Engineering Mechanics

Engineering Mechanics is a foundational discipline that applies the principles of physics to analyze the effects of forces on physical bodies and systems. It is broadly divided into two main areas: statics, which deals with bodies at rest or in equilibrium, and dynamics, which studies bodies in motion. By mastering concepts such as force, torque, stress, and strain, engineers can predict how structures and machines will respond to loads, making it an essential analytical cornerstone for designing everything from bridges and buildings to engines and robotic systems.

1. Introduction to Engineering Mechanics
   1. Scope and Applications of Engineering Mechanics
      1. Role in Civil Engineering
      2. Role in Mechanical Engineering
      3. Role in Aerospace Engineering
      4. Role in Structural Engineering
      5. Historical Development
         1. Classical Mechanics Foundations
         2. Modern Engineering Applications
      6. Relationship to Physics
      7. Relationship to Mathematics
      8. Relationship to Materials Science
   2. Fundamental Concepts
      1. Branches of Mechanics
         1. Statics
            1. Equilibrium of Bodies at Rest
            2. Force Systems
         2. Dynamics
            1. Kinematics
               1. Motion Description
               2. Geometric Aspects of Motion
            2. Kinetics
               1. Forces and Motion Relationships
               2. Mass and Acceleration
      2. Basic Quantities
         1. Space
            1. Position and Displacement
            2. Coordinate Systems
         2. Time
            1. Duration and Intervals
            2. Reference Frames
         3. Mass
            1. Inertial Properties
            2. Conservation Principles
         4. Force
            1. Vector Nature
            2. Units and Measurement
      3. Derived Quantities
         1. Weight
            1. Gravitational Force
            2. Distinction from Mass
         2. Volume
            1. Geometric Properties
            2. Density Relationships
         3. Density
            1. Mass per Unit Volume
            2. Material Properties
         4. Acceleration
            1. Rate of Velocity Change
            2. Vector Characteristics
      4. Idealizations in Mechanics
         1. Particle Model
            1. Point Mass Assumption
            2. Applications and Limitations
         2. Rigid Body Model
            1. Non-deformable Body Assumption
            2. Practical Applications
         3. Continuum Model
            1. Continuous Matter Distribution
            2. Fluid and Solid Applications
         4. Concentrated Force Model
            1. Point Force Assumption
            2. Load Simplifications
      5. Newton's Laws of Motion
         1. First Law
            1. Law of Inertia
            2. Equilibrium Conditions
         2. Second Law
            1. Force-Acceleration Relationship
            2. Mathematical Formulation
         3. Third Law
            1. Action-Reaction Principle
            2. Force Pairs
      6. Newton's Law of Universal Gravitation
         1. Gravitational Force Formula
         2. Gravitational Constant
         3. Weight Calculations
         4. Planetary Motion Applications
      7. Systems of Units
         1. International System of Units
            1. Base Units
               1. Meter
               2. Kilogram
               3. Second
            2. Derived Units
               1. Newton
               2. Pascal
               3. Joule
         2. U.S. Customary Units
            1. Base Units
               1. Foot
               2. Pound Mass
               3. Second
            2. Derived Units
               1. Pound Force
               2. Slug
         3. Unit Conversion
            1. Conversion Factors
            2. Dimensional Analysis
      8. Dimensional Homogeneity
         1. Principle of Dimensional Consistency
         2. Dimensional Analysis Techniques
         3. Error Detection in Equations
   3. Vector Operations
      1. Scalars and Vectors
         1. Scalar Quantities
            1. Magnitude Only
            2. Examples in Mechanics
         2. Vector Quantities
            1. Magnitude and Direction
            2. Examples in Mechanics
      2. Vector Representation
         1. Graphical Representation
         2. Magnitude Calculation
         3. Direction Specification
         4. Unit Vectors
            1. Definition and Properties
            2. Coordinate System Unit Vectors
      3. Vector Addition and Subtraction
         1. Parallelogram Law
            1. Geometric Construction
            2. Mathematical Application
         2. Triangle Rule
            1. Head-to-Tail Method
            2. Vector Chains
         3. Polygon Method
            1. Multiple Vector Addition
            2. Closed Polygon Rule
      4. Vector Components
         1. Rectangular Components in 2D
            1. X and Y Components
            2. Component Calculation
         2. Rectangular Components in 3D
            1. X, Y, and Z Components
            2. Three-Dimensional Analysis
      5. Cartesian Vector Notation
         1. Unit Vector System
            1. i Unit Vector
            2. j Unit Vector
            3. k Unit Vector
         2. Component Form Expression
         3. Vector Algebra in Component Form
      6. Dot Product
         1. Definition and Formula
         2. Geometric Interpretation
         3. Properties of Dot Product
         4. Work Calculations
         5. Angle Between Vectors
      7. Cross Product
         1. Definition and Formula
         2. Right-Hand Rule
         3. Properties of Cross Product
         4. Moment Calculations
         5. Area Calculations