Engineering Mechanics

  1. Center of Gravity, Centroid, and Moment of Inertia
    1. Center of Gravity and Center of Mass
      1. Definitions and Physical Meaning
        1. Distinction Between Concepts
          1. Discrete Body Systems
            1. Continuous Body Systems
              1. Calculation Methods
              2. Centroids of Lines, Areas, and Volumes
                1. Centroid Definition
                  1. First Moment Concept
                    1. Line Centroids
                      1. Integration Method
                        1. Composite Line Method
                        2. Area Centroids
                          1. Integration Method
                            1. Rectangular Coordinates
                              1. Polar Coordinates
                              2. Composite Area Method
                                1. Area Decomposition
                                  1. Tabular Calculations
                                2. Volume Centroids
                                  1. Integration Method
                                    1. Composite Volume Method
                                  2. Theorems of Pappus-Guldinus
                                    1. First Theorem
                                      1. Surface Area Generation
                                        1. Centroidal Path Length
                                        2. Second Theorem
                                          1. Volume Generation
                                            1. Centroidal Area
                                            2. Applications to Complex Shapes
                                            3. Distributed Loading Resultants
                                              1. General Loading Functions
                                                1. Resultant Force Magnitude
                                                  1. Resultant Force Location
                                                    1. Pressure Distribution Applications
                                                    2. Area Moments of Inertia
                                                      1. Definition and Physical Meaning
                                                        1. Second Moment of Area
                                                          1. Calculation by Integration
                                                            1. Rectangular Coordinates
                                                              1. Polar Coordinates
                                                              2. Parallel-Axis Theorem
                                                                1. Theorem Statement
                                                                  1. Transfer Formula
                                                                  2. Radius of Gyration
                                                                    1. Physical Interpretation
                                                                    2. Composite Area Method
                                                                      1. Area Decomposition
                                                                        1. Tabular Calculations
                                                                          1. Positive and Negative Areas
                                                                          2. Principal Moments of Inertia
                                                                            1. Principal Axes
                                                                              1. Maximum and Minimum Values
                                                                            2. Mass Moment of Inertia
                                                                              1. Definition and Physical Meaning
                                                                                1. Rotational Inertia
                                                                                  1. Simple Geometric Shapes
                                                                                    1. Composite Body Method
                                                                                      1. Parallel-Axis Theorem for Mass
                                                                                        1. Radius of Gyration for Mass

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                                                                                      7. Friction

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                                                                                      9. Kinematics of a Particle