Efnisyfirlit

• Cover
• Title
• Copyright
• 1. Overview
  • 1.1 Introduction
  • 1.2 Why This Book is Needed
  • 1.3 Who Will Benefit From This Book?
  • 1.4 Assumed Prior Knowledge
  • 1.5 Structure and Topics
  • Feedback for the Author
• 2. Introductory Concepts
  • 2.1 Quantities, Units, and Coordinate Systems
    • 2.1.1 Scalar and Vector Quantities
    • 2.1.2 When Vectors Will Be Used and What Knowledge Will Be Assumed
    • 2.1.3 Vector Notation in Print and in Handwriting
    • 2.1.4 Knowing When a Quantity is Scalar or Vector
    • 2.1.5 Units
    • 2.1.6 Standard SI Prefixes
    • 2.1.7 Coordinate Systems
  • 2.2 Time, Displacement, Velocity, and Acceleration
    • 2.2.1 Time
    • 2.2.2 What is Meant By “Time is Linear and Universal” and Some Musing on Time Travel?
    • 2.2.3 Displacement
    • 2.2.4 Velocity
    • 2.2.5 Acceleration
  • 2.3 Force, Mass (and Acceleration)
    • 2.3.1 Mass
    • 2.3.2 Force
    • 2.3.3 Relating Force, Mass, and Acceleration
    • 2.3.4 F = ma as a Cause-to-Effect Ratio and Other Examples in Physics
    • 2.3.5 Watch out for Careless Alternative Definitions
    • 2.3.6 Definitions of the Second, Metre, and Kilogram
• 3. 1D Motion
  • 3.1 The Equations for Constant Acceleration
    • 3.1.1 Setting up the Basic Situation
    • 3.1.2 Finding x as a Function of t
    • 3.1.3 Finding v as a Function of x
    • 3.1.4 Two More Equations
    • 3.1.5 Using the Equations for Constant Acceleration
  • 3.2 Time-Dependent Forces
  • 3.3 Displacement-Dependent Forces
  • 3.4 Velocity-Dependent Forces
  • 3.5 More Complicated Forces
• 4. Newton’s First and Second Laws of Motion
  • 4.1 Newton’s First Law of Motion
    • 4.1.1 The Law is Not Valid in Accelerating Reference Frames
    • 4.1.2 Nor is the Law Valid on Subatomic Scales
  • 4.2 Introducing Linear Momentum Before Stating Newton’s Second Law
  • 4.3 Newton’s Second Law of Motion
  • 4.4 Derivation of F =ma and the Definition of the Newton
  • 4.5 Simple F = ma Examples for a Point Particle
    • 4.5.1 No Velocity, Balanced Forces
    • 4.5.2 Constant Velocity, Balanced Forces
    • 4.5.3 Constant Acceleration, Unbalanced Forces
    • 4.5.4 Non-Constant Acceleration, Unbalanced Forces
    • 4.5.5 Force Implies Acceleration and Acceleration Implies Force; Deduction and Induction
  • 4.6 Alternative Statements of the Laws
• 5. Types of Force and Free Body Diagrams
  • 5.1 Free Body Diagrams
  • 5.2 Types of Mechanical Force
    • 5.2.1 Weight
    • 5.2.2 Normal Contact Force
    • 5.2.3 Friction
    • 5.2.4 Tension and Compression
    • 5.2.5 Upthrust
    • 5.2.6 Drag Force
    • 5.2.7 Lift
• 6. Newton’s Third Law of Motion
  • 6.1 Newton’s Third Law of Motion
  • 6.2 Newton’s Third Law Pairs
    • 6.2.1 Type 1: Long Range Forces (“Action at a Distance”)
    • 6.2.2 Type 2: Contact Forces
    • 6.2.3 Type 3: Fluid Pressure Difference Forces
  • 6.3 Misuses and Apparent Paradoxes
    • 6.3.1 Action and Reaction
• 7. Linear Momentum
  • 7.1 Linear Momentum
  • 7.2 Change in Momentum: Impulse
  • 7.3 The Conservation of Linear Momentum
    • 7.3.1 Proof of the Conservation of Momentum for a General Two Particle System
    • 7.3.2 Conservation of Momentum for an N-Particle System
  • 7.4 Using the Conservation of Linear Momentum
  • 7.5 Splitting Momentum Into Components
    • 7.5.1 Situations with a Resultant External Force Along One Component
  • 7.6 Two Classic Physics Puzzles
    • 7.6.1 The Sailing Boat and The Hair Dryer
    • 7.6.2 The Lorry Driver and the Geese
• 8. Work, Energy and Power
  • 8.1 Work
    • 8.1.1 Definition, Units, and Values
    • 8.1.2 More on the Angle between the Force and the Displacement
    • 8.1.3 Non-Constant Forces
    • 8.1.4 Is the Work Done by Friction Positive or Negative? Some Words on Terrestrial Locomotion
  • 8.2 Energy, its Conservation, and Types of Energy
  • 8.3 Kinetic Energy and the Work–Energy Theorem
  • 8.4 Power
    • 8.4.1 Does the Work Done When Lifting an Object Depend on How Fast it is Lifted?
