Lýsing:
Newtonian mechanics is a cornerstone topic in physics. Regardless of the path an aspiring physicist takes, an intimate and intuitive understanding of how objects behave within Newton's law of motion is essential. Yet the transition from high school physics to university level physics can be — and should be — difficult. The aim of this book is to teach Newtonian mechanics suitable for the first two years of university study.
Using carefully chosen and detailed examples to expose areas of frequent misunderstanding, the first two thirds of the book introduces material familiar to high school students from the ground up, with a more mature point of view. The final third of the book contains new material, introducing detailed sections on the rotation of rigid objects and providing an insight into subtleties that can be troubling to the first-time learner.
Annað
- Höfundur: Vijay Tymms
- Útgáfudagur: 2015-11-25
- Blaðsíður: 268
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- Format:ePub
- ISBN 13: 9781786340108
- Print ISBN: 9781786340078
- ISBN 10: 1786340100
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
- 2.1 Quantities, Units, and Coordinate Systems
- 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
- 4.1 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
- 5.1 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
- 6.1 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
- 7.1 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
- 8.1 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?
- 9.1 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
- 10.1 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.
- 11.1 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
- 12.1 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
- 13.1 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
- 14.1 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
- 15.1 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
- 16.1 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
- 17.1 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
- 18.1 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
- 19.1 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
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- Gerð : 208
- Höfundur : 8718
- Útgáfuár : 2015
- Leyfi : 379