Classical Mechanics

  1. Work and Energy
    1. Work
      1. Work Done by a Constant Force
        1. Mathematical Definition
          1. Work-Angle Relationship
            1. Positive and Negative Work
            2. Work Done by a Varying Force
              1. Calculating Work from Force vs. Displacement Graphs
                1. Work as an Integral
                  1. Path Dependence
                  2. Work and the Scalar Product
                    1. Dot Product in Work Calculations
                      1. Component Analysis
                    2. Kinetic Energy
                      1. Definition of Kinetic Energy
                        1. Translational Kinetic Energy
                          1. Derivation from Newton's Laws
                          2. The Work-Energy Theorem
                            1. Statement and Proof
                              1. Net Work and Energy Change
                            2. Potential Energy
                              1. Conservative and Non-Conservative Forces
                                1. Path Independence
                                  1. Examples of Conservative Forces
                                    1. Gravitational Force
                                      1. Spring Force
                                      2. Examples of Non-Conservative Forces
                                        1. Friction
                                          1. Air Resistance
                                        2. Gravitational Potential Energy
                                          1. Near Earth's Surface
                                            1. mgh Formula
                                            2. General Formulation
                                              1. Universal Gravitation
                                            3. Elastic Potential Energy
                                              1. Springs and Hooke's Law
                                                1. Derivation
                                                2. Potential Energy Diagrams
                                                  1. Energy Landscapes
                                                    1. Equilibrium Points
                                                      1. Stable Equilibrium
                                                        1. Unstable Equilibrium
                                                          1. Neutral Equilibrium
                                                          2. Turning Points
                                                        2. Conservation of Mechanical Energy
                                                          1. The Principle of Conservation of Energy
                                                            1. Isolated Systems
                                                              1. Conservative Forces Only
                                                              2. Total Mechanical Energy
                                                                1. Sum of Kinetic and Potential Energy
                                                                2. Problem Solving with Energy Conservation
                                                                  1. Identifying Energy Transformations
                                                                    1. Including Non-conservative Forces
                                                                      1. Energy Methods vs. Force Methods
                                                                    2. Power
                                                                      1. Average and Instantaneous Power
                                                                        1. Power as Rate of Work
                                                                          1. Mathematical Definitions
                                                                          2. Power in Mechanical Systems
                                                                            1. P = F·v Formula
                                                                              1. Applications
                                                                                1. Engines
                                                                                  1. Motors
                                                                                2. Efficiency
                                                                                  1. Energy Conversion
                                                                                    1. Power Losses

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                                                                                5. Common Forces in Mechanics

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                                                                                7. Systems of Particles and Linear Momentum