# Vector Mechanics for Engineers: Dynamics (SI units)

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Preface *

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Acknowledgments *

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List of Symbols *

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**Chapter 11 Kinematics of
Particles **

**
11.1 **
Introduction to Dynamics

**
Rectilinear Motion of Particles **

**
11.2 **
Position, Velocity, and Acceleration

**
11.3 **
Determination of the Motion of a Particle

**
11.4 **
Uniform Rectilinear Motion

**
11.5 **
Uniformly Accelerated Rectilinear Motion

**
11.6 **
Motion of Several Particles

**
*11.7 **
Graphical Solution of Rectilinear-Motion
Problems

**
*11.8 **
Other Graphical Methods

**
Curvilinear Motion of Particles **

**
11.9 **
Position Vector, Velocity, and Acceleration

**
11.10 **
Derivatives of Vector Functions

**
11.11 **
Rectangular Components of Velocity and
Acceleration

**
11.12 **
Motion Relative to a Frame in Translation

**
11.13 **
Tangential and Normal Components

**
11.14 **
Radial and Transverse Components

Review and Summary

Review Problems

Computer Problems

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**

**Chapter 12 Kinetics of
Particles: Newtonâ€™s Second Law **

**
12.1 **
Introduction

**
12.2 **
Newtonâ€™s Second Law of Motion

**
12.3 **
Linear Momentum of a Particle. Rate of Change of Linear Momentum

**
12.4 **
Systems of Units

**
12.5 **
Equations of Motion

**
12.6 **
Dynamic Equilibrium

**
12.7 **
Angular Momentum of a Particle. Rate of Change of Angular Momentum

**
12.8 **
Equations of Motion in Terms of Radial and Transverse Components

**
12.9 **
Motion under a Central Force. Conservation of Angular Momentum

**
12.10 **
Newtonâ€™s Law of Gravitation

**
*12.11 **
Trajectory of a Particle under a Central Force

**
*12.12 **
Application to Space Mechanics

**
*12.13 **
Keplerâ€™s Laws of Planetary Motion

Review and Summary

Review Problems

Computer Problems

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**

**Chapter 13 Kinetics of
Particles: Energy and Momentum Methods **

**
13.1 **
Introduction

**
13.2 **
Work of a Force

**
13.3 **
Kinetic Energy of a Particle. Principle of Work and Energy

**
13.4 **
Applications of the Principle of Work and Energy

**
13.5 **
Power and Efficiency

**
13.6 **
Potential Energy

**
*13.7 **
Conservative Forces

**
13.8 **
Conservation of Energy

**
13.9 **
Motion under a Conservative Central Force. Application to Space Mechanics

**
13.10 **
Principle of Impulse and Momentum 806

**
13.11 **
Impulsive Motion

**
13.12 **
Impact

**
13.13 **
Direct Central Impact

**
13.14 **
Oblique Central Impact

**
13.15 **
Problems Involving Energy and Momentum

Review and Summary

Review Problems

Computer Problems 852

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**

**Chapter 14 Systems of
Particles **

**
14.1 **
Introduction

**
14.2 **
Application of Newtonâ€™s Laws to the Motion of a System of Particles. Effective
Forces

**
14.3 **
Linear and Angular Momentum of a System of Particles

**
14.4 **
Motion of the Mass Center of a System of Particles

**
14.5 **
Angular Momentum of a System of Particles about Its Mass Center

**
14.6 **
Conservation of Momentum for a System of Particles

**
14.7 **
Kinetic Energy of a System of Particles

**
14.8 **
Work-Energy Principle. Conservation of Energy for a System of Particles

**
14.9 **
Principle of Impulse and Momentum for a System of Particles

**
*14.10 **
Variable Systems of Particles

**
*14.11 **
Steady Stream of Particles

**
*14.12 **
Systems Gaining or Losing Mass

Review and Summary

Review Problems

Computer Problems

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**

**
Chapter 15 Kinematics of Rigid Bodies**

**
15.1 **
Introduction

**
15.2 **
Translation

**
15.3 **
Rotation about a Fixed Axis

