Chapter 1

Introduction

Application of Trigonometry: Laws of Right-, Oblique-, Acute-, Obtuse-Triangle. Pythagorean Theory, Sine Law, and Cosine Law.

1. Trigonometry

2. Right Triangle Formula

3. Pythagorean Formula

4. Sine Law Application 1

5. Sine Law Application 2

6. Cosine Law Application

7. Measuring the Height of a Pyramid Without Climbing It

8. Measuring the Depth of a River Without Diving

9. How to Round Numbers in Practical Situations

Chapter 2

Force

Resolve Forces using the Right Triangle & Sine Law. Application of Trigonometry in Solving Engineering Mechanics Problems

1. Resolving and Adding Forces

2. Sine Law Short Cut in Resolving Forces

3. Theory of Parallelogram Proof Using Cosine Law

4. Law of Parallelogram Proof by Resolving Forces

Applications

5. Running

6. Vehicle Climbing Hill

7. Resolve Force Sine Law Application 1

8. Resolve Force Sine Law Application 2

9. Resolve Force Sine Law Application 3

10. Right Triangle vs Sine Law

11. Pull-up Exercise

12. Tow Truck Pulling

13. Resultant and Component Forces

14. Resultant and Component Forces Using the Resolving Technique

15. When to Apply Sine Law in Finding Unknown Forces

Adding More than Two Forces

16. Resultant of Multiple Forces

Chapter 3

Equilibrium of a Particle

Chapter 4

Moment

Theory of Parallelogram, Moment/Torque, Principle of Moments (Varignon’s Theorem), Resultant by Resolving Forces, Resultant of Multiple Forces, including Parallel, Concurrent, Nonconcurrent, Uniform & Nonuniformly Distributed Load

1. Moment Torque Explained

2. Understanding Moment Signs | Clarifying the Common Misconception

3. Moment Calculation Basics

4. Principle of Moments (Varignon’s Theorem)

5. Moments using the Force Resolving Technique

6. Moments Using the Shortest Distance Technique

7. Moments from Multiple Forces by the Resultant and Resolving it

8. Moments from Multiple Forces by the Resultant Force and its Shortest Distance

Common Mistakes

9. Moment Calculation in Statics

10. Force Resultant Moment in Statics

11. Force Moment Calculation Basics

12. Simple Application of Force-Moment Concept

13. Moment Concept Application

Chapter 5

Resultant

Resultant by Resolving Forces, Resultant of Multiple Forces, including Parallel, Concurrent, Nonconcurrent, Uniform & Nonuniformly Distributed Load

1. Resultants of Parallel Force Systems

2. Resultants of Uniform Force Systems

3. Resultants of Nonuniform Force Systems

4. Resultants of Noncurrent Force Systems

5. Surprising Results! The Location of Resultant Forces

Chapter 6

Equilibrium of a Rigid Body

Free-Body Diagram, Reaction Force Calculations for Various Types of Forces, including Parallel, Concurrent, Nonconcurrent, Uniform & Nonuniformly Distributed Load

1. Free-Body Diagram

2. Reaction Force Calculation

3. Reaction Force Calculation for Uniform Force Systems

4. Reaction Force Calculation Nonuniform Force Systems

5. Reaction Force Calculation Nonconcurrent Force Systems

Common Mistakes

6. Foundations for Solving Problems in Mechanics, Statics, and Dynamics

Chapter 7

Structure

Analysis of Trusses, Frames, and Machine Members | Method of Joints and Sections

1. Introduction

2. Analysis Basics

3. Method of Joints

4. Method of Sections

5. Frame Analysis

6. Reaction Forces

Chapter 8

Friction

Friction, Friction Coefficient, Friction Force, Tension, Torque & Power, Rope, Flat Belt, V Belt, Tension, Torque, Square Threaded Screw, Ladder, & Wedge

1. Introduction

2. Inclined Surface

3. Rope/Belt

4. Pulley

5. V-Belt

6. Ladder

7. Jackscrew

Chapter 9

Centroid and Center of Gravity

Centroid, Center of Gravity, CG, mass moment & area moment 

1. Center of Gravity

2. Centroid

Chapter 10

Inertia

Inertia, Transfer Formula, Radius Gyration, Polar Moment of Inertia, 

1. Area Moment of Inertia | Radius Gyration | Polar Moment of Inertia

Reference

1. Limbrunner, G. F., D'Allaird, C., & Spiegel, L. Applied Statics and Strength of Materials

2. Beer, F. P.,‎ Johnston E. R., DeWolf, J. T., & Mazurek, D. Statics and mechanics of materials

3. Hibbeler, R. C. Mechanics of materials