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Samuel J. Ling
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Front Matter
Colophon
Author Biography
Dedication
Acknowledgements
Preface
I
Mechanics
1
Introduction
1.1
The World of Physics
1.2
Fundamental Quantities in Mechaanics
1.2.1
Length
1.2.2
Time
1.2.3
Mass
1.3
Metric and Other Units
1.3.1
Imperial Units
1.3.2
Unit Prefixes
1.3.3
The SI AND CGS Systems of Units
1.3.4
Base Units
1.3.5
Conversion of Units
1.3.5
Exercises
1.4
Uncertainty, Precision, Accuracy
1.4.1
Uncertainty
1.4.2
Precision
1.4.3
Accuracy
1.4.4
Significant Figures
1.4.5
Reason for Uncetainty
1.4.6
Absolute and Relative Uncertainty
1.4.7
The Scientific Notation for Numbers
1.4.8
Exercises
1.5
Propagation of Uncertainty
1.5.1
Derived Quantity is a Function of the Measured Quantity
1.5.2
Derived Quantity is a Function of Two Measured Quantities
1.5.3
Exercises
1.6
Order of Magnitude
1.6
Exercises
1.7
Dimensional Analysis
1.7.1
How to Perform Dimensional Analysis
1.7.2
Exercises
1.8
Chapter Summary
1.9
Introduction Bootcamp
1.9
Exercises
2
Motion on a Straight Path
2.1
Basics of Motion
2.1.1
Time
2.1.2
Distance
2.1.3
Direction
2.1.4
All Motion is Relative
2.2
Tracking Motion
2.2
Exercises
2.3
Position, Displacement, and Distance
2.3.1
Position
2.3.2
Displacement
2.3.3
Distance
2.3.4
Exercises
2.4
Velocity and Speed
2.4.1
Average Speed
2.4.2
Average Velocity
2.4.3
Instantaneous Velocity
2.4.4
Graphical Definition of Velocity
2.4.5
Displacement from Velocity
2.4.6
Exercises
2.5
Acceleration
2.5.1
Average Acceleration
2.5.2
Instantaneous Acceleration
2.5.3
Graphical Definition of Acceleration
2.5.4
Change in Velocity from Acceleration
2.5.5
Exercises
2.6
Position, Velocity, Acceleration Summary
2.6.1
(Calculus) Position, Velocity, Acceleration Summary
2.7
Constant Acceleration Motion
2.7
Exercises
2.8
Freely Falling Motion
2.8
Exercises
2.9
Chapter Summary
2.10
One-Dimensional Motion Bootcamp
2.10
Exercises
3
Vectors
3.1
Vectors as Arrows
3.1.1
Drawing Vector Arrows
3.1.2
Multiplication of a Vector by a Scalar
3.1.3
Unit Vector
3.1.4
Adding Vector Arrows
3.1.5
Subtraction of Vectors
3.1.6
Vector Equations and Polygons
3.1.7
Projection of one Vector Over Another
3.1.8
Multiplication of a Vector with Another Vector
3.1.8.1
Scalar Or Dot Product
3.1.8.2
Vector or Cross Product
3.1.9
Exercises
3.2
Unit Vectors and Components
3.2.1
Definition
3.2.2
Using Multiples of Unit Vectors
3.2.3
Cartesian Unit Vectors
3.2.4
Direction Cosines
3.2.5
Exercises
3.3
Adding Vectors
3.3.1
Adding Vectors Graphically
3.3.2
Adding Vectors Analytically Component-by-Component
3.3.3
Exercises
3.4
Vector Equations
3.4
Exercises
3.5
Scalar Product
3.5
Exercises
3.6
Vector Product
3.6
Exercises
3.7
Working with Cartesian Unit Vectors
3.7.1
Dot and Cross Products of Cartesian Unit Vectors
3.7.1.1
Dot Product of Two Vectors Using Cartesian Unit Vectors
3.7.1.2
Cross Product of Two Vectors Using Cartesian Unit Vectors
3.7.2
Exercises
3.8
Chapter Summary
3.9
Vectors Bootcamp
3.9
Exercises
4
Kinematics
4.1
Position
4.1.1
Position Vector in the Component Form
4.1.2
Magnitude and Direction of Position
4.1.3
Exercises
4.2
Displacement
4.2.1
Independence of Displacement Vectors from Coordinate System
4.2.2
Exercises
4.3
Velocity and Speed
4.3.1
Average Velocity
4.3.2
Average Speed
4.3.3
Instantaneous Velocity - Formal Definition
4.3.3.1
Computing Derivatives from the Slopes of Tangents
4.3.4
Direction of Instantaneous Velocity from Trajectory
4.3.5
Exercises
4.4
Acceleration
4.4.1
Average Acceleration
4.4.2
Instantaneous Acceleration - Formal Definition
4.4.3
Acceleration from Slopes of
\((v_x,\ v_y,\ v_z) \)
vs
\(t \)
Plots.
