Phys 111: Physics, Symmetry, and Conservation

by Mitch Powers

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This text is an introductory calculus-based course focusing on classical mechanics, emphasizing the fundamental link between symmetries and conservation laws (Noether's Theorem). It covers conservation of energy, linear momentum, and angular momentum, alongside forces, kinematics, and rotational motion.

Description from LibreTexts.

Publisher
Gettysburg College
Subjects
Physics
Licence
CC BY-SA, as LibreTexts states it
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Conservation and Symmetry
  7. 1.1: Abstraction and Modeling
  8. 1.1.1: About this Text
  9. 1.1.2: Modeling in Physics
  10. 1.1.3: Units and Standards
  11. 1.1.4: Unit Conversion
  12. 1.1.5: Dimensional Analysis
  13. 1.1.6: Estimates and Fermi Calculations
  14. 1.1.E: Exercises
  15. 1.2: Particles and Interactions
  16. 1.2.1: Inertia
  17. 1.2.2: Momentum
  18. 1.2.3: Force and Impulse
  19. 1.2.4: Examples
  20. 1.2.5: Particles and Interactions (Exercises)
  21. 1.3: Vector Analysis
  22. 1.3.1: Position Vectors and Components
  23. 1.3.2: Vector Algebra in 1 Dimension
  24. 1.3.3: Vector Algebra in 2 Dimensions- Graphical
  25. 1.3.4: Vector Algebra in Multiple Dimensions- Calculations
  26. 1.3.E: Vectors (Exercises)
  27. 1.4: Systems and The Center of Mass
  28. 1.4.1: The Law of Inertia
  29. 1.4.2: Extended Systems and Center of Mass
  30. 1.4.3: Reference Frame Changes and Relative Motion
  31. 1.4.4: Examples
  32. 1.4.E: Systems and the Center of Mass Exercises
  33. 1.5: Conservation of Momentum
  34. 1.5.1: Conservation of Linear Momentum
  35. 1.5.2: The Problem Solving Framework
  36. 1.5.3: Examples
  37. 1.5.4: More Examples
  38. 1.5.E: Conservation of Momentum (Exercises)
  39. 1.6: Conservation of Energy- Kinetic and Gravitational
  40. 1.6.1: Kinetic Energy
  41. 1.6.2: Conservative Interactions
  42. 1.6.3: The Inverse-Square Law
  43. 1.6.4: Conservation of Energy
  44. 1.6.5: Dissipation of Energy and Thermal Energy
  45. 1.6.6: Relative Velocity and the Coefficient of Restitution
  46. 1.6.7: Examples
  47. 1.6.E: Potential Energy and Conservation of Energy (Exercises)
  48. 1.7: Potential Energy- Graphs and Springs
  49. 1.7.1: Potential Energy of a System
  50. 1.7.2: Potential Energy Functions
  51. 1.7.3: Potential Energy Graphs
  52. 1.7.4: Examples
  53. 1.7.E: Potential Energy and Conservation of Energy (Exercises)
  54. 1.8: Work
  55. 1.8.1: Introduction- Work and Impulse
  56. 1.8.2: Work on a Single Particle
  57. 1.8.3: The "Center of Mass Work"
  58. 1.8.4: Examples
  59. 1.8.E: Work and Kinetic Energy (Exercises)
  60. 1.9: Conservation of Angular Momentum I
  61. 1.9.1: Angular Momentum
  62. 1.9.2: Angular Momentum and Torque
  63. 1.9.3: Examples
  64. 1.9.E: Angular Momentum (Exercises)
  65. 1.10: Rotational Energy
  66. 1.10.1: Rotational Kinetic Energy, and Moment of Inertia
  67. 1.10.2: Rolling Motion
  68. 1.10.3: Examples
  69. 1.10.E: Fixed-Axis Rotation Introduction (Exercises)
  70. 1.11: Conservation of Angular Momentum II
  71. 1.11.1: The Angular Momentum of a Point and The Cross Product
  72. 1.11.2: Torque
  73. 1.11.3: Examples
  74. 1.11.4: Extended Mass Distributions
  75. 1.11.E: Angular Momentum (Exercises)
  76. 1.12: Thermal Energy
  77. 1.12.1: "Lost" Energy and the Discovery of Conservation of Energy
  78. 1.12.2: Kinetic Theory of Heat
  79. 1.12.3: Thermometers and Temperature Scales
  80. 1.12.4: Heat Transfer, Specific Heat, and Calorimetry
  81. 1.12.5: Microscopic Origins of Thermal Expansion
  82. 1.12.6: Thermal Energy (Exercises)
  83. 1.13: Other Forms of Energy
  84. 1.13.1: Phase Changes
  85. 1.13.2: Mechanisms of Heat Transfer
  86. 1.13.3: Temperature and Heat (Exercises)
  87. 1.14: Collisions in Summary
  88. 1.14.1: Types of Collisions
  89. 1.14.2: Examples
  90. 1.14.E: Collisions (Exercises)
  91. 2: Forces and Kinematics
  92. 2.1: N1) Newton's Laws
  93. 2.1.1: Forces and Newton's Three Laws
  94. 2.1.2: Details on Newton's First Law
  95. 2.1.3: Details on Newton's Second Law
  96. 2.1.4: Details on Newton’s Third Law
  97. 2.1.5: Free-Body Diagrams
  98. 2.1.6: Motion on a Circle (Or Part of a Circle)
  99. 2.1.7: Newton's Laws of Motion (Exercises)
  100. 2.2: N2) 1 Dimensional Kinematics
