# Physics: Modeling Nature

## Preface for Teachers |

1. Student Audience and Preparedness |

2. Our Emphasis on Mastery, Integration, and Kingdom |

3. Recommendations for Teaching With This Text |

4. Laboratory Work and Lab Reports |

## Preface for Students |

1. Why Physics is Difficult |

2. Strategies for Making Physics Manageable |

3. Studying for Mastery |

## Chapter 1: Mathematical Tools |

1.1 Science and Measurements |

1.1.1 No Measurements, No Science |

1.1.2 Matter, Volume, and Mass |

1.1.3 The SI Unit System |

1.1.4 MKS Units |

1.2 Uncertainty in Measurements |

1.2.1 Error and Uncertainty |

1.2.2 Distinguishing Between Accuracy and Precision |

1.2.3 Significant Digits |

1.2.4 Random and Systematic Error |

1.2.5 Standard Deviation |

1.2.6 Calculating Percent Difference |

1.3 Modeling Nature |

1.3.1 Science as Mental Model Building |

1.3.2 Truth and Facts |

1.3.3 Facts, Theories, Hypotheses, and Experiments |

1.4 Vector Methods |

1.4.1 Scalars and Vectors |

1.4.2 How to Learn Vector Addition |

1.4.3 Vector Addition—The Graphical Method |

1.4.4 Additional details About the Direction of a Vector |

1.4.5 Vector Addition—the Trigonometric Method |

1.4.6 Multiplying a Vector by a Scalar |

1.4.7 Vector Multiplication |

Connections in Physics: Vector Fields |

## Chapter 2: Uniform Motion |

2.1 How Physics Is Organized |

2.2 Rectilinear Motion |

2.2.1 The Terminology of Motion |

2.2.2 Coordinate Systems |

2.2.3 Velocity and Acceleration |

Connections to Calculus: Derivatives |

2.2.4 The Equations of Kinematics |

Connections in Physics: Correct Problem-Solving Method |

Connections in Physics: Free Fall |

2.2.5 Symmetry in Kinematics Problems |

2.3 Projectile Motion |

2.3.1 Modeling Assumptions |

2.3.2 Vector Analysis and Calculation Method |

Connections in Physics: Fictitious Forces |

2.4 Relative Velocity |

## Chapter 3: Forces, Fields, and Newton’s Laws of Motion |

3.1 Forces and Fields: The Big Picture |

3.1.1 The Four Fundamental Interactions |

3.1.2 Fields |

3.2 Historical Views on Motion |

3.3 Newton’s Laws of Motion |

3.3.1 The Laws of Motion |

Connections in Physics: The Laws of Motion |

Connections in Physics: Motion at Relativistic Speeds |

3.3.2 Shells, Subshells, and Orbitals |

3.3.2 Mass and Weight |

3.3.3 General Principles for Modeling Complex Systems |

3.3.4 Free Body Diagrams and Force Components |

3.4 Friction |

3.4.1 The Source of Friction |

3.4.2 Modeling Friction |

3.4.3 Solving Dynamics Problems Involving Friction |

Connections to Calculus: The Second Law and Impulse |

## Chapter 4: Static Equilibrium and Torque |

4.1 Static Equilibrium |

4.1.1 Static Equilibrium |

4.1.2 Tow Conditions for Static Equilibrium |

4.2 Modeling Torque |

4.2.1 Torque as a Vector Quantity |

4.2.2 Visualizing and Calculating Torque |

4.3 Modeling Static Equilibrium |

4.3.1 Free Body Diagrams for Static Equilibrium |

4.3.3 Solving Problems in Static Equilibrium |

## Chapter 5: Energy |

5.1 Defining Energy |

5.1.1 Energy, Matter, and the Beginning of the Universe |

5.1.2 The Quantization of Energy |

5.2 Forms of Energy |

5.2.1 Units for Energy and Power |

5.2.2 Forms of Energy |

5.2.3 The Mechanical Equivalent of Heats |

5.2.4 Energy Loss in Mechanical Systems |

5.3 The Conservation of Mass-Energy |

5.3.1 The Energy Fundamentals |

5.3.2 The Law of Conservation of Energy |

5.3.3 Conservative Fields |

5.3.4 The Work-Energy Theorem |

Connections to Calculus: Energy Rates of Change |

