Welcome to the Mechanics Map Digital Textbook:
The Mechanics Map is an open textbook for engineering statics and dynamics containing written explanations, video lectures, worked examples, and homework problems. All content is licensed under a Creative Commons Share-alike license, so feel free to use, share, or remix the content. The table of contents below links to all available topics, while the About, Instructor Resources, and Get Involved tabs provide information to those looking to learn more about the project in general.
Mechanics Basics:
1. Newtonian Mechanics Basics:
Newtonian Mechanics Video Introduction
1.1 Bodies
1.2 Position, Displacement, Velocity, and Acceleration
1.3 Forces
1.4 Orientation, Angular Displacement, Angular Velocity, and Angular Acceleration
1.5 Moments
1.6 Free Body Diagrams
1.7 Newton's First Law
1.8 Newton's Second Law
1.9 Newton's Third Law
Chapter 1 Homework Problems
Statics Basics:
2. Static Equilibrium in Concurrent Force Systems:
Equilibrium in Concurrent Force Systems Video Introduction
2.1 Static Equilibrium
2.2 Point Forces as Vectors
2.3 Principle of Transmissibility
2.4 Concurrent Forces
2.5 Equilibrium Analysis for a Concurrent Force System
Chapter 2 Homework Problems
3. Static Equilibrium in Rigid Body Systems:
Equilibrium in Rigid Body Systems Video Introduction
3.1 Moment of a Force About a Point (Scalar Calculation)
3.2 Varignon's Theorem
3.3 Couples
3.4 Moment About a Point (Vector)
3.5 Moment About an Axis
3.6 Equilibrium Analysis of a Rigid Body
Chapter 3 Homework Problems
Statics Advanced Topics:
4. Statically Equivalent Systems
Statically Equivalent Systems Video Introduction
4.1 Statically Equivalent Systems
4.2 Resolution of a Force into a Force and a Couple
4.3 Equivalent Force Couple System
4.4 Distributed Forces
4.5 Equivalent Point Load via Integration
4.6 Equivalent Point Load via Composite Parts
Chapter 4 Homework Problems
5. Engineering Structures:
Engineering Structures Video Introduction
5.1 Structures
5.2 Two Force Members
5.3 Method of Joints
5.4 Method of Sections
5.5 Analysis of Frames and Machines
Chapter 5 Homework Problems
6. Internal Forces
Internal Forces Video Introduction
6.1 Internal Forces
6.2 Finding Internal Forces via Equilibrium Analysis
6.3 Axial Force Diagrams and Torsion Diagrams
6.4 Shear and Moment Diagrams
Chapter 6 Homework Problems
7. Friction and Friction Applications:
Friction and Friction Applications Video Introduction
7.1 Dry Friction
7.2 Slipping vs. Tipping
7.3 Wedges
7.4 Power Screws
7.5 Bearing Friction
7.6 Disc Friction
7.7 Belt Friction
Chapter 7 Homework Problems
Particle Dynamics:
8. Particle Kinematics:
Particle Kinematics Video Introduction
8.1 One Dimensional Continuous Motion
8.2 One Dimensional Non-Continuous Motion
8.3 Two Dimensional Motion with Rectangular Coordinates
8.4 Two Dimensional Motion with Normal-Tangential Coordinates
8.5 Two Dimensional Motion with Polar Coordinates
8.6 Dependent Motion Systems
8.7 Relative Motion Systems
Chapter 8 Homework Problems
9. Newton's Second Law for Particles:
Newton's Second Law for Particles Video Introduction
9.1 One Dimensional Equations of Motion
9.2 Equations of Motion in Rectangular Coordinates
9.3 Equations of Motion in Normal-Tangential Coordinates
9.4 Equations of Motion in Polar Coordinates
Chapter 9 Homework Problems
10. Work and Energy in Particles:
Work and Energy in Particles Video Introduction
10.1 Work, Kinetic Energy and Potential Energy for Particles
10.2 Work and Energy Principle for Particles
10.3 Power for Particles
10.4 Efficiency for Particles
10.5 Work and Energy for Systems of Particles
Chapter 10 Homework Problems
11. Impulse and Momentum in Particles:
Impulse Momentum Methods Video Introduction
11.1 Impulse and Momentum for a Particle
11.2 The Impulse-Momentum Principle for Particles
11.3 Surface Collisions and the Coefficient of Restitution
11.4 One Dimensional Particle Collisions
11.5 Two Dimensional Particle Collisions
11.6 Steady Flow Devices
Chapter 11 Homework Problems
Rigid Body Dynamics:
12. Rigid Body Kinematics:
Rigid Body Kinematics Video Introduction
12.1 Fixed Axis Rotation Systems (Scalar)
12.2 Fixed Axis Rotation Systems (Vector)
12.3 Belt and Gear Driven Systems
12.4 Absolute Motion Analysis
12.5 Relative Motion Analysis (Scalar)
12.6 Relative Motion Analysis (Vector)
12.7 Instantaneous Center of Zero Velocity
12.8 Rotating Frame Analysis (Vector)
Chapter 12 Homework Problems
13. Newton's Second Law for Rigid Bodies:
Newton's Second Law for Rigid Bodies Video Introduction
13.1 Translational Systems
13.2 Fixed Axis Rotation Systems
13.3 Rigid Body General Planar Motion
13.4 Multi-Body General Planar Motion
Chapter 13 Homework Problems
14. Work and Energy in Rigid Bodies
Rigid Body Work and Energy Video Introduction
14.1 Work, Kinetic Energy, and Potential Energy for Rigid Bodies
14.2 Principle of Work and Energy for Rigid Bodies
14.3 Power in Rigid Body Systems
14.4 Efficiency in Rigid Body Systems
Chapter 14 Homework Problems
15. Impulse and Momentum in Rigid Bodies
Rigid Body Impulse Momentum Video Introduction
15.1 Impulse and Momentum for a Rigid Body System
15.2 The Impulse Momentum Theorem for a Rigid Body
15.3 Rigid Body Surface Collisions
15.4 Free Rigid Body Collisions
Vibrations:
16. One Degree of Freedom (1 DOF) Vibrations
16.1 Undamped Free Vibrations
16.2 Viscous Damped Free Vibrations
16.3 Friction (Coulomb) Damped Free Vibrations
16.4 Undamped Harmonic Forced Vibrations
16.5 Viscous Damped Harmonic Forced Vibrations
Appendix:
A1. Vector and Matrix Math:
A 1.1 Vectors
A 1.2 Vector Addition
A 1.3 Dot Product
A 1.4 Cross Product
A 1.5 Solving Systems of Equations with Matrices
Appendix 1 Homework Problems
A2. Moment Integrals:
A 2.1 Moment Integrals
A 2.2 Centroids of Areas via Integration
A 2.3 Centroids in Volumes and Center of Mass via Integration
A 2.4 Centroids and Center of Mass via the Method of Composite Parts
A 2.5 Area Moments of Inertia via Integration
A 2.6 Mass Moments of Inertia via Integration
A 2.7 Moments of Inertia via Composite Parts and the Parallel Axis Theorem
Appendix 2 Homework Problems