Classical Mechanics

1. Dynamics
   1. Force and Its Effects
      1. Types of Forces
         1. Gravitational Force
            1. Universal Law of Gravitation
               1. Mathematical expression
               2. Dependence on mass and distance
            2. Impact on planetary motion
            3. Effects in everyday contexts
         2. Normal Force
            1. Definition and direction
            2. Role in support interactions between surfaces
            3. Applications in inclined planes
         3. Frictional Force
            1. Types of friction
               1. Static friction
               2. Kinetic (sliding) friction
               3. Rolling friction
            2. Coefficients of friction
               1. Definition and significance
               2. Factors affecting frictional coefficients
            3. Real-world scenarios
               1. Vehicle braking
               2. Walking dynamics
         4. Tension
            1. Role in connected bodies
            2. Applications in pulleys and ropes
            3. Example problems involving tension
         5. Applied Force
            1. Concepts of action and resulting motion
            2. Importance in problem-solving
            3. Example scenarios in mechanical systems
         6. Additional Forces
            1. Spring Force
               1. Hooke’s Law
               2. Applications in spring systems
            2. Buoyant Force
               1. Archimedes’ Principle
               2. Importance in fluid dynamics
   2. Equations of Motion
      1. Newton’s Second Law Applications
         1. Algebraic formulations
         2. Complex systems involving multiple forces
         3. Dimensional analysis in dynamics problems
      2. Equations for Uniform Acceleration
         1. Derivation from first principles
         2. Application in simple mechanical systems
         3. Analyzing motion graphs
      3. Non-Uniform Acceleration
         1. Variable forces and complexity in calculations
         2. Numerical methods for solving equations
      4. Kinematic Equations
         1. Derivation and significance
         2. Use in predicting motion outcomes
         3. Examples in vertical and horizontal motion scenarios
   3. Analysis of Forces
      1. Free Body Diagrams (FBD)
         1. Importance in visualizing force interactions
         2. Steps to creating an effective FBD
         3. Application in problem-solving
      2. Equilibrium and Dynamics
         1. Conditions for static and dynamic equilibrium
         2. Role of net force in motion determination
         3. Analyzing systems in different states of motion
   4. Dynamics of Systems
      1. Motion Under Variable Forces
         1. Impact of force variation with time
         2. Graphical analysis over time
      2. Dynamics of Multi-Body Systems
         1. Pulleys and inclined plane problems
         2. Interactions within complex mechanical systems
      3. Rotational Dynamics
         1. Torque and rotational force interactions
         2. Angular equivalents of linear dynamics principles
         3. Moment of inertia and its significance in rotational motion
   5. Practical Applications
      1. Vehicle Dynamics
         1. Forces in vehicle acceleration and braking
         2. Dynamics of cornering and stability
      2. Aerospace Dynamics
         1. Impact of aerodynamic forces
         2. Dynamics in flight and space exploration
      3. Structural Dynamics
         1. Loading effects on structural integrity
         2. Vibrational analysis in engineering structures