Classical Mechanics

  1. Rotational Motion
    1. Rotational Kinematics
      1. Angular Position, Velocity, and Acceleration
        1. Definitions and Units
          1. Radians
            1. Angular Displacement
            2. Sign Conventions
            3. Rotational Motion with Constant Angular Acceleration
              1. Kinematic Equations for Rotation
                1. Analogy with Linear Motion
                2. Relationship Between Linear and Angular Variables
                  1. Tangential and Radial Components
                    1. Arc Length Relationships
                      1. Velocity and Acceleration Connections
                    2. Rotational Dynamics
                      1. Torque
                        1. Definition and Calculation
                          1. Vector Nature of Torque
                            1. Lever Arm Concept
                              1. Perpendicular Distance
                              2. Right-Hand Rule for Torque
                              3. Moment of Inertia
                                1. Definition and Calculation
                                  1. Physical Interpretation
                                    1. Parallel Axis Theorem
                                      1. Steiner's Theorem
                                      2. Perpendicular Axis Theorem
                                        1. Moments of Inertia for Common Shapes
                                          1. Rod
                                            1. Disk
                                              1. Sphere
                                                1. Ring
                                              2. Newton's Second Law for Rotation
                                                1. τ = Iα
                                                  1. Rotational Analog of F = ma
                                                2. Work and Energy in Rotation
                                                  1. Rotational Kinetic Energy
                                                    1. Energy of Rotating Bodies
                                                      1. ½Iω² Formula
                                                      2. Work and Power in Rotational Motion
                                                        1. Work Done by Torque
                                                          1. Power in Rotational Systems
                                                            1. P = τω
                                                          2. Rolling Motion Energy
                                                            1. Combined Translational and Rotational Energy
                                                          3. Angular Momentum
                                                            1. Definition of Angular Momentum
                                                              1. Point Particles
                                                                1. L = r × p
                                                                2. Rigid Bodies
                                                                  1. L = Iω
                                                                3. Conservation of Angular Momentum
                                                                  1. Isolated Systems
                                                                    1. No External Torques
                                                                    2. Applications
                                                                      1. Gyroscopes
                                                                        1. Figure Skating
                                                                          1. Planetary Motion
                                                                        2. Rolling Motion
                                                                          1. Kinematics of Rolling
                                                                            1. Pure Rolling Condition
                                                                              1. v = ωr
                                                                              2. Rolling Without Slipping
                                                                                1. Constraint Condition
                                                                              3. Dynamics of Rolling
                                                                                1. Forces in Rolling Motion
                                                                                  1. Friction's Role
                                                                                  2. Energy Considerations
                                                                                    1. Kinetic Energy Distribution
                                                                                  3. Rolling on Inclined Planes
                                                                                    1. Acceleration Analysis
                                                                                      1. Energy Methods

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                                                                                  7. Systems of Particles and Linear Momentum

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                                                                                  9. Static Equilibrium and Elasticity