## 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 Forces

1.3 Moments

1.4 Free Body Diagrams

1.5 Newton's First Law

1.6 Newton's Second Law

1.7 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

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. Friction and Friction Applications:

Friction and Friction Applications Video Introduction

6.1 Dry Friction

6.2 Slipping vs. Tipping

6.3 Wedges

6.4 Power Screws

6.5 Bearing Friction

6.6 Disc Friction

6.7 Belt Friction

Chapter 6 Homework Problems

## Particle Dynamics:

### 7. Particle Kinematics:

Particle Kinematics Video Introduction

7.1 One Dimensional Continuous Motion

7.2 One Dimensional Non-Continuous Motion

7.3 Two Dimensional Motion with Rectangular Coordinates

7.4 Two Dimensional Motion with Normal-Tangential Coordinates

7.5 Two Dimensional Motion with Polar Coordinates

7.6 Dependent Motion Systems

7.7 Relative Motion Systems

Chapter 7 Homework Problems

### 8. Newton's Second Law for Particles:

Newton's Second Law for Particles Video Introduction

8.1 One Dimensional Equations of Motion

8.2 Equations of Motion in Rectangular Coordinates

8.3 Equations of Motion in Normal-Tangential Coordinates

8.4 Equations of Motion in Polar Coordinates

Chapter 8 Homework Problems

### 9. Work and Energy in Particles:

Work and Energy in Particles Video Introduction

9.1 The Conservation of Energy for Particles

9.2 Power and Efficiency for Particles

9.3 The Conservation of Energy for Systems of Particles

Chapter 9 Homework Problems

### 10. Impulse and Momentum in Particles:

Impulse Momentum Methods Video Introduction

10.1 The Impulse-Momentum Equations for a Particle

10.2 Surface Collisions and the Coefficient of Restitution

10.3 One Dimensional Particle Collisions

10.4 Two Dimensional Particle Collisions

10.5 Steady Flow Devices

Chapter 10 Homework Problems

## Rigid Body Dynamics:

### 11. Rigid Body Kinematics:

11.1 Fixed Axis Rotation Systems

11.2 Belt and Gear Driven Systems

11.3 Absolute Motion Analysis

11.4 Relative Motion Analysis

11.5 Rotating Frame Analysis

Chapter 11 Homework Problems

### 12. Newton's Second Law for Rigid Bodies:

12.1 Translational Systems

12.2 Fixed Axis Rotation Systems

12.3 Rigid Body General Planar Motion

12.4 Multi-Body General Planar Motion

Chapter 12 Homework Problems

### 13. Work and Energy in Rigid Bodies

Work and Energy Methods Video Introduction

13.1 The Conservation of Energy for Rigid Bodies

13.2 Power and Efficiency for Rigid Bodies

Chapter 13 Homework Problems

### 14. Impulse and Momentum in Rigid Bodies

Impulse Momentum Methods Video Introduction

14.1 The Impulse Momentum Equations for a Rigid Body

14.2 Rigid Body Surface Collisions

Chapter 14 Homework Problems

## Vibrations:

### 15. One Degree of Freedom:

One Degree of Freedom Vibrations Video Introduction

15.1 Undamped Free Vibrations

15.2 Viscous Damped Free Vibrations

15.3 Friction (Coulomb) Damped Free Vibrations

15.4 Undamped Harmonic Forced Vibrations

15.5 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