Mechanics Map Digital Textbook

Illustrations from Mechanics Map textbook illustrating mechanic principles

Images from the Mechanics Map Digital Textbook are licensed under CC BY-SA 4.0

Resource Description

The Mechanics Map is an open textbook for engineering statics and dynamics containing written explanations, video lectures, worked examples, and homework problems.

The Mechanics Map Digital Textbook Project is an open digital textbook founded on the idea that expert-generated concept maps can serve as a powerful advance organizer for textbook content. The overview at the beginning of each chapter consists of a video showing how all the topics in the chapter are linked together by the author. By providing this overview, the author is seeking to help users organize the knowledge they are developing in a way that matches the expert's organization of knowledge.

Dr. Moore has been assisted by Dr. Majid Chatsaz at Penn State Scranton, Dr. Agnes d'Entremont at The University of British Columbia, Joan Kowalski at Penn State New Kensington, and Dr. Douglas Miller at Penn State Dubois.

Course Number

EMCH 211, EMCH 212

License

CC BY-SA 4.0

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Author(s)
Table of Contents

Online Resource

View the entire resource online here: Mechanics Map Digital Textbook

Dr. Jacob Moore

Hello, my name is Jacob Moore and I am an Associate Professor of Engineering at Penn State Mont Alto.

As a teacher I cover a broad variety of basic engineering subjects including design, statics, dynamics, strength of materials, and thermodynamics. I also run the engineering lab located on the Penn State Mont Alto Campus, giving students access to the tools they need to design, prototype, and test their designs as practicing engineers would. For more details on my teaching interests and experiences please visit my personal website.

