Vector Mechanics for Engineers Beer & Johnston  
About the Book 

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. 

FreeBody 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 
FreeBody Diagram 
155 
Equilibrium in Two Dimensions 
156 

4.3 
Reactions at Supports and Connections 

for a TwoDimensional 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 TwoForce Body 
177 
4.7 
Equilibrium of a ThreeForce 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 ThreeDimensional 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 TwoDimensional 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 PappusGuldinus 
229 
*5.8 
Distributed Loads on Beams 
240 
*5.9 
Forces on Submerged Surfaces 
241 
Volumes 
251 

5.1 
Center of Gravity of a ThreeDimensional 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 BendingMoment 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 
SquareThreaded 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 
ParallelAxis 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 
ParallelAxis Theorem 
498 
9.13 
Moments of Inertia of Thin Plates 
499 
9.14 
Determination of the Moment of Inertia of a ThreeDimensional 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 RectilinearMotion 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 
WorkEnergy 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 
ThreeDimensional 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 ThreeDimensional 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 
feedback form 
permissions 
international 
locate your campus rep 
request a review copy
digital solutions 
publish with us 
customer service 
mhhe home
Copyright ©2001 The McGrawHill Companies.
Any use is subject to the
Terms of Use and Privacy Policy.
McGrawHill Higher Education is one of the many fine businesses of the
The McGrawHill Companies.