• 9. Potential Energy
  • 9.1 Gravitational Potential Energy
    • 9.1.1 More Familiar Interpretation
    • 9.1.2 Potential Energy is Shared between Two or More Objects
  • 9.2 General Case in 1D
  • 9.3 Elastic Potential Energy
    • 9.3.1 Stored Energy = 1/2 × Constant × Variable2 Formulae Appear Quite a Lot in Physics
  • 9.4 Conservative and Non-Conservative Forces
    • 9.4.1 Introduction
    • 9.4.2 Other Properties
    • 9.4.3 Lifting a Box
  • 9.5 Potential Wells
  • 9.6 Mass–Energy Equivalence and E = mc2
    • 9.6.1 Mass–Energy in General
    • 9.6.2 Stretching a Spring
    • 9.6.3 Charging a Battery
    • 9.6.4 Kinetic Energy, Dissipation of Heat, and Cups of Tea
    • 9.6.5 Climbing a Mountain
    • 9.6.6 Combustion, Breathing, and Weight Loss
    • 9.6.7 Nuclear Reactions
• 10. Collisions and Rockets
  • 10.1 Collisions
    • 10.1.1 Elastic Collisions
    • 10.1.2 Inelastic Collisions
    • 10.1.3 Superelastic Collisions
  • 10.2 Reference Frames
  • 10.3 Particle–Wall Collisions
  • 10.4 Fluid Jet Pressure
  • 10.5 Rocket Propulsion
    • 10.5.1 The Basic Principle of Rocketry
    • 10.5.2 Rocket Propulsion for a Constant Velocity Fuel Ejection.
• 11. Motion on a Curved Path
  • 11.1 Uniform Circular Motion
    • 11.1.1 General Kinematic Analysis
    • 11.1.2 What This Tells Us
    • 11.1.3 Example of An Object Travelling Around a Circular Banked Track
  • 11.2 Motion on a General Curve with Changing Speed
    • 11.2.1 More on the General Radius of Curvature and How to Use it with the Circular Motion Equation
    • 11.2.2 Example of an Object Sliding Off a Round, Frictionless Hill
• 12. Simple Harmonic Motion
  • 12.1 Amplitude, Period, Frequency and Angular Frequency
  • 12.2 Sinusoidal Oscillations
    • 12.2.1 A Simple Harmonic Oscillator Does not Necessarily Exhibit SHM
  • 12.3 Two Examples of SHM
    • 12.3.1 What Does “Small Angle” Mean?
  • 12.4 SHM and Uniform Circular Motion
  • 12.5 Energy in SHM
    • 12.5.1 Kinetic and Potential Energies
    • 12.5.2 The Constant, k
    • 12.5.3 The Potential Well Approach
    • 12.5.4 Example with the Simple Pendulum Revisited
  • 12.6 Other Features of SHM
• 13. Gravitation
  • 13.1 Newton’s Law of Gravitation
    • 13.1.1 The Gravitational Force is Weak
    • 13.1.2 Point Masses
    • 13.1.3 Example: Circular orbits about a planet (with a preface on Newton’s cannon)
    • 13.1.4 The Inaccuracy of the Term “Weightless”
  • 13.2 Gravitational Field Strength
    • 13.2.1 Gravitational Field Strength and Weight
    • 13.2.2 g: Gravitational Field Strength in Nkg–1 or Acceleration Due to Gravity in ms–2?