**
15.4 **
Equations Defining the Rotation of a Rigid Body about a Fixed Axis

**
15.5 **
General Plane Motion

**
15.6 **
Absolute and Relative Velocity in Plane Motion

**
15.7 **
Instantaneous Center of Rotation in Plane Motion

**
15.8 **
Absolute and Relative Acceleration in Plane Motion

**
*15.9 **
Analysis of Plane Motion in Terms of a Parameter

**
15.10 **
Rate of Change of a Vector with Respect to a
Rotating Frame

**
15.11 **
Plane Motion of a Particle Relative to a
Rotating Frame. Coriolis Acceleration

**
*15.12 **
Motion about a Fixed Point 984

**
*15.13 **
General Motion 987

**
*15.14 **
Three-Dimensional Motion of a Particle Relative
to a Rotating Frame. Coriolis Acceleration

**
*15.15 **
Frame of Reference in General Motion

Review and Summary

Review Problems

Computer Problems

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**
Chapter 16 Plane Motion of Rigid Bodies:
Forces and Accelerations **

**
16.1 **
Introduction

**
16.2 **
Equations of Motion for a Rigid Body

**
16.3 **
Angular Momentum of a Rigid Body in Plane Motion

**
16.4 **
Plane Motion of a Rigid Body. Dâ€™Alembertâ€™s Principle

**
*16.5 **
A Remark on the Axioms of the Mechanics of Rigid
Bodies

**
16.6 **
Solution of Problems Involving the Motion of a Rigid Body

**
16.7 **
Systems of Rigid Bodies

**
16.8 **
Constrained Plane Motion

Review and Summary

Review Problems

Computer Problems 1079

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**

**
Chapter 17 Plane Motion of Rigid Bodies: Energy
and Momentum Methods **

**
17.1 **
Introduction

**
17.2 **
Principle of Work and Energy for a Rigid Body

**
17.3 **
Work of Forces Acting on a Rigid Body

**
17.4 **
Kinetic Energy of a Rigid Body in Plane Motion

**
17.5 **
Systems of Rigid Bodies

**
17.6 **
Conservation of Energy

**
17.7 **
Power

**
17.8 **
Principle of Impulse and Momentum for the Plane Motion of a Rigid Body

**
17.9 **
Systems of Rigid Bodies

**
17.10 **
Conservation of Angular Momentum

**
17.11 **
Impulsive Motion

**
17.12 **
Eccentric Impact

Review and Summary

Review Problems

Computer Problems

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**

**
Chapter 18 Kinetics of Rigid Bodies in Three
Dimensions**

**
*18.1 **
Introduction

**
*18.2 **
Angular Momentum of a Rigid Body in Three
Dimensions

**
*18.3 **
Application of the Principle of Impulse and
Momentum to the Three-Dimensional Motion of a Rigid Body

**
*18.4 **
Kinetic Energy of a Rigid Body in Three
Dimensions

**
*18.5 **
Motion of a Rigid Body in Three Dimensions

**
*18.6 **
Eulerâ€™s Equations of Motion. Extension of
Dâ€™Alembertâ€™s Principle to the Motion of a Rigid Body in Three Dimensions

**
*18.7 **
Motion of a Rigid Body about a Fixed Point

**
*18.8 **
Rotation of a Rigid Body about a Fixed Axis

**
*18.9 **
Motion of a Gyroscope. Eulerian Angles

**
*18.10 **
Steady Precession of a Gyroscope

**
*18.11 **
Motion of an Axisymmetrical Body under No Force

Review and Summary

Review Problems

Computer Problems

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**
Chapter 19 Mechanical Vibrations **

**
19.1 **
Introduction

**
Vibrations without Damping**

**
19.2 **
Free Vibrations of Particles. Simple Harmonic Motion

**
19.3 **
Simple Pendulum (Approximate Solution)

**
*19.4 **
Simple Pendulum (Exact Solution)

**
19.5 **
Free Vibrations of Rigid Bodies

**
19.6 **
Application of the Principle of Conservation of Energy

**
19.7 **
Forced Vibrations

**
Damped Vibrations **

**
*19.8 **
Damped Free Vibrations

**
*19.9 **
Damped Forced Vibrations

**
*19.10 **
Electrical Analogues

Review and Summary

Review Problems

Computer Problems

Appendix A Some Useful Definitions and Properties of Vector Algebra

Appendix B Moments of Inertia of Masses

Appendix C Fundamentals of Engineering Examination

Photo Credits

Index

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