## 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 contributing 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 Trusses

5.4 Method of Joints

5.5 Method of Sections

5.6 Frames and Machines

5.7 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 The Conservation of Energy for Particles

10.2 Power for Particles

10.3 Efficiency for Particles

10.4 The Conservation of Energy for Systems of Particles

Chapter 10 Homework Problems

### 11. Impulse and Momentum in Particles:

Impulse Momentum Methods Video Introduction

11.1 The Impulse-Momentum Equations for a Particle

11.2 Surface Collisions and the Coefficient of Restitution

11.3 One Dimensional Particle Collisions

11.4 Two Dimensional Particle Collisions

11.5 Steady Flow Devices

Chapter 11 Homework Problems

## Rigid Body Dynamics:

### 12. Rigid Body Kinematics:

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:

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

Work and Energy Methods Video Introduction

14.1 Kinetic Energy for Rigid Bodies

14.2 Principle of Work-Energy for Rigid Bodies

14.3 The Conservation of Energy for Rigid Bodies or a System of Rigid Bodies

14.4 Power and Efficiency for Rigid Bodies

Chapter 14 Homework Problems

### 15. Impulse and Momentum in Rigid Bodies

Impulse Momentum Methods Video Introduction

15.1 Linear and Angular Momentum for a Rigid Body

15.2 The Impulse Momentum Equations for a Rigid Body

15.3 Conservation of Momentum in Rigid Bodies and Systems of Rigid Bodies

15.4 Rigid Body Surface Collisions

15.5 Free Rigid Body Collisions

Chapter 15 Homework Problems

## Vibrations:

### 16. One Degree of Freedom (1 DOF) Vibrations

One Degree of Freedom Vibrations Video Introduction

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