5.3.5 Einstein and Mass-Energy Equivalence |

Connections in Physics: The Photoelectric Effect |

## Chapter 6: Momentum |

6.1 Momentum and Impulse |

6.1.1 Momentum |

6.1.2 Impulse and Newton’s Second Law |

6.2 Conservation of Momentum |

6.2.1 Conservation Laws in Physics |

6.2.2 The Law of Conservation of Momentum and Newton’s Laws of Motion |

6.3 Elastic and Inelastic Collisions |

6.3.1 Collisions and Energy Loss in Systems |

6.3.2 Combining Momentum and Energy |

Connections in Physics: Discovery of the Neutron |

Connections in Physics: Compton Scattering |

## Chapter 7: Rotating Systems |

7.1 Angular Quantities |

7.1.1 Radian Measure |

7.1.2 Angular Displacement, Angular Velocity, and Angular Acceleration |

7.1.3 Tangential Quantities |

7.2 Torque and Angular Acceleration |

7.2.1 Moment of Inertia |

7.2.2 Newton’s Second Law for Rotation |

7.3 Centripetal Force |

7.3.1 Motion in a Circle |

7.3.2 Calculations With Centripetal Force |

Connections to Calculus: Moment of Inertia |

7.4 Newton’s Law of Universal Gravitation |

Connections in Physics: Henry Cavendish and G |

## Chapter 8: Energy and Momentum in Rotating Systems |

8.1 Rotational Kinetic Energy |

8.1.1 More Translational-Rotational Parallels |

8.1.2 Rotational Kinetics Energy as an Energy Storage Medium |

8.1.3 Conservation of energy with Rotating Systems |

8.2 Combining Rotational and Translational Kinetic Energy |

8.3 Angular Momentum |

Connections in Physics: Quantization of Angular Momentum |

Connections in Physics: Precession |

## Chapter 9: Pressure and Buoyancy |

9.1 Pressure |

9.1.1 Pressure as Force Applied to an Area |

9.1.2 Pressure In a Fluid Medium |

9.1.3 Air Pressure |

9.1.4 Absolute Pressure and Gauge Pressure |

9.1.5 Pascal’s Law |

9.1.6 Bernoulli’s Principle |

9.2 Buoyancy and Archimedes’ Principle |

9.2.1 Buoyancy |

9.2.2 Archimedes’ Principle |

9.2.3 Flotation |

## Chapter 10: Gases, Kinetic Theory, and Heat |

10.1 Moles and Molar Masses |

10.1.1 Moles and the Avogadro Constant |

10.1.2 Molar Mass |

10.1.3 Gram Masses of Atoms and Molecules |

10.2 The Gas Laws |

10.2.1 Boyle’s Law |

10.2.2 Charles’ Law |

10.2.3 Avogadro’s Law |

10.2.4 The Ideal Gas Law |

10.3 The Kinetic-Molecular Theory of Gases |

10.3.1 Velocity Distribution of Gases |

Connections in Physics: Fundamental Constants in Nature |

10.3.2 The Kinetic-Molecular Theory of Gases |

10.3.3 Temperature and Molecular Energy |

10.4 Thermal Properties of Matter |

10.4.1 States of Matter |

10.4.2 Heat Transfer |

10.4.3 Phase Transitions and Phase Diagrams |

10.4.4 Thermal Properties of Matter |

110.4.5 Calorimetry |

10.4.6 Evaporation |

10.4.7 Vapor Pressure |

## Chapter 11: Thermodynamics |

11.1 The First Law of Thermodynamics |

11.1.1 The Ideal Gas Systems Model |

11.1.2 The First Law of Thermodynamics |

11.1.3 State Variables and Thermodynamic States |

11.1.4 Work and Thermodynamic States |

Connections to Calculus: Work as Area Under the PV Curve |

11.2 Thermodynamic Processes |

11.2.1 Thermodynamic Processes |

11.2.2 Qualitative First Law Applications |

11.3 The Second Law of Thermodynamics |

11.3.1 Disorder and Directionality |

11.3.2 Microstates, Entropy, and Reversibility |

11.3.3 Heat Engines and Maximum Theoretical Efficiency |

11.3.4 Refrigeration |

## Chapter 12: Simple Harmonic Motion, Waves, and Sound |

12.1 Simple Harmonic Motion |

12.1.1 Modeling Oscillation |

12.1.2 Simple Harmonic Motion |

Connections to Calculus: Simple Harmonic Motion |

