This book is based on the author’s lecture notes for his Introductory Newtonian Mechanics course at the Hellenic Naval Academy. In order to familiarize students with the use of several basic mathematical tools, such as vectors, differential operators and differential equations, it first presents the elements of vector analysis that are needed in the subsequent chapters. Further, the Mathematical Supplement at the end of the book offers a brief introduction to the concepts of differential calculus mentioned.
The main text is divided into three parts, the first of which presents the mechanics of a single particle from both the kinetic and the dynamical perspectives. The second part then focuses on the mechanics of more complex structures, such as systems of particles, rigid bodies and ideal fluids, while the third part consists of 60 fully solved problems.
Though chiefly intended as a primary text for freshman-level physics courses, the book can also be used as a supplemental (tutorial) resource for introductory courses on classical mechanics for physicists and engineers
Author(s): Costas J. Papachristou
Publisher: Springer
Year: 2020
Language: English
Pages: 280
City: Cham
Preface
Contents
1 Vectors
1.1 Basic Notions
1.2 Rectangular Components of a Vector
1.3 Position Vectors
1.4 Scalar (“Dot”) Product of Two Vectors
1.5 Vector (“Cross”) Product of Two Vectors
References
2 Kinematics
2.1 Rectilinear Motion
2.2 Special Types of Rectilinear Motion
2.3 Curvilinear Motion in Space
2.4 Change of Speed
2.5 Motion with Constant Acceleration
2.6 Tangential and Normal Components
2.7 Circular Motion
2.8 Relative Motion
References
3 Dynamics of a Particle
3.1 The Law of Inertia
3.2 Momentum, Force, and Newton’s 2nd and 3rd Laws
3.3 Force of Gravity
3.4 Frictional Forces
3.5 Systems with Variable Mass
3.6 Tangential and Normal Components of Force
3.7 Angular Momentum and Torque
3.8 Central Forces
References
4 Work and Energy
4.1 Introduction
4.2 Work of a Force
4.3 Kinetic Energy and the Work-Energy Theorem
4.4 Potential Energy and Conservative Forces
4.5 Conservation of Mechanical Energy
4.6 Examples of Conservative Forces
4.7 Kinetic Friction as a Non-Conservative Force
References
5 Oscillations
5.1 Simple Harmonic Motion (SHM)
5.2 Force in SHM
5.3 Energy Relations
5.4 Oscillations of a Mass-Spring System
5.5 Oscillation of a Pendulum
5.6 Differential Equation of SHM
References
6 Systems of Particles
6.1 Center of Mass of a System of Particles
6.2 Newton’s Second Law and Conservation of Momentum
6.3 Angular Momentum of a System of Particles
6.4 Kinetic Energy of a System of Particles
6.5 Total Mechanical Energy of a System of Particles
6.6 Collisions
References
7 Rigid-Body Motion
7.1 Rigid Body
7.2 Center of Mass of a Rigid Body
7.3 Revolution of a Particle About an Axis
7.4 Angular Momentum of a Rigid Body
7.5 Rigid-Body Equations of Motion
7.6 Moment of Inertia and the Parallel-Axis Theorem
7.7 Conservation of Angular Momentum
7.8 Equilibrium of a Rigid Body
7.9 Kinetic and Total Mechanical Energy
7.10 Rolling Bodies
7.11 The Role of Static Friction in Rolling
7.12 Gyroscopic Motion
References
8 Elementary Fluid Mechanics
8.1 Ideal Fluid
8.2 Hydrostatic Pressure
8.3 Fundamental Equation of Hydrostatics
8.4 Units of Pressure
8.5 Communicating Vessels
8.6 Pascal’s Principle
8.7 Archimedes’ Principle
8.8 Dynamics of the Submerged Body
8.9 Equilibrium of a Floating Body
8.10 Fluid Flow
8.11 Equation of Continuity
8.12 Bernoulli’s Equation
8.13 Horizontal Flow
Reference
Appendix A Composition of Forces Acting in Space
Appendix B Some Theorems on the Center of Mass
Appendix C Table of Moments of Inertia
Appendix D Principal Axes of Rotation
Appendix E Variation of Pressure in the Atmosphere
Appendix F Proof of Bernoulli’s Equation
Solved Problems
Mathematical Supplement
1. Differential of a Function
2. Differential Operators
3. Geometrical Significance of the Differential
4. Derivative of a Composite Function
5. Differential Equations
Basic Integrals
Index