Learn more

Mechanics Basics
- Newtonian Mechanics Basics
  - Newtonian Mechanics Video Introduction
  - Bodies
  - Position, Displacement, Velocity, and Acceleration
  - Forces
  - Orientation, Angular Displacement, Angular Velocity, and Angular Acceleration
  - Moments
  - Free Body Diagrams
  - Newton's First Law
  - Newton's Second Law
  - Newton's Third Law
  - Chapter 1 Homework Problems
Statics Basics
- Static Equilibrium in Concurrent Force Systems
  - Equilibrium in Concurrent Force Systems Video Introduction
  - Static Equilibrium
  - Point Forces as Vectors
  - Principle of Transmissibility
  - Concurrent Forces
  - Equilibrium Analysis for a Concurrent Force System
  - Chapter 2 Homework Problems
- Static Equilibrium in Rigid Body Systems
  - Equilibrium in Rigid Body Systems Video Introduction
  - Moment of a Force About a Point (Scalar Calculation)
  - Varignon's Theorem
  - Couples
  - Moment About a Point (Vector)
  - Moment About an Axis
  - Equilibrium Analysis of a Rigid Body
  - Chapter 3 Homework Problems
Statics Advanced Topics
- Statically Equivalent Systems
  - Statically Equivalent Systems Video Introduction
  - Statically Equivalent Systems
  - Resolution of a Force into a Force and a Couple
  - Equivalent Force Couple System
  - Distributed Forces
  - Equivalent Point Load via Integration
  - Equivalent Point Load via Composite Parts
  - Chapter 4 Homework Problems
- Engineering Structures
  - Engineering Structures Video Introduction
  - Structures
  - Two Force Members
  - Trusses
  - Method of Joints
  - Method of Sections
  - Frames and Machines
  - Analysis of Frames and Machines
  - Chapter 5 Homework Problems
- Internal Forces
  - Internal Forces Video Introduction
  - Internal Forces
  - Finding Internal Forces via Equilibrium Analysis
  - Axial Force Diagrams and Torsion Diagrams
  - Shear and Moment Diagrams
  - Chapter 6 Homework Problems
- Friction and Friction Applications
  - Friction and Friction Applications Video Introduction
  - Dry Friction
  - Slipping vs. Tipping
  - Wedges
  - Power Screws
  - Bearing Friction
  - Disc Friction
  - Belt Friction
  - Chapter 7 Homework Problems
Particle Dynamics
- Particle Kinematics
  - Particle Kinematics Video Introduction
  - One Dimensional Continuous Motion
  - One Dimensional Non-Continuous Motion
  - Two Dimensional Motion with Rectangular Coordinates
  - Two Dimensional Motion with Normal-Tangential Coordinates
  - Two Dimensional Motion with Polar Coordinates
  - Dependent Motion Systems
  - Relative Motion Systems
  - Chapter 8 Homework Problems
- Newton's Second Law for Particles
  - Newton's Second Law for Particles Video Introduction
  - One Dimensional Equations of Motion
  - Equations of Motion in Rectangular Coordinates
  - Equations of Motion in Normal-Tangential Coordinates
  - Equations of Motion in Polar Coordinates
  - Chapter 9 Homework Problems
- Work and Energy in Particles
  - Work and Energy in Particles Video Introduction
  - The Conservation of Energy for Particles
  - Power for Particles
  - Efficiency for Particles
  - The Conservation of Energy for Systems of Particles
  - Chapter 10 Homework Problems
- Impulse and Momentum in Particles
  - Impulse Momentum Methods Video Introduction
  - The Impulse-Momentum Equations for a Particle
  - Surface Collisions and the Coefficient of Restitution
  - One Dimensional Particle Collisions
  - Two Dimensional Particle Collisions
  - Steady Flow Devices
  - Chapter 11 Homework Problems
Rigid Body Dynamics
- Rigid Body Kinematics
  - Fixed Axis Rotation Systems (Scalar)
  - Fixed Axis Rotation Systems (Vector)
  - Belt and Gear Driven Systems
  - Absolute Motion Analysis
  - Relative Motion Analysis (Scalar)
  - Relative Motion Analysis (Vector)
  - Instantaneous Center of Zero Velocity
  - Rotating Frame Analysis (Vector)
  - Chapter 12 Homework Problems
- Newton's Second Law for Rigid Bodies
  - Translational Systems
  - Fixed Axis Rotation Systems
  - Rigid Body General Planar Motion
  - Multi-Body General Planar Motion
  - Chapter 13 Homework Problems
- Work and Energy in Rigid Bodies
  - Work and Energy Methods Video Introduction
  - Kinetic Energy for Rigid Bodies
  - Principle of Work-Energy for Rigid Bodies
  - The Conservation of Energy for Rigid Bodies or a System of Rigid Bodies
  - Power and Efficiency for Rigid Bodies
  - Chapter 14 Homework Problems
- Impulse and Momentum in Rigid Bodies
  - Impulse Momentum Methods Video Introduction
  - Linear and Angular Momentum for a Rigid Body
  - The Impulse Momentum Equations for a Rigid Body
  - Conservation of Momentum in Rigid Bodies and Systems of Rigid Bodies
  - Rigid Body Surface Collisions
  - Free Rigid Body Collisions
  - Chapter 15 Homework Problems
Vibrations
- One Degree of Freedom (1 DOF) Vibrations
  - One Degree of Freedom Vibrations Video Introduction
  - Undamped Free Vibrations
  - Viscous Damped Free Vibrations
  - Friction (Coulomb) Damped Free Vibrations
  - Undamped Harmonic Forced Vibrations
  - Viscous Damped Harmonic Forced Vibrations
Appendix
- Vector and Matrix Math
  - Vectors
  - Vector Addition
  - Dot Product
  - Cross Product
  - Solving Systems of Equations with Matrices
  - Appendix 1 Homework Problems
- Moment Integrals
  - Moment Integrals
  - Centroids of Areas via Integration
  - Centroids in Volumes and Center of Mass via Integration
  - Centroids and Center of Mass via the Method of Composite Parts
  - Area Moments of Inertia via Integration
  - Mass Moments of Inertia via Integration
  - Moments of Inertia via Composite Parts and the Parallel Axis Theorem