Classical Mechanics

1. Rigid Body Dynamics
   1. Rotational Motion
      1. Definition and Explanation
         1. Rigid Body vs. Point Mass
         2. Fixed Axis Rotation
         3. Compound Rotation
      2. Torque
         1. Definition and Formula
         2. Torque as a Vector Quantity
         3. Calculating Torque
            1. Lever Arm Concept
            2. Cross Product Approach
         4. Applications
            1. Simple Machines (e.g., Levers, Wheels, Pulleys)
            2. Balancing Beams and Rotational Equilibrium
      3. Moment of Inertia
         1. Definition and Physical Meaning
         2. Calculation for Simple Geometries
            1. Solid Cylinder
            2. Hollow Cylinder
            3. Solid Sphere
            4. Rod vs. Disk
         3. Parallel Axis Theorem
         4. Perpendicular Axis Theorem
      4. Rotational Kinetic Energy
         1. Formula Derivation
         2. Comparison with Translational Kinetic Energy
         3. Examples in Everyday Objects
         4. Energy Conservation in Rolling Motion
   2. Angular Momentum and Its Conservation
      1. Definition and Formula
         1. Angular Momentum as a Vector
         2. Relationship to Linear Momentum
      2. Conservation Principle
         1. Closed System Requirement
         2. Implications for Rotating Bodies (Conservation in Absence of External Torque)
      3. Gyroscopic Effects
         1. Precession Phenomena
         2. Applications in Navigation Systems (e.g., Gyroscopes in Aircraft)
      4. Angular Impulse
         1. Concept of Angular Impulse
         2. Angular Impulse-Momentum Theorem
   3. Equilibrium of Rigid Bodies
      1. Conditions for Equilibrium
         1. Static Equilibrium
         2. Dynamic Equilibrium
      2. Analysis of Force Systems
         1. Concurrent Forces
         2. Non-Concurrent Forces
      3. Applications
         1. Trusses and Frameworks
         2. Structural Stability (e.g., Bridges and Buildings)
         3. Balancing and Center of Mass Adjustments
   4. Kinematics of Rigid Body Motion
      1. Translational and Rotational Motion
         1. Combined Motion Dynamics
      2. Instantaneous Center of Rotation
         1. Definition and Significance
         2. Determining the Instantaneous Center
      3. Angular Variables
         1. Angular Displacement
         2. Angular Velocity
            1. Relationship with Tangential Velocity
         3. Angular Acceleration
            1. Rotational Equations of Motion
   5. Dynamics of Rigid Bodies
      1. Equations of Rotational Motion
         1. Analogies to Translational Motion
         2. Newton’s Second Law for Rotation
      2. Application of Forces and Torques
         1. Dynamics of Rotating Systems
         2. Identifying and Analyzing Applied Forces and Resultant Torques
      3. Real-World Applications
         1. Engineering and Mechanical Design
         2. Sports (e.g., Spinning and Twisting Motions in Gymnastics)
      4. Dynamic Stability
         1. Factors Affecting Stability
         2. Example of Vehicles and Aircraft Stability Control Systems