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Engineering Dynamics
Cho W.S. To
www.morganclaypool.com
ISBN: 9781681733708 paperback
ISBN: 9781681733715 ebook
ISBN: 9781681733722 hardcover
DOI 10.2200/S00853ED1V01Y201805MEC015
A Publication in the Morgan & Claypool Publishers series
SYNTHESIS LECTURES ON MECHANICAL ENGINEERING
Lecture #15
Series ISSN
Print 2573-3168 Electronic 2573-3176
Engineering Dynamics
Cho W.S. To
University of Nebraska, Lincoln
SYNTHESIS LECTURES ON MECHANICAL ENGINEERING #15
C
M
&
cLaypoolMor
gan publishers
&
ABSTRACT
Engineering Dynamics is an introductory textbook covering the kinematics and dynamics of par-
ticles, systems of particles, and kinematics and dynamics of rigid bodies. It has been developed
from lecture notes given by the author since 1982. It includes sufficient topics normally covered
in a single-semester three credit hour course taken by sophomores in an undergraduate degree
program majoring in various engineering disciplines.
e primary focus of the book is on kinematics and dynamics of particles, kinematics and
dynamics of systems of particles, and kinematics and dynamics of rigid bodies in two- and three-
dimensional spaces. It aims at providing a short book, relative to many available in literature,
but with detailed solutions to representative examples. Exercise questions are included.
KEYWORDS
kinematics, dynamics, particles, systems of particles, rigid bodies
vii
Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Classical Water Molecule and Ozone Molecule . . . . . . . . . . . . . . . . . . . 1
1.1.2 Newton’s Cradle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Simple Toy Rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.4 Falling Cat Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Organization of Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2
Kinematics of Particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Rectilinear Motion of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Uniform and Uniformly Accelerated Rectilinear Motion . . . . . . . . . . . . . . . . . 12
2.4 Curvilinear Motion of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 Motion in Rectangular Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6 Motion in Tangential and Normal Components . . . . . . . . . . . . . . . . . . . . . . . 21
2.7 Motion in Radial and Transverse Components . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3
Dynamics of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Newton’s Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Equations of Motion and Dynamic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Equations of Motion in Radial and Transverse Components . . . . . . . . . . . . . . 32
3.5 Momentum and Rate of Change of Momentum of a Particle . . . . . . . . . . . . . 39
3.6 Angular Momentum and Rate of Change of Angular Momentum of a
Particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
viii
3.7 Differential Equation for Trajectory of a Particle Under a Central Force . . . . 41
3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4
Work and Energy of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Work of a Force and Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Potential Energy and Strain Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4 Kinetic Energy of a Particle and Principle of Work and Energy . . . . . . . . . . . 50
4.5 Principle of Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.6 Power and Mechanical Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5
Impulse, Momentum, and Impact of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Principle of Impulse and Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3 Impulsive Motion and Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.1 Direct Central Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.2 Oblique Central Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.3 Constrained Oblique Central Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.4 Consideration of Energy and Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6
Systems of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2 Newton’s Laws of Motion for Systems of Particles . . . . . . . . . . . . . . . . . . . . . . 85
6.3 Linear and Angular Momentum of a System of Particles . . . . . . . . . . . . . . . . 88
6.4 Motion of Mass Center of a System of Particles . . . . . . . . . . . . . . . . . . . . . . . . 89
6.5 Angular Momentum of a System of Particles About its Mass Center . . . . . . . 91
6.6 Conservation of Momentum for a System of Particles . . . . . . . . . . . . . . . . . . . 93
6.7 Work Energy Principle for a System of Particles . . . . . . . . . . . . . . . . . . . . . . . 93
6.8 Conservation of Energy for a System of Particles . . . . . . . . . . . . . . . . . . . . . . . 94
6.9 Principle of Impulse and Momentum for a System of Particles . . . . . . . . . . . . 95
6.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
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