4.4.4
(Calculus) Instantaneous Acceleration
4.4.5
Exercises
4.5
Displacement from Velocity
4.5
Exercises
4.6
Velocity from Acceleration
4.6
Exercises
4.7
Constant Acceleration
4.7.1
The Plane of Constant Acceleration Motion
4.7.2
Constant Acceleration Along
\(x \)
Axis
4.7.3
The Projectile Motion
4.7.4
Exercises
4.8
Variable Acceleration
4.8.1
(Calculus) Arbitrarily Varying Acceleration
4.8.2
Exercises
4.9
Relative Motion in Different Frames
4.9.1
Observers Moving at Uniform Velocity With Respect to Each Other
4.9.2
Observers Accelerating with Respect to Each Other
4.9.3
Exercises
4.10
Kinematics Bootcamp
4.10
Exercises
5
Circular Motion
5.1
Position on a Circle
5.1.1
Arc Length and Angle Subtended
5.1.2
Position and Displacement on a Circle
5.1.3
Exercises
5.2
Velocity of a Circular Motion
5.2
Exercises
5.3
Uniform Circular Motion
5.3.1
Velocity Directions in a Circular Motion
5.3.2
Centripetal Acceleration
5.3.3
Exercises
5.4
Centripetal and Tangential Accelerations
5.4.1
(Calculus) Velocity and Speed for a Circular Motion
5.4.2
(Calculus) Acceleration of a Circular Motion
5.5
Motion in Polar Coordinates
5.5.1
The Polar Coordinates
5.5.2
Unit Vectors
\(\hat u_r\)
and
\(\hat u_\theta\)
5.5.2.1
Definition of
\(\hat u_r\)
and
\(\hat u_\theta\)
5.5.2.2
\(\hat u_r\)
and
\(\hat u_\theta \)
as Basis Vectors
5.5.2.3
Relation Among Components in
\((\hat i, \hat j)\)
and
\((\hat u_r, \hat u_\theta)\)
Bases
5.5.3
(Calculus) Position, Velocity, Acceleration
5.5.3.1
Position
5.5.3.2
Displacement and Distance on Trajectory
5.5.3.3
Velocity.
5.5.3.4
(Calculus) Acceleration
5.5.4
Exercises
5.6
Circular Motion Bootcamp
5.6
Exercises
6
Newton’s Laws of Motion
6.1
Forces
6.1.1
Measuring Forces
6.2
Forces as Vectors
6.2.1
Resultant Force
6.2.2
Component of a Force in a Given Direction
6.3
First Law of Motion
6.4
Second Law of Motion
6.4.1
Second Law for Fixed Mass
6.4.2
Changing Mass System
6.4.3
(Calculus) Fundamental Second Law of Motion
6.4.4
What is mass?
6.5
Third Law of Motion
6.6
Net Force
6.6.1
Free-body Diagram
6.6.2
Exercises
6.7
Problem Solving
6.8
Common Forces
6.9
Weight
6.10
Normal Force
6.10
Exercises
6.11
Static Friction
6.11.1
Maximum Static Friction Force
6.11.2
Exercises
6.12
Sliding/Kinetic Friction
6.12
Exercises
6.13
Rolling Friction
6.14
Drag Force
6.14.1
Viscous Drag Force
6.14.2
Inertial Drag Force
6.14.3
Reynold’s Number
6.14.4
Terminal Speed
6.14.5
Exercises
6.15
Spring Force
6.16
Tension Force
6.16.1
String Connecting Bodies
6.16.2
Exercises
6.17
Coupled Motion and Constraints
6.17.1
Objects Pushing on Each Other
6.17.2
Motion Connected by Strings and Pulleys
6.17.3
Exercises
6.18
Dynamics of Cicular Motion
6.18
Exercises
6.19
Dynamics in Polar Coordinates
6.19
Exercises
6.20
Forces Bootcamp
6.20
Exercises
7
Impulse and Momentum
7.1
Momentum
7.1.1
Definition of Momentum
7.1.2
Momentum is Relative
7.1.3
Total Momentum of a Multi-part System
7.1.4
Exercises
7.2
Impulse
7.2.1
Impulse as Area under/over Force Components
7.2.2
(Calculus) Impulse as an Integral
7.2.3
Net Impulse
7.2.4
Exercises
7.3
Impulse and Change in Momentum
7.3.1
Vectorial Nature of Impulse and Change in momentum
7.3.2
(Calculus) Derivation of the Integral Form of Second Law
7.3.3
Exercises
7.4
Center of Mass
7.4.1
Center of Mass of Object Made up of Point Particles
7.4.2
(Calculus) Center of Mass of Continuous Objects
7.4.2.1
Simplification for One- and Two-Dimensional Objects
7.4.2.2
General Procedure for CM of Continous Bodies
7.4.3
Exercises
7.5
Translational Motion of Macroscopic Bodies
7.5.1
Two-Particle System
7.5.2
Generalization to Multiparticle Systems
7.5.3
Center of Mass Motion
7.5.4
Center of Mass Motion - Constant Mass Case
7.5.5
Exercises
7.6
Conservation of Momentum
7.7
Collisions
7.7.1
Elastic Collision
7.7.2
Impulse of Internal Forces
7.7.3
Summary of Formulas for Collision
7.7.4
Exercises
7.8
The CM Frame
7.8.1
Relation between CM and LAB frames
7.8.2
Velocities in CM and LAB Frame of Two Bodies
7.8.3
Collision in CM Frame
7.9
Mass Varying System
7.9.1
Motion of a Rocket in Free Space
7.9.2
Rocket Motion With Constant External Force
7.9.3
Example of Mass Accretion
7.9.4
Momentum Transport by Massless Radiation
7.9.5
Exercises
7.10
Momentum Bootcamp
7.10
Exercises
8
Energy and Power
8.1
Work
8.1.1
Work by a Constant Force on a Straight Displacement
8.1.2
(Calculus) Fundamental Definition of Work
8.1.3
Exercises
8.2
Power of a Force
8.2.1
Instantaneous Power
8.2.1.1
Instantaneous Power (Calculus)
8.2.2
Average Power
8.2.3
(Calculus) Time Averaging of Instantaneous Power
8.2.4
Exercises
8.3
Kinetic Energy
8.3.1
Kinetic Energy for Circular Motion
8.3.2
Exercises
8.4
The Work-Energy Theorem
8.4.1
Kinetic Energy and Net Work
8.4.2
(Calculus) Work-Energy Theorem
8.4.2.1
Application to Multiparticle Systems
8.4.3
Uses of Work-Energy Theorem
8.4.4
Exercises
8.5
Potential Energy
8.5.1
Derivation of Potential Energy Due to Weight
8.5.2
(Calculus) Potential Energy Due to Spring Force
8.5.3
(Calculus) Potential Energy Due to Universal Gravitational Force
8.5.4
(Calculus) Potential Energy and Force
8.5.5
(Calculus) Potential Energy and Equilibrium
8.6
Energy
8.6.1
Energy of a Particle Subject to Gravity
8.6.2
Energy of a Particle Subject to Gravity and Spring Forces
8.7
Conservation of Energy
8.7
Exercises
8.8
Non-Conservation of Energy
8.8
Exercises
8.9
Energy in Collisions
8.9.1
Elastic Collision
8.9.2
Coefficient of Restitution
8.9.3
Internal Forces in Elastic Collision
8.9.4
Elastic Collision in Center of Mass Frame
8.9.5
Exercises
8.10
Energy Flow
8.10.1
Energy Flow Diagram
8.10.2
Multiple forms of energy
8.11
Energy Bootcamp
8.11
Exercises
9
Rotation about a Fixed Axis
9.1
Describing Rotation
9.1.1
Sense of Rotation
9.1.2
Angle of Rotation
9.2
Rotation Angle as a Vector
9.3
Rotational Speed and Velocity
9.3.1
Average Rotational Speed
9.3.2
Average Rotational Velocity
9.3.3
Instantaneous Rotational Velocity
9.3.4
Instantaneous Rotational Velocity and Speed - Graphically
9.3.5
Net Angle Rotated from Rotational Velocity - Graphically
9.3.6
Angular Velocity Vector
9.3.7
(Calculus) Instantaneous Rotational Velocity and Speed - Analytically
9.3.8
(Calculus) Net Angle Rotated from Rotational Velocity
9.3.9
(Calculus) Angular Velocity Vector
9.3.10
Velocity and Angular Velocity
9.4
Rotational Acceleration
9.4.1
Average Angular Acceleration
9.4.2
Instantaneous Angular Acceleration
9.4.3
Instantaneous Angular Acceleration - Graphically
9.5
Constant Rotational Acceleration
9.5
Exercises
9.6
Angular Momentum
9.6.1
Angular Momentum of a Particle
9.6.2
Angular Momentum of a Particle in a Circular Motion
9.6.3
A Particle in Circular Motion as Rotation
9.6.4
Angular Momentum of a Collection of Particles
9.6.5
Angular Momentum of a Rotating Rigid Body of Point Masses
9.6.6
Angular Momentum of a Rotating Rigid Body
9.6.7
Exercises
9.7
Moment of Inertia
9.7.1
Moment of Inertia of Single Particle
9.7.2
Moment of Inertia of Systems of Particles
9.7.3
Moment of Inertia of a Uniform Rod
9.7.4
The Parallel-Axis Theorem
9.7.5
Radius of Gyration
9.7.6
(Calculus) Moment of Inertia of a Uniform Rod
9.7.7
(Calculus) Proof of the Parallel Axis Theorem
9.7.8
(Calculus) Moment of Inertia of a Uniform Body
9.7.9
(Calculus) Principal Axes and Moment of Inertia Tensor
9.7.10
Exercises
9.8
Torque
9.8.1
Torque of a Force that is in a Plane Perpendicular to the Axis
9.8.2
Zero Torque Situations
9.8.3
The Lever Arm Picture
9.8.4
The Sense of Rotation and Torque
9.8.5
Net Torque
9.9
Rotational Second Law
9.9.1
(Calculus) Derivation of the Rotational Second Law
9.9.2
(Calculus) Rotational Second Law for Multiparticle System
9.10
Rotational Impulse
9.10.1
(Calculus) Fundamental Definition of Rotational Impulse
9.11
Rotational Impulse and Angular Momentum
9.11.1
(Calculus) Change in Angular Momentum by a Rotational Impulse
9.12
Conservation of Angular Momentum
9.13
Collision and Angular Momentum
9.14
Rotational Work
9.15
Rotational Kinetic Energy
9.15
Exercises
9.16
Rolling Motion
9.16.1
(Calculus) Separation of Kinetic Energy
9.16.2
(Calculus) Separation of Angular Momentum
9.16.3
Exercises
9.17
Rotation Bootcamp
9.17
Exercises
10
Rigid Body Motion
10.1
Angular Velocity
10.1.1
Where to Place the Origin of Moving Coordinates
10.2
Angular Momentum
10.2
Exercises
10.3
Principal Axes
10.3.1
Parallel Axis Theorem
10.3.2
Exercises
10.4
Dynamics of Rigid Bodies
10.5
The Gyroscope
10.5.1
Gyroscope as a Compass
10.6
Kinetic Energy of a Rigid Body
10.6.1
Kinetic Energy About Center of Mass
10.6.2
Exercises
10.7
Rigid Body Motion Bootcamp
10.7
Exercises
11
Noninertial Frames
11.1
Accelerating Frame
11.1.1
Kinematics in Accelerating Frame
11.1.2
Newton’s Second Law in Accelerating Frame
11.1.3
Exercises
11.2
Rotating Frame
11.2.1
A particle fixed at the
\(x\)
-axis of a uniformly rotating frame
11.2.2
Vector Notation
11.2.3
A particle moving in the
\(xy\)
-plane of a uniformly rotating frame
11.2.4
Newton’s Second Law in Uniformly Rotating Frame
11.2.5
Exercises
11.3
Physics in Earth’s Frame
11.3
Exercises
11.4
Coriolis Force
11.5
Noninertial Frame Bootcamp
11.5
Exercises
II
Applications of Mechanics
12
Gravitation
12.1
Kepler’s Laws of Planetary Motion
12.1.1
Math of Ellipse
12.1.2
Kepler’s Laws
12.1.3
Kepler’s Impact on the Development of Physics
12.1.4
Exercises
12.2
The Universal Law of Gravitation
12.2.1
Applying the Law of Gravitation to Spherical Bodies
12.2.2
Applying the Law of Gravitation to Arbitrary Bodies
12.2.3
Exercises
12.3
Gravitational Potential Energy
12.3.1
Energy of Two Bodies Interacting by Gravitational Force
12.3.2
Exercises
12.4
The Gravitational Two-Body Problem
12.4
Exercises
12.5
Angular Momentum Conservation and Kepler’s Second Law
12.6
Energy Conservation
12.6.1
(Calculus) Effective Potential Energy
12.6.2
Interpreting Effective Potential Energy
12.7
The Orbit Equation
12.7.1
Four Types of Orbits
12.7.2
(Calculus) The Equation of Motion for Orbit Equation and Kepler’s First Law
12.7.3
Exercises
12.8
Deriving Kepler’s Third Law
12.9
Tidal Forces
12.9.1
(Calculus) Understanding Origin of Tides
12.9.2
Roche Limit
12.9.3
Roche Radius
12.10
Gravitation Bootcamp
12.10
Exercises
13
Simple Harmonic Motion
13.1
Sine and Cosine Functions
13.2
Simple Harmonic Oscillator
13.2.1
Equation of Motion and Solution
13.2.2
Multiple Ways of Writing the Solution
13.2.3
Meaning of
\(\omega \)
13.2.4
Amplitude and Phase
13.2.5
Exercises
13.3
Simple Harmonic Systems
13.3.1
Motion Near Potential Minima
13.3.2
Exercises
13.4
Plane Pendulum
13.4.1
Plane Pendulum for Small Angle
13.4.2
Exercises
13.5
Physical Pendulum
13.5
Exercises
13.6
Torsion Pendulum
13.7
Energy of a Harmonic Oscillator
13.7.1
Potential Energy and Turning Points
13.7.2
Exercises
13.8
Damped Harmonic Oscillator
13.8.1
Equation of Motion
13.8.2
Three Types of Damped Oscillators
13.8.3
Underdamped Oscillator Solution
13.8.4
Overdamped Solution
13.8.5
Critically Damped Solution
13.8.6
Exercises
13.9
Dissipation of Energy and Q Factor
13.9.1
Energy of an Underdamped Oscillator
13.9.2
Quality Factor of Underdamped Oscillator
13.9.3
Quality Factor of a Lightly Damped Oscillator
13.9.4
Exercises
13.10
Driven Oscillator
13.10.1
Equation of Motion
13.10.2
Solution of the Equation of Motion
13.10.3
Long Term Steady Behavior and Short Term Transients
13.10.4
Steady State and Resonance of Amplitude
13.10.5
Uses of Resonance Phenomeenon
13.10.6
Role of Damping in Resonance
13.10.7
Resonance of Average Power
13.10.8
Exercises
13.11
Harmonic Oscillator Bootcamp
13.11
Exercises
14
Vibrations and Waves
14.1
Sinusoidal Waves
14.1.1
Mathematical Description of Wave
14.1.2
Exercises
14.2
Coupled Vibrations of Two Blocks
14.2.1
(Calculus) Analytic Solution
14.3
Polarization of Waves
14.4
Normal Modes of a String
14.4.1
(Calculus) Motion of Two Beads on a Taut String
14.4.2
Normal Modes of a String
14.4.3
Exercises
14.5
Resonