Principles of Mechanics : : Fundamental University Physics.

• Superior document: Advances in Science, Technology and Innovation Series
• Author: Alrasheed, Salma.
• Place / Publishing House: Cham : : Springer International Publishing AG,, 2019.; ©2019.
• Year of Publication: 2019
• Edition: 1st ed.
• Language: English
• Series: Advances in Science, Technology and Innovation Series
• Physical Description: 1 online resource (179 pages)

Table of Contents

• Intro
• Preface
• Contents
• 1 Units and Vectors
• 1.1 Introduction
• 1.2 The SI Units
• 1.3 Conversion Factors
• 1.4 Dimension Analysis
• 1.5 Vectors
• 1.6 Vector Algebra
• 1.6.1 Equality of Two Vectors
• 1.6.2 Addition
• 1.6.3 Negative of a Vector
• 1.6.4 The Zero Vector
• 1.6.5 Subtraction of Vectors
• 1.6.6 Multiplication of a Vector by a Scalar
• 1.6.7 Some Properties
• 1.6.8 The Unit Vector
• 1.6.9 The Scalar (Dot) Product
• 1.6.10 The Vector (Cross) Product
• 1.7 Coordinate Systems
• 1.8 Vectors in Terms of Components
• 1.8.1 Rectangular Unit Vectors
• 1.8.2 Component Method
• 1.9 Derivatives of Vectors
• 1.9.1 Some Rules
• 1.9.2 Gradient, Divergence, and Curl
• 1.10 Integrals of Vectors
• 1.10.1 Line Integrals
• 1.10.2 Independence of Path
• 2 Kinematics
• 2.1 Introduction
• 2.2 Displacement, Velocity, and Acceleration
• 2.2.1 Displacement
• 2.2.2 Average Speed
• 2.2.3 Velocity
• 2.2.4 Speed
• 2.2.5 Acceleration
• 2.3 Motion in Three Dimensions
• 2.3.1 Normal and Tangential Components of Acceleration
• 2.4 Some Applications
• 2.4.1 One-Dimensional Motion with Constant Acceleration
• 2.4.2 Free-Falling Objects
• 2.4.3 Motion in Two Dimensions with Constant Acceleration
• 2.4.4 Projectile Motion
• 2.4.5 Uniform Circular Motion
• 2.4.6 Nonuniform Circular Motion
• 2.5 Relative Velocity
• 2.6 Motion in a Plane Using Polar Coordinates
• 3 Newton's Laws
• 3.1 Introduction
• 3.1.1 The Concept of Force
• 3.1.2 The Fundamental Forces in Nature
• 3.2 Newton's Laws
• 3.2.1 Newton's First Law
• 3.2.2 The Principle of Invariance
• 3.2.3 Mass
• 3.2.4 Newton's Second Law
• 3.2.5 Newton's Third Law
• 3.3 Some Particular Forces
• 3.3.1 Weight
• 3.3.2 The Normal Force
• 3.3.3 Tension
• 3.3.4 Friction
• 3.3.5 The Drag Force
• 3.4 Applying Newton's Laws
• 3.4.1 Uniform Circular Motion.
• 3.4.2 Nonuniform Circular Motion
• 4 Work and Energy
• 4.1 Introduction
• 4.2 Work
• 4.2.1 Work Done by a Constant Force
• 4.2.2 Work Done by Several Forces
• 4.2.3 Work Done by a Varying Force
• 4.3 Kinetic Energy (KE) and the Work-Energy Theorem
• 4.3.1 Work Done by a Spring Force
• 4.3.2 Work Done by the Gravitational Force (Weight)
• 4.3.3 Power
• 4.4 Conservative and Nonconservative Forces
• 4.4.1 Potential Energy
• 4.5 Conservation of Mechanical Energy
• 4.5.1 Changes of the Mechanical Energy of a System due to External Nonconservative Forces
• 4.5.2 Friction
• 4.5.3 Changes in Mechanical Energy due to Internal Nonconservative Forces
• 4.5.4 Changes in Mechanical Energy due to All Forces
• 4.5.5 Power
• 4.5.6 Energy Diagrams
• 4.5.7 Turning Points
• 4.5.8 Equilibrium Points
• 4.5.9 Positions of Stable Equilibrium
• 4.5.10 Positions of Unstable Equilibrium
• 4.5.11 Positions of Neutral Equilibrium
• 5 Impulse, Momentum, and Collisions
• 5.1 Linear Momentum and Collisions
• 5.2 Conservation of Linear Momentum
• 5.3 Impulse and Momentum
• 5.4 Collisions
• 5.4.1 Elastic Collisions
• 5.4.2 Inelastic Collisions
• 5.4.3 Elastic Collision in One Dimension
• 5.4.4 Inelastic Collision in One Dimension
• 5.4.5 Coefficient of Restitution
