Preface

xvii

List of Symbols

xxiii

Chapter 1

INTRODUCTION

1.1

What Is Mechanics?

2

1.2

Fundamental Concepts and Principles

2

1.3

Systems of Units

5

1.4

Conversion from One System of Units to Another

10

1.5

Method of Problem Solution

12

1.6

Numerical Accuracy

13

Chapter 2

STATICS OF PARTICLES

2.1

Introduction

16

Forces in a Plane

16

2.2

Force on a Particle. Resultant of Two Forces

16

2.3

Vectors

17

2.4

Addition of Vectors

18

2.5

Resultant of Several Concurrent Forces

20

2.6

Resolution of a Force into Components

21

2.7

Rectangular Components of a Force. Unit Vectors

27

2.8

Addition of Forces by Summing x and y Components

30

2.9

Equilibrium of a Particle

35

2.1

Newton's First Law of Motion

36

2.11

Problems Involving the Equilibrium of a Particle.

Free-Body Diagrams

36

Forces in Space

45

2.12

Rectangular Components of a Force in Space

45

2.13

Force Defined by Its Magnitude and Two Points

on Its Line of Action

48

2.14

Addition of Concurrent Forces in Space

49

2.15

Equilibrium of a Particle in Space

57

Review and Summary for Chapter 2

64

Review Problems

67

Chapter 3

RIGID BODIES: EQUIVALENT SYSTEMS OF FORCES

71

3.1

Introduction

72

3.2

External and Internal Forces

72

3.3

Principle of Transmissibility. Equivalent Forces

73

3.4

Vector Product of Two Vectors

75

3.5

Vector Products Expressed in Terms of Rectangular Components

77

3.6

Moment of a Force about a Point

79

3.7

Varignon's Theorem

81

3.8

Rectangular Components of the Moment of a Force

81

3.9

Scalar Product of Two Vectors

91

3.1

Mixed Triple Product of Three Vectors

93

3.11

Moment of a Force about a Given Axis

95

3.12

Moment of a Couple

105

3.13

Equivalent Couples

106

3.14

Addition of Couples

108

3.15

Couples Can Be Represented by Vectors

108

3.16

Resolution of a Given Force Into a Force at O

and a Couple

109

3.17

Reduction of a System of Forces to One Force

and One Couple

120

3.18

Equivalent Systems of Forces

122

3.19

Equipollent Systems of Vectors

122

3.2

Further Reduction of a System of Forces

123

*3.21

Reduction of a System of Forces to a Wrench

125

Review and Summary for Chapter 3

144

Review Problems

149

Chapter 4

EQUILIBRIUM OF RIGID BODIES

4.1

Introduction

154

4.2

Free-Body Diagram

155

Equilibrium in Two Dimensions

156

4.3

Reactions at Supports and Connections

for a Two-Dimensional Structure

156

4.4

Equilibrium of a Rigid Body in Two Dimensions

158

4.5

Statically Indeterminate Reactions. Partial Constraints

160

4.6

Equilibrium of a Two-Force Body

177

4.7

Equilibrium of a Three-Force Body

178

Equilibrium in Three Dimensions

185

4.8

Equilibrium of a Rigid Body in Three Dimensions

185

4.9

Reactions at Supports and Connections

for a Three-Dimensional Structure

185

Review and Summary for Chapter 4

202

Review Problems

204

Chapter 5

DISTRIBUTED FORCES: CENTROIDS AND CENTERS OF GRAVITY

5.1

Introduction

210

Areas and Lines

210

5.2

Center of Gravity of a Two-Dimensional Body

210

5.3

Centroids of Areas and Lines

212

5.4

First Moments of Areas and Lines

213

5.5

Composite Plates and Wires

216

5.6

Determination of Centroids by Integration

227

5.7

Theorems of Pappus-Guldinus

229

*5.8

Distributed Loads on Beams

240

*5.9

Forces on Submerged Surfaces

241

Volumes

251

5.1

Center of Gravity of a Three-Dimensional Body.

Centroid of a Volume

251

5.11

Composite Bodies

254

5.12

Determination of Centroids of Volumes by Integration

254

Review and Summary for Chapter 5

266

Review Problems

270

Chapter 6

ANALYSIS OF STRUCTURES

6.1

Introduction

275

Trusses

276

6.2

Definition of a Truss

276

6.3

Simple Trusses

278

6.4

Analysis of Trusses by the Method of Joints

279

*6.5

Joints under Special Loading Conditions

281

*6.6

Space Trusses

283

6.7

Analysis of Trusses by the Method of Sections

293

*6.8

Trusses Made of Several Simple Trusses

294

Frames and Machines

305

6.9

Structures Containing Multiforce Members

305

6.1

Analysis of a Frame

305

6.11

Frames Which Cease to Be Rigid When Detached

from Their Supports

306

6.12

Machines

321

Review and Summary for Chapter 6

333

Review Problems

336

Chapter 7

FORCES IN BEAMS AND CABLES

*7.1

Introduction

342

*7.2

Internal Forces in Members

342

Beams

349

*7.3

Various Types of Loading and Support

349

*7.4

Shear and Bending Moment in a Beam

350

*7.5

Shear and Bending-Moment Diagrams

352

*7.6

Relations among Load, Shear, and Bending Moment

360

Cables

371

*7.7

Cables with Concentrated Loads

371

*7.8

Cables with Distributed Loads

372

*7.9

Parabolic Cable

373

*7.10

Catenary

382

Review and Summary for Chapter 7

390

Review Problems

393

Chapter 8

FRICTION

8.1

Introduction

397

8.2

The Laws of Dry Friction. Coefficients of Friction

397

8.3

Angles of Friction

400

8.4

Problems Involving Dry Friction

401

8.5

Wedges

417

8.6

Square-Threaded Screws

417

*8.7

Journal Bearings. Axle Friction

426

*8.8

Thrust Bearings. Disk Friction

428

*8.9

Wheel Friction. Rolling Resistance

429

*8.10

Belt Friction

436

Review and Summary for Chapter 8

447

Review Problems

450

Chapter 9

DISTRIBUTED FORCES: MOMENTS OF INERTIA

9.1

Introduction

456

Moments of Inertia of Areas

457

9.2

Second Moment, or Moment of Inertia, of an Area

457

9.3

Determination of the Moment of Inertia of an Area

by Integration

458

9.4

Polar Moment of Inertia

459

9.5

Radius of Gyration of an Area

460

9.6

Parallel-Axis Theorem

467

9.7

Moments of Inertia of Composite Areas

468

*9.8

Product of Inertia

481

*9.9

Principal Axes and Principal Moments of Inertia

482

*9.10

Mohr's Circle for Moments and Products of Inertia

490

Moments of Inertia of Masses

496

9.11

Moment of Inertia of a Mass

496

9.12

Parallel-Axis Theorem

498

9.13

Moments of Inertia of Thin Plates

499

9.14

Determination of the Moment of Inertia of a Three-Dimensional Body by Integration

500

9.15

Moments of Inertia of Composite Bodies

500

*9.16

Moment of Inertia of a Body with Respect to an Arbitrary Axis through O. Mass Products of Inertia

515

*9.17

Ellipsoid of Inertia. Principal Axes of Inertia

516

*9.18

Determination of the Principal Axes and Principal Moments

of Inertia of a Body of Arbitrary Shape

518

Review and Summary for Chapter 9

529

Review Problems

535

Chapter 10

METHOD OF VIRTUAL WORK

*10.1

Introduction

540

*10.2

Work of a Force

540

*10.3

Principle of Virtual Work

543

*10.4

Applications of the Principle of Virtual Work

544

*10.5

Real Machines. Mechanical Efficiency

546

*10.6

Work of a Force during a Finite Displacement

560

*10.7

Potential Energy

562

*10.8

Potential Energy and Equilibrium

563

*10.9

Stability of Equilibrium

564

Review and Summary for Chapter 10

574

Review Problems

577

Chapter 11

KINEMATICS OF PARTICLES

581

11.1

Introduction to Dynamics

582

Rectilinear Motion of Particles

583

11.2

Position, Velocity, and Acceleration

583

11.3

Determination of the Motion of a Particle

587

11.4

Uniform Rectilinear Motion

596

11.5

Uniformly Accelerated Rectilinear Motion

597

11.6

Motion of Several Particles

598

*11.7

Graphical Solution of Rectilinear-Motion Problems

610

*11.8

Other Graphical Methods

611

Curvilinear Motion of Particles

621

11.9

Position Vector, Velocity, and Acceleration

621

11.1

Derivatives of Vector Functions

623

11.11

Rectangular Components of Velocity and Acceleration

625

11.12

Motion Relative to a Frame in Translation

626

11.13

Tangential and Normal Components

643

11.14

Radial and Transverse Components

646

Review and Summary for Chapter 11

659

Review Problems

663

Chapter 12

KINETICS OF PARTICLES: NEWTON'S SECOND LAW

12.1

Introduction

668

12.2

Newton's Second Law of Motion

669

12.3

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

670

12.4

Systems of Units

671

12.5

Equations of Motion

673

12.6

Dynamic Equilibrium

675

12.7

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

695

12.8

Equations of Motion in Terms of Radial and Transverse Components

696

12.9

Motion under a Central Force. Conservation of Angular Momentum

697

12.1

Newton's Law of Gravitation

698

*12.11

Trajectory of a Particle under a Central Force

707

*12.12

Application to Space Mechanics

708

*12.13

Kepler's Laws of Planetary Motion

711

Review and Summary for Chapter 12

720

Review Problems

724

Chapter 13

KINETICS OF PARTICLES: ENERGY AND MOMENTUM METHODS

13.1

Introduction

730

13.2

Work of a Force

730

13.3

Kinetic Energy of a Particle. Principle of Work and Energy

734

13.4

Applications of the Principle of Work and Energy

736

13.5

Power and Efficiency

737

13.6

Potential Energy

755

*13.7

Conservative Forces

757

13.8

Conservation of Energy

758

13.9

Motion under a Conservative Central Force. Application to Space Mechanics

760

13.1

Principle of Impulse and Momentum

779

13.11

Impulsive Motion

782

13.12

Impact

794

13.13

Direct Central Impact

794

13.14

Oblique Central Impact

797

13.15

Problems Involving Energy and Momentum

800

Review and Summary for Chapter 13

816

Review Problems

822

Chapter 14

SYSTEMS OF PARTICLES

14.1

Introduction

828

14.2

Application of Newton's Laws to the Motion of a System of Particles. Effective Forces

828

14.3

Linear and Angular Momentum of a System of Particles

831

14.4

Motion of the Mass Center of a System of Particles

832

14.5

Angular Momentum of a System of Particles about Its Mass Center

834

14.6

Conservation of Momentum for a System of Particles

836

14.7

Kinetic Energy of a System of Particles

845

14.8

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

847

14.9

Principle of Impulse and Momentum for a System of Particles

847

*14.10

Variable Systems of Particles

858

*14.11

Steady Stream of Particles

858

*14.12

Systems Gaining or Losing Mass

861

Review and Summary for Chapter 14

876

Review Problems

880

Chapter 15

KINEMATICS OF RIGID BODIES

15.1

Introduction

886

15.2

Translation

888

15.3

Rotation about a Fixed Axis

889

15.4

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

892

15.5

General Plane Motion

902

15.6

Absolute and Relative Velocity in Plane Motion

904

15.7

Instantaneous Center of Rotation in Plane Motion

915

15.8

Absolute and Relative Acceleration in Plane Motion

926

*15.9

Analysis of Plane Motion in Terms of a Parameter

928

15.1

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

940

15.11

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

942

*15.12

Motion about a Fixed Point

953

*15.13

General Motion

956

*15.14

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

967

*15.15

Frame of Reference in General Motion

968

Review and Summary for Chapter 15

979

Review Problems

986

Chapter 16

PLANE MOTION OF RIGID BODIES: FORCES AND ACCELERATIONS

16.1

Introduction

991

16.2

Equations of Motion for a Rigid Body

992

16.3

Angular Momentum of a Rigid Body in Plane Motion

993

16.4

Plane Motion of a Rigid Body. D'Alembert's Principle

994

*16.5

A Remark on the Axioms of the Mechanics of Rigid Bodies

995

16.6

Solution of Problems Involving the Motion of a Rigid Body

996

16.7

Systems of Rigid Bodies

997

16.8

Constrained Plane Motion

1016

Review and Summary for Chapter 16

1039

Review Problems

1041

Chapter 17

PLANE MOTION OF RIGID BODIES: ENERGY AND MOMENTUM METHODS

17.1

Introduction

1046

17.2

Principle of Work and Energy for a Rigid Body

1046

17.3

Work of Forces Acting on a Rigid Body

1047

17.4

Kinetic Energy of a Rigid Body in Plane Motion

1048

17.5

Systems of Rigid Bodies

1049

17.6

Conservation of Energy

1050

17.7

Power

1051

17.8

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

1068

17.9

Systems of Rigid Bodies

1071

17.1

Conservation of Angular Momentum

1071

17.11

Impulsive Motion

1084

17.12

Eccentric Impact

1084

Review and Summary for Chapter 17

1098

Review Problems

1102

Chapter 18

KINETICS OF RIGID BODIES IN THREE DIMENSIONS

*18.1

Introduction

1107

*18.2

Angular Momentum of a Rigid Body in Three Dimensions

1108

*18.3

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

1112

*18.4

Kinetic Energy of a Rigid Body in Three Dimensions

1113

*18.5

Motion of a Rigid Body in Three Dimensions

1126

*18.6

Euler's Equations of Motion. Extension of d'Alembert's Principle to the Motion of a Rigid Body in Three Dimensions

1127

*18.7

Motion of a Rigid Body about a Fixed Point

1128

*18.8

Rotation of a Rigid Body about a Fixed Axis

1129

*18.9

Motion of a Gyroscope. Eulerian Angles

1144

*18.10

Steady Precession of a Gyroscope

1146

*18.11

Motion of an Axisymmetrical Body under No Force

1147

Review and Summary for Chapter 18

1160

Review Problems

1165

Chapter 19

MECHANICAL VIBRATIONS

19.1

Introduction

1172

Vibrations without Damping

1172

19.2

Free Vibrations of Particles. Simple Harmonic Motion

1172

19.3

Simple Pendulum (Approximate Solution)

1176

*19.4

Simple Pendulum (Exact Solution)

1177

19.5

Free Vibrations of Rigid Bodies

1186

19.6

Application of the Principle of Conservation of Energy

1198

19.7

Forced Vibrations

1209

Damped Vibrations

1219

*19.8

Damped Free Vibrations

1219

*19.9

Damped Forced Vibrations

1222

*19.10

Electrical Analogues

1223

Review and Summary for Chapter 19

1234

Review Problems

1239

Index

1243

Answers to Problems

1255