1st Edition

Elements of Mechanics

By P.F. Kelly Copyright 2014
    444 Pages 163 B/W Illustrations
    by CRC Press

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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.

    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


    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.

    "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