Newtonian Mechanics for Undergraduates

Name: Newtonian Mechanics for Undergraduates
Price: 4490 ISK
Availability: InStock
Author: Vijay Tymms
ISBN: 9781786340108

Höfundur: Vijay Tymms (Útgáfa: 0)

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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.

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Útgefandi: World Scientific Publishing

ISBN: 9781786340108

Print ISBN: 9781786340078

Format: ePub

Útgáfa: 0

Höfundar: Vijay Tymms

Tungumál: English

Útgefið: 2015-11-25

Prent takmörkun á líftíma: 100

Prent takmörkun: 2

Afritunar takmörkun: 2

Flokkar: Náttúruvísindi

Efnisflokkar: Vísindi › Almennt Vísindi › Hreyfifræði Vísindi › Þyngdarafl

Kaflar

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