Classical Mechanics

1. Systems of Particles
   1. Center of Mass
      1. Definition and Importance
         1. Finding Center of Mass for Different Systems
         2. Role in Understanding System Behavior
      2. Calculation
         1. Discrete Systems
            1. Point Masses
            2. Weighted Averages
         2. Continuous Distributions
            1. Integration Techniques
            2. Symmetry Considerations
      3. Applications
         1. Balancing Bodies
         2. Applications in Vehicle Dynamics
         3. Biomechanics and Human Movement
   2. Motion of System of Particles
      1. Translational Motion
         1. Description Using Center of Mass
         2. Relation to External Forces
      2. Rotational Motion
         1. Torque Effects on Systems
         2. Angular Momentum Considerations
      3. Constrained Systems
         1. Understanding Constraints
         2. Application to Dynamical Systems
      4. Multi-Particle Dynamics
         1. Representation of Internal Forces
         2. Simplification of Complex Systems
   3. Collision and Impulse
      1. Types of Collisions
         1. Elastic Collisions
            1. Conservation of Kinetic Energy
            2. Symmetrical vs. Asymmetrical Collisions
         2. Inelastic Collisions
            1. Partial Energy Loss
            2. Completely Inelastic Collisions
               1. Coalescence Phenomenon
         3. Real-World Implications
            1. Automobile Safety Systems
            2. Sports Collisions
      2. Impulse-Momentum Theorem
         1. Definition and Formula
         2. Use in Solving Impact Problems
         3. Real-Life Examples
            1. Applications in Martial Arts
            2. Force-Time Graphs Interpretation
      3. Coefficient of Restitution
         1. Understanding and Calculation
         2. Role in Collision Analysis
         3. Correlation with Material Properties
   4. Conservation Laws for Systems
      1. Linear Momentum Conservation
         1. Systems of Particles and Isolated Systems
         2. Problem Solving and Applications
            1. Rocket Propulsion
            2. Recoil in Firearms
      2. Angular Momentum Conservation
         1. Rotational Dynamics in Collisions
         2. Real-World Applications
            1. Figure Skating Rotations
            2. Gyroscopes and Navigation
      3. Energy Considerations
         1. Mechanical Energy in Systems
         2. Impact of Non-Conservative Forces
            1. Effect of Friction and Air Resistance