**Contents**

**12 Kinematics of a Particle**

12.1 Introduction

12.2 Rectilinear Kinematics: Continuous Motion

12.3 Rectilinear Kinematics: Erratic Motion

12.4 General Curvilinear Motion

12.5 Curvilinear Motion: Rectangular Components

12.6 Motion of a Projectile

12.7 Curvilinear Motion: Normal and Tangential Components

12.8 Curvilinear Motion: Cylindrical Components

12.9 Absolute Dependent Motion Analysis of Two Particles

12.10 Relative-Motion of Two Particles Using Translating Axes

**13 Kinetics of a Particle: Force and Acceleration**

13.1 Newton’s Second Law of Motion

13.2 The Equation of Motion

13.3 Equation of Motion for a System of Particles

13.4 Equations of Motion: Rectangular Coordinates

13.5 Equations of Motion: Normal and Tangential Coordinates

13.6 Equations of Motion: Cylindrical Coordinates

*13.7 Central-Force Motion and Space Mechanics

**14 Kinetics of a Particle: Work and Energy**

14.1 The Work of a Force

14.2 Principle of Work and Energy

14.3 Principle of Work and Energy for a System of Particles

14.4 Power and Efficiency

14.5 Conservative Forces and Potential Energy

14.6 Conservation of Energy

**15 Kinetics of a Particle: Impulse and Momentum**

15.1 Principle of Linear Impulse and Momentum

15.2 Principle of Linear Impulse and Momentum for a System of Particles

15.3 Conservation of Linear Momentum for a System of Particles

15.4 Impact

15.5 Angular Momentum

15.6 Relation Between Moment of a Force and Angular Momentum

15.7 Principle of Angular Impulse and Momentum

15.8 Steady Flow of a Fluid Stream

*15.9 Propulsion with Variable Mass

**16 Planar Kinematics of a Rigid Body**

16.1 Planar Rigid-Body Motion

16.2 Translation

16.3 Rotation about a Fixed Axis

16.4 Absolute Motion Analysis

16.5 Relative-Motion Analysis: Velocity

16.6 Instantaneous Center of Zero Velocity

16.7 Relative-Motion Analysis: Acceleration

16.8 Relative-Motion Analysis using Rotating Axes

**17 Planar Kinetics of a Rigid Body: Force and Acceleration**

17.1 Mass Moment of Inertia

17.2 Planar Kinetic Equations of Motion

17.3 Equations of Motion: Translation

17.4 Equations of Motion: Rotation about a Fixed Axis

17.5 Equations of Motion: General Plane Motion

**18 Planar Kinetics of a Rigid Body: Work and Energy**

18.1 Kinetic Energy

18.2 The Work of a Force

18.3 The Work of a Couple Moment

18.4 Principle of Work and Energy

18.5 Conservation of Energy

**19 Planar Kinetics of a Rigid Body: Impulse and Momentum**

19.1 Linear and Angular Momentum

19.2 Principle of Impulse and Momentum

19.3 Conservation of Momentum

*19.4 Eccentric Impact

**20 Three-Dimensional Kinematics of a Rigid Body**

20.1 Rotation About a Fixed Point

*20.2 The Time Derivative of a Vector Measured from Either a Fixed or Translating-Rotating System

20.3 General Motion

*20.4 Relative-Motion Analysis Using Translating and Rotating Axes

**21 Three-Dimensional Kinetics of a Rigid Body**

*21.1 Moments and Products of Inertia 21.2 Angular Momentum

21.3 Kinetic Energy

*21.4 Equations of Motion

*21.5 Gyroscopic Motion

21.6 Torque-Free Motion

**22 Vibrations**

*22.1 Undamped Free Vibration

*22.3 Undamped Forced Vibration

*22.4 Viscous Damped Free Vibration

*22.5 Viscous Damped Forced Vibration

*22.6 Electrical Circuit Analogs

A Mathematical Expressions

B Vector Analysis

C The Chain Rule

Fundamental Problems Partial

Solutions and Answers