Elements of Mechanics: 1st Edition (Hardback) book cover

Elements of Mechanics

1st Edition

By P.F. Kelly

CRC Press

444 pages | 163 B/W Illus.

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pub: 2014-05-07
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The first volume in a three-part series, Elements of Mechanics provides a rigorous calculus-based introduction to classical physics. It considers diverse phenomena in a systematic manner and emphasises the development of consistent and coherent models guided by symmetry considerations and the application of general principles. Modern developments colour the presentation and are alluded to when most relevant, but the focus remains firmly on the classical formulations and model descriptions of particular physical systems.

The specific topics covered in Elements of Mechanics include:

  • Kinematics in one and more dimensions in Cartesian and polar coordinates
  • Dynamics, Galilean Relativity and Newton’s Laws of Motion
  • Energetics, work–energy theorems, conservative forces, and potential energy
  • Impulse and momentum, systems of particles and rigid bodies
  • Rigid body rotational kinematics, dynamics, and energetics
  • Statics
  • Newton’s Law of Universal Gravitation

The book prepares undergraduate students majoring in the natural sciences and engineering for intermediate and advanced classes in their disciplines which rely upon this foundational material. It also supplies a comprehensive review in preparation for graduate or professional exams. Therefore, the series is structured in such manner that the second and third books, Properties of Materials and Electricity and Magnetism, follow upon the first, but may be read independently of each other. Written in a conversational and accessible style, the material is presented in standard, canonical sequence. Worked examples and collections of problems serve to illustrate and illuminate subject material in each volume.


"This textbook is unique in many respects. It gives the reader a sense of being part of a lively and personal conversation about physics, engaging your attention from the first page. Advanced mathematical concepts are introduced as a prelude to further study while still maintaining the appropriate level for a first-year calculus-based course. But the most innovative feature of this text is the emphasis on thinking and reasoning about physics starting from basic principles. As a teacher, I often have the goal of developing critical analysis skills in my students; this textbook shows the way."

—Dr. Tom Steele, University of Saskatchewan

"In this delightfully fresh take on the well-worn subject of classical Newtonian mechanics, Patrick Kelly adopts the informal approach of a classroom teacher, using a wealth of thoroughly worked examples to illustrate and develop the concepts introduced at each step of the journey on which his readers are taken. The journey actually covers a lot of ground. Starting from basic kinematical notions, such as average velocity, we are eventually led to appreciate ideas (for example, the fact that orbits under an inverse-square law of force are conic sections) that are quite sophisticated at this introductory level.

Students faced with learning, more or less simultaneously, both basic physics and essential mathematical tools, such as calculus, will appreciate the deftness with which Kelly uses each set of ideas to illuminate the other. Readers will quickly warm to his engaging, and distinctively personal style, with its frequent flashes of humour, and will value the depth of understanding afforded both by the many sidelights he offers and by the alternative treatments he gives for many of the examples from complementary points of view. Those who work systematically through the text, and at least a selection of the 428 problems that supplement it, will gain not only the ability to tackle standard problems with confidence but also the sense that this territory is now home turf."

—Ian D. Lawrie, UnifiedGrandTours.org, and author of A Unified Grand Tour of Theoretical Physics, Third Edition

Table of Contents


Physics and Measurement

Kinematics in One Dimension

More Kinematics in One Dimension

Still More Kinematics in One Dimension


Motion in Two and Three Dimensions

Projectile Motion

Circular Motion

Dynamics and Newton’s First Law

Inertia and Newton’s Second and Third Laws

Solving Dynamics Problems Using Newton’s Laws

Ropes and Pulleys

Blocks in Trains and in Contact

Planes and Fancies

Spring Fever

Fact and Friction

Fun with Friction

Cornering: Flat and Banked

Non-Uniform Circular Motion

Drag Forces

Work and Energy

All Work and Some Play

The Work–Energy Theorem

Conservative Forces

Potential Energy

Dynamics from Potential Energy

Total Mechanical Energy

Non-Conservative Forces and Power

Momentum and Impulse

Systems of Particles and Centre of Mass

Seven Amazing Properties of the Centre of Mass


Completely Inelastic Collisions


Rotation and Translation

Introduction to Rotational Dynamics

Mo’ Moments of Inertia

Moment of Inertia Theorems


Torque-y Topics

Pulleys with Rotational Inertia

Angular Momentum

Rolling Motion

Static Equilibrium

Statics: Levers and Ladders

Step It Up

Universal Gravitation

Extended Sources and Energetics

Gravitational Effects and Dynamics

Kepler’s Laws


Mechanics Problems

K Kinematics Problems

D Dynamics Problems

E Energetics Problems

M Momentum and Systems Problems

R Rotation Problems

S Statics Problems

G Gravitation Problems

List of Symbols


About the Author

P.F. Kelly is an associate professor of physics at Ave Maria University in Florida. He previously held a faculty position at North Dakota State University and he undertook post-doctoral studies at the Center for Theoretical Physics, Massachusetts Institute of Technology, and at the Winnipeg Institute for Theoretical Physics, University of Winnipeg. He holds a Ph.D from the University of Toronto. His areas of interest include theoretical, particle, gravitational, mathematical, and computational physics.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Physics