12.1.3 Energy In Simple Harmonic Motion |

12.1.4 The Simple Pendulum and the Small-Angle Approximation |

12.2 Wave Modeling and Interactions |

12.2.1 Modeling Waves |

12.2.2 Reflection, Refraction, and Dispersion |

12.2.3 Standing Waves and Resonance |

12.2.4 Diffraction and Interference |

12.3 Sound |

12.3.1 Sound Intensity and the Inverse Square Law |

12.3.3 Frequency Response |

12.3.4 The Doppler Effect |

12.3.5 The Speed of Sound |

## Chapter 13: Electrostatics and Electric Circuits |

13.1 Charge and Static Electricity |

13.1.1 Charge |

13.1.2 Static Electricity |

13.2 Conservation of Charge and Coulomb’s Law |

13.2.1 Conservation of Charge |

Connections in Physics: Feynman Diagrams |

13.2.2 Coulomb’s Law |

13.3 Electric Fields and Charge Symmetries |

13.3.1 Spherical Field Symmetry |

13.3.2 Cylindrical Field Symmetry |

13.3.3 Planar Field Symmetry |

13.4 Energy in Electric Fields |

13.4.1 Work, Potential, and Voltage |

Connections to Calculus: Absolute Potential |

13.4.2 Potential and Equipotentials |

13.4.3 Capacitors |

13.4.4 Energy Storage in Capacitors |

13.5 DC Circuits |

13.5.1 Electric Circuits |

13.5.2 Resistance in Conductors |

13.5.3 Resistor Combinations and Equivalent Resistance |

13.5.4 Kirchhoff’s Analysis |

13.5.6 DC Circuit Analysis |

## Chapter 14: Electrostatics and Electric Circuits |

14.1 Forces Caused by Magnetic Fields |

14.1.1 Field and Flux |

14.1.2 Magnetic Forces on Wires and Ampere’s Law |

Connections to Calculus: Magnetic Flux and the B-Field |

14.1.3 Forces on Moving Charges |

Connections in Physics: Bubble Chambers |

14.1.4 Torque on a Current Loop and the DC Motor |

14.2 Faraday’s Law, Generators, and Transformers/p> |

14.2.1 Faraday’s Law of Magnetic Induction |

14.2.2 Generators |

Connections to Calculus: Faraday’s Law of Magnetic Induction |

14.2.3 Transformers |

14.3 Inductance and Time-Varying Circuits |

14.3.1 Inductance |

14.3.2 Steady-State AC Circuits |

14.3.3 RC Circuits |

14.3.4 RL Circuits |

14.3.5 RLC Circuits |

14.4 Lenz’s Law |

14.4.1 Lenz’s Law |

14.4.2 Back-EMF |

## Chapter 15: Geometric Optics: A Brief Introduction |

15.1 Ray Optics |

15.1.1 Light As Rays |

15.1.2 Human Image Perception |

15.1.3 Flat Mirrors and Ray Diagrams |

15.1.3 Real and Virtual Images |

15.2 Optics and Curves Mirrors |

15.2.1 Concave and Convex Optics |

15.2.2 Approximations in Geometric Optics |

15.2.3 Spherical Mirrors |

15.2.4 The Mirror Equation |

15.3 Lenses |

15.3.1 Light Through a Lens |

15.3.2 Single-Lens Applications |

15.3.3 The Lens Equation |

15.3.4 Multiple-Lens Systems |

Connections in Physics: Rainbows |

15.3.5 Imaging with the Eye |

## Chapter 16: Nuclear Physics: A Brief Introduction |

16.1 Nuclides and Isotopes |

16.1.1 Isotopes |

16.1.2 Atomic Mass Unit |

16.1.3 Nuclear Size and Density |

16.1.4 Binding Energy and Mass Defect |

16.1.5 Nuclear Equations |

16.2 Radioactivity |

16.2.1 Nuclear Stability |

16.2.2 Nuclear Decay and Decay Series |

16.2.3 Nuclear Half-life |

16.2.4 Radiometric Dating |

16.3 Fission and Fusion Reactions |

16.3.1 Nuclear Fission |

Connections in Physics: The Beginning of Nuclear Power |

16.3.2 Nuclear Fusion |

## Glossary |

## Answers to Selected Exercises |

## Appendix A: Reference Data |

## Appendix B: Unit Conversions Tutorial |

B.1 Basic Principles of Unit Conversion Factors |

B.2 Tips for Converting Units of Measure |

B.3 Converting Temperature Units |

## References and Citations |

## Image Credits |

## Index |