Engineering Mechanics

Part I Dynamics of Particles 1


1 Introduction to Dynamics 3


1/1 History and Modern Applications 3


1/2 Basic Concepts 4


1/3 Newton's Laws 5


1/4 Units 6


1/5 Gravitation 7


1/6 Dimensions 10


1/7 Solving Problems in Dynamics 11


1/8 Chapter Review 13


2 Kinematics of Particles 16


2/1 Introduction 16


2/2 Rectilinear Motion 17


2/3 Plane Curvilinear Motion 25


2/4 Rectangular Coordinates (x-y) 27


2/5 Normal and Tangential Coordinates (n-t) 32


2/6 Polar Coordinates (r-?) 37


2/7 Space Curvilinear Motion 42


2/8 Relative Motion (Translating Axes) 47


2/9 Constrained Motion of Connected Particles 51


2/10 Chapter Review 54


3 Kinetics of Particles 56


3/1 Introduction 56


Section A Force, Mass, and Acceleration 57


3/2 Newton's Second Law 57


3/3 Equation of Motion and Solution of Problems 60


3/4 Rectilinear Motion 62


3/5 Curvilinear Motion 67


Section B Work and Energy 71


3/6 Work and Kinetic Energy 71


3/7 Potential Energy 81


Section C Impulse and Momentum 87


3/8 Introduction 87


3/9 Linear Impulse and Linear Momentum 87


3/10 Angular Impulse and Angular Momentum 93


Section D Special Applications 99


3/11 Introduction 99


3/12 Impact 99


3/13 Central-Force Motion 105


3/14 Relative Motion 112


3/15 Chapter Review 118


4 Kinetics of Systems of Particles 119


4/1 Introduction 119


4/2 Generalized Newton's Second Law 120


4/3 Work-Energy 121


4/4 Impulse-Momentum 122


4/5 Conservation of Energy and Momentum 126


4/6 Steady Mass Flow 132


4/7 Variable Mass 138


4/8 Chapter Review 144


Part II Dynamics of Rigid Bodies 145


5 Plane Kinematics of Rigid Bodies 147


5/1 Introduction 147


5/2 Rotation 149


5/3 Absolute Motion 154


5/4 Relative Velocity 158


5/5 Instantaneous Center of Zero Velocity 165


5/6 Relative Acceleration 168


5/7 Motion Relative to Rotating Axes 173


5/8 Chapter Review 183


6 Plane Kinetics of Rigid Bodies 184


6/1 Introduction 184


Section A Force, Mass, and Acceleration 186


6/2 General Equations of Motion 186


6/3 Translation 192


6/4 Fixed-Axis Rotation 196


6/5 General Plane Motion 199


Section B Work and Energy 205


6/6 Work-Energy Relations 205


6/7 Acceleration from Work-Energy; Virtual Work 213


Section C Impulse and Momentum 217


6/8 Impulse-Momentum Equations 217


6/9 Chapter Review 225


7 Introduction to Three-Dimensional Dynamics of Rigid Bodies 226


7/1 Introduction 226


Section A Kinematics 227


7/2 Translation 227


7/3 Fixed-Axis Rotation 227


7/4 Parallel-Plane Motion 228


7/5 Rotation about a Fixed Point 228


7/6 General Motion 234


Section B Kinetics 240


7/7 Angular Momentum 240


7/8 Kinetic Energy 243


7/9 Momentum and Energy Equations of Motion 246


7/10 Parallel-Plane Motion 248


7/11 Gyroscopic Motion: Steady Precession 250


7/12 Chapter Review 259


8 Vibration and Time Response 260


8/1 Introduction 260


8/2 Free Vibration of Particles 261


8/3 Forced Vibration of Particles 270


8/4 Vibration of Rigid Bodies 278


8/5 Energy Methods 282


8/6 Chapter Review 286


Appendix A Area Moments of Inertia 287


Appendix B Mass Moments of Inertia 288


B/1 Mass Moments of Inertia about an Axis 288


B/2 Products of Inertia 296


Appendix C Selected Topics of Mathematics 302


C/1 Introduction 302


C/2 Plane Geometry 302


C/3 Solid Geometry 303


C/4 Algebra 303


C/5 Analytic Geometry 304


C/6 Trigonometry 304


C/7 Vector Operations 305


C/8 Series 308


C/9 Derivatives 308


C/10 Integrals 309


C/11 Newton's Method for Solving Intractable Equations 312


C/12 Selected Techniques for Numerical Integration 314


Appendix D Useful Tables 317


Table D/1 Physical Properties 317


Table D/2 Solar System Constants 318


Table D/3 Properties of Plane Figures 319


Table D/4 Properties of Homogeneous Solids 321


Table D/5 Conversion Factors; SI Units 325


Problems P-1


Index I-1


Problem Answers PA-1