORQUE AND EQUILIBRIUM 228

11.1 Torque 228

11.2 How to Set Up Torque Problems 231

11.3 Equilibrium for “Rigid” Bodies 232

11.4 Equilibrium—With Only 90° Angles 232

11.5 Equilibrium—With Non-90° Angles 245

11.6 How to Set Up Equilibrium Problems 251

CHAPTER 12 MORE ANGULAR MOTION 252

12.1 Moment of Inertia 252

12.2 Torque and Angular Acceleration Problems 254

12.3 How to Set Up Torque and Angular Acceleration Problems 259

12.4 Rotational Kinetic Energy and Conservation of Energy 259

12.5 Conservation of Angular Momentum 264

12.6 Conservation of Angular Momentum Problems—First Type 265

12.7 Conservation of Angular Momentum Problems—Second Type 268

12.8 How to Set Up Conservation of Angular Momentum Problems 271

INDEX 273