  101. 2.2.1: Vector Calculus
  102. 2.2.2: Position, Displacement, Velocity
  103. 2.2.3: Acceleration
  104. 2.2.4: Free Fall
  105. 2.2.5: The Connection Between Displacement, Velocity, and Acceleration
  106. 2.2.6: Examples
  107. 2.2.E: Motion Along a Straight Line (Exercises)
  108. 2.3: N3) 2 Dimensional Kinematics and Projectile Motion
  109. 2.3.1: Dealing with Forces in Two Dimensions
  110. 2.3.2: Motion in Two Dimensions and Projectile Motion
  111. 2.3.3: Inclined Planes
  112. 2.3.4: Examples
  113. 2.3.E: Projectile Motion (Exercises)
  114. 2.4: N4) Motion from Forces
  115. 2.4.1: Solving Problems with Newton's Laws (Part 1)
  116. 2.4.2: Solving Problems with Newton's Laws (Part 2)
  117. 2.4.3: Examples
  118. 2.4.E: Newton's Laws of Motion (Exercises)
  119. 2.5: N5) Friction
  120. 2.5.1: Friction (Part 1)
  121. 2.5.2: Friction (Part 2)
  122. 2.5.3: More Examples
  123. 2.5.E: Friction (Exercises)
  124. 2.6: N6) Statics and Springs
  125. 2.6.1: Conditions for Static Equilibrium
  126. 2.6.2: Springs
  127. 2.6.3: Examples
  128. 2.6.E: Static Equilibrium and Elasticity (Exercises)
  129. 2.7: N7) Circular Motion
  130. 2.7.1: Banking
  131. 2.7.2: Examples
  132. 2.7.E: Applications of Newton's Laws (Exercises)
  133. 2.8: N8) Forces, Energy, and Work
  134. 2.8.1: Forces and Potential Energy
  135. 2.8.2: Work Done on a System By All the External Forces
  136. 2.8.3: Forces Not Derived From a Potential Energy
  137. 2.8.4: Examples
  138. 2.8.E: Work and Kinetic Energy (Exercises)
  139. 2.9: N9) Rotational Motion
  140. 2.9.1: Rotational Variables
  141. 2.9.2: Rotation with Constant Angular Acceleration
  142. 2.9.3: Relating Angular and Translational Quantities
  143. 2.9.4: Newton’s Second Law for Rotation
  144. 2.9.5: Examples
  145. 2.9.E: Fixed-Axis Rotation Introduction (Exercises)
  146. 2.10: N10) Simple Harmonic Motion
  147. 2.10.1: Introduction- The Physics of Oscillations
  148. 2.10.2: Simple Harmonic Motion
  149. 2.10.3: Pendulums
  150. 2.10.4: In Summary
  151. 2.10.5: Examples
  152. 2.10.6: Advanced Topics
  153. 2.10.7: Simple Harmonic Motion- Exercises
  154. 3: Relativity (in progress)
  155. 3.1: Einstein’s Postulates
  156. 3.2: The Relativity Principle
  157. 3.3: The Nature of Time
  158. 3.4: Measuring Lengths and Coincidences
  159. 3.5: Waves and Aether
  160. 3.6: (Optional - Includes more math) Derivation of the Lorentz Transformations
  161. 3.7: Relativistic Velocity Transformation
  162. 3.8: Doppler Effect for Light
  163. 3.9: An Invariant Measure of Length
  164. 3.10: Ultrarelativistic particles
  165. 3.11: E=mc²
  166. 3.12: Relativistic Momentum
  167. 3.13: Relativistic Energy
  168. 3.14: Time Dialation and Space Contraction Revisited
  169. 3.15: (Graphical Derivation using World lines) Addition of Velocities
  170. 3.16: Twin Paradox
  171. 3.17: Paradoxes
  172. 3.A: Relativity (Answers)
  173. 3.E: Relativity (Exercises)
  174. 4: Miscellanea
  175. 4.1: Problem Solving
  176. 4.1.1: All models are wrong, some models are useful
  177. 4.2: Math Review
  178. 4.2.1: Introduction
  179. 4.2.2: Geometrical Shapes
  180. 4.2.3: Triangles
  181. 4.2.4: The Rectangular Coordinate Systems and Graphs
  182. 4.2.5: Finding Angle Measurements
  183. 4.2.6: Parallel and Perpendicular Lines
  184. 4.2.7: Solving Linear Equations and Inequalities
  185. 4.2.7.1: Solving Linera Equations
  186. 4.2.7.2: Solving Inequalities
  187. 4.2.7.3: Solving Quadratic Equations
  188. 4.2.7.4: Solving a System of Linear Equations
  189. 4.2.7.5: Solving a System of Linear Equations with Cramer's Rule
  190. 4.2.8: Functions
  191. 4.2.8.1: Basic Functions
  192. 4.2.8.2: Trigonometric Functions
  193. 4.2.8.3: Exponential_and_Logarithmic_Functions
  194. 4.2.8.4: Properties_of_Logarithms
  195. 4.2.8.5: Exponential and Logarithmic Models
  196. 4.2.9: Vectors
  197. 4.2.9.1: Review of Trigonometry
  198. 4.2.9.2: Right Angle Triangle Trigonometry
  199. 4.2.9.3: Scalars and Vectors
  200. 4.2.9.4: Coordinate Systems and Components of a Vector
  201. 4.2.9.5: Algebra of Vectors
  202. 4.2.9.6: Products of Vectors
  203. 4.2.9.7: Further Topics
  204. 4.2.9.E: Practice
  205. 4.2.10: Vectors
  206. Back Matter
  207. Index
  208. Glossary
  209. Detailed Licensing
  210. Detailed Licensing