• 5.4.6 Collision in Two Dimension
• 5.5 Torque
• 5.6 Angular Momentum
• 5.6.1 Newton's Second Law in Angular Form
• 5.6.2 Conservation of Angular Momentum
• 6 System of Particles
• 6.1 System of Particles
• 6.2 Discrete and Continuous System of Particles
• 6.2.1 Discrete System of Particles
• 6.2.2 Continuous System of Particles
• 6.3 The Center of Mass of a System of Particles
• 6.3.1 Two Particle System
• 6.3.2 Discrete System of Particles
• 6.3.3 Continuous System of Particles (Extended Object)
• 6.3.4 Elastic and Rigid Bodies
• 6.3.5 Velocity of the Center of Mass.
• 6.3.6 Momentum of a System of Particles
• 6.3.7 Motion of a System of Particles
• 6.3.8 Conservation of Momentum
• 6.3.9 Angular Momentum of a System of Particles
• 6.3.10 The Total Torque on a System
• 6.3.11 The Angular Momentum and the Total External Torque
• 6.3.12 Conservation of Angular Momentum
• 6.3.13 Kinetic Energy of a System of Particles
• 6.3.14 Work
• 6.3.15 Work-Energy Theorem
• 6.3.16 Potential Energy and Conservation of Energy of a System of Particles
• 6.3.17 Impulse
• 6.4 Motion Relative to the Center of Mass
• 6.4.1 The Total Linear Momentum of a System of Particles Relative to the Center of Mass
• 6.4.2 The Total Angular Momentum About the Center of Mass
• 6.4.3 The Total Kinetic Energy of a System of Particles About the Center of Mass
• 6.4.4 Total Torque on a System of Particles About the Center of Mass of the System
• 6.4.5 Collisions and the Center of Mass Frame of Reference
• 7 Rotation of Rigid Bodies
• 7.1 Rotational Motion
• 7.2 The Plane Motion of a Rigid Body
• 7.2.1 The Rotational Variables
• 7.3 Rotational Motion with Constant Acceleration
• 7.4 Vector Relationship Between Angular and Linear Variables
• 7.5 Rotational Energy
• 7.6 The Parallel-Axis Theorem
• 7.7 Angular Momentum of a Rigid Body Rotating about a Fixed Axis
• 7.8 Conservation of Angular Momentum of a Rigid Body Rotating About a Fixed Axis
• 7.9 Work and Rotational Energy
• 7.10 Power
• 8 Rolling and Static Equilibrium
• 8.1 Rolling Motion
• 8.2 Rolling Without Slipping
• 8.3 Static Equilibrium
• 8.4 The Center of Gravity
• 9 Central Force Motion
• 9.1 Motion in a Central Force Field
• 9.1.1 Properties of a Central Force
• 9.1.2 Equations of Motion in a Central Force Field
• 9.1.3 Potential Energy of a Central Force
• 9.1.4 The Total Energy
• 9.2 The Law of Gravity.
• 9.2.1 The Gravitational Force Between a Particle and a Uniform Spherical Shell
• 9.2.2 The Gravitational Force between a Particle and a Uniform Solid Sphere
• 9.2.3 Weight and Gravitational Force
• 9.2.4 The Gravitational Field
• 9.3 Conic Sections
• 9.3.1 The Polar Equation of a Conic Section
• 9.3.2 Motion in a Gravitational Force Field
• 9.3.3 The Gravitational Potential Energy
• 9.3.4 Energy in a Gravitational Force Field
• 9.4 Kepler's Laws
• 9.4.1 Kepler's First Law
• 9.4.2 Kepler's Second Law
• 9.4.3 Kepler's Third Law
• 9.5 Circular Orbits
• 9.6 Elliptical Orbits
• 9.7 The Escape Speed
• 10 Oscillatory Motion
• 10.1 Oscillatory Motion
• 10.2 Free Vibrations
• 10.3 Free Undamped Vibrations
• 10.3.1 Mass Attached to a Spring
• 10.3.2 Simple Harmonic Motion and Uniform Circular Motion
• 10.3.3 Energy of a Simple Harmonic Oscillator
• 10.3.4 The Simple Pendulum
• 10.3.5 The Physical Pendulum
• 10.3.6 The Torsional Pendulum
• 10.4 Damped Free Vibrations
• 10.4.1 Light Damping (Under-Damped) (γ&lt
• 2ωn)
• 10.4.2 Critically Damped Motion (γ=2ωn)
• 10.4.3 Over Damped Motion (Heavy Damping) (γ&gt
• 2ωn)
• 10.4.4 Energy Decay
• 10.5 Forced Vibrations
• References.