    • 13.2.3 Inertial and Gravitational Mass
  • 13.3 Gravitational Potential and Binding Energy
    • 13.3.1 Proof of Equation 13.3
    • 13.3.2 Escape Velocity
    • 13.3.3 Black Holes and the Schwarzschild Radius
  • 13.4 Gravitational Effects of A Spherical Shell
    • 13.4.1 The Force on a Mass Outside a Hollow Sphere
    • 13.4.2 The Force on a Mass Inside a Hollow Sphere
  • 13.5 Planetary Variations in Field Strength
• 14. Rotational Analogues
  • 14.1 Angular Velocity
  • 14.2 Angular Acceleration
  • 14.3 Rotational Kinetic Energy and Moment of Inertia
    • 14.3.1 Single Particle
    • 14.3.2 Several Particles
    • 14.3.3 Continuum of Particles
    • 14.3.4 Meaning of Moment of Inertia
    • 14.3.5 Common Examples
  • 14.4 Torque
    • 14.4.1 Rotational Equivalent of Newton’s Second Law
  • 14.5 Angular Momentum
  • 14.6 A Bit More on Scalars, Vectors, and Tensors
    • 14.6.1 Angular Velocity vs. Linear Velocity
    • 14.6.2 The Moment of Inertia Tensor
• 15. Equilibrium and Balance
  • 15.1 Centre of Mass
    • 15.1.1 Discrete Particle System
    • 15.1.2 Continuum System
    • 15.1.3 L-Shaped Object
    • 15.1.4 Importance
  • 15.2 Centre of Gravity
  • 15.3 Centre of Buoyancy
  • 15.4 Equilibrium
  • 15.5 Examples of Equilibrium
    • 15.5.1 See-Saw
    • 15.5.2 Balancing Pencil
    • 15.5.3 Leaning Ladder
• 16. Unbalanced Objects
  • 16.1 An Unbalanced Light See-Saw
  • 16.2 Rigid Object Toppling About A Pivot
    • 16.2.1 The Forces
    • 16.2.2 Unstable Equilibrium
    • 16.2.3 Stable Equilibrium
    • 16.2.4 Toppling
    • 16.2.5 Accelerations for a Uniform Rod (with a Note on Why Balancing a Pencil on Your Fingertip is Difficult But Balancing a Broom Handle is Easy)
    • 16.2.6 The Tangential Linear Acceleration and a Surprising Result
    • 16.2.7 Energy Approach
    • 16.2.8 Variation of Forces with Angle
    • 16.2.9 Oscillations About the Stable Equilibrium Point
• 17. Rolling and Sliding
  • 17.1 The Condition for Rolling
    • 17.1.1 Think About Riding a Bicycle
  • 17.2 Rolling Friction — Why Rolling Objects Stop at All
  • 17.3 Rolling Down an Inclined Plane
    • 17.3.1 Analysis Using Energy
    • 17.3.2 Analysis Using Dynamics
    • 17.3.3 The Condition for No Slipping
  • 17.4 An External Force Causing Rolling on a Flat Surface
• 18. Angular Momentum
  • 18.1 Definition
  • 18.2 Torque and Angular Momentum
  • 18.3 Moment of Inertia and Angular Momentum
  • 18.4 The Conservation of Angular Momentum
  • 18.5 Examples of the Conservation of Angular Momentum
    • 18.5.1 The Ice Skater (Or Less Agile Person Sat on a Rotating Platform)
    • 18.5.2 The Bicycle Wheel Variant
    • 18.5.3 Turning Yourself Around Without Translational Motion on An Ice Rink
    • 18.5.4 The Physics of the Falling Cat
    • 18.5.5 Kepler’s Second Law
• 19. Angular Momentum, Gyroscopes, and Precession
  • 19.1 The Gyroscope
  • 19.2 Application of Torque about the Pivot to a Spinning Gyro
  • 19.3 Precession Formula
  • 19.4 Analogy with Linear Circular Motion
  • 19.5 Analysis of Precession in Terms of Forces and Velocities
  • 19.6 Precession is Nothing to do with the Conservation of Angular Momentum
  • 19.7 More Subtle Features of Gyroscopic Motion
  • 19.8 The Earth’s Precession
  • 19.9 Examples and Uses of Gyroscopic Motion
• Bibliography
• Index

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