Elements of Mechanics

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Summary

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.

Table of Contents

Mechanics
Physics and Measurement
Kinematics in One Dimension
More Kinematics in One Dimension
Still More Kinematics in One Dimension
Vectors
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
Collisions
Completely Inelastic Collisions
Rotation
Rotation and Translation
Introduction to Rotational Dynamics
Mo’ Moments of Inertia
Moment of Inertia Theorems
Torque
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
Epilogue

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
Index

Author Bio(s)

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.

Editorial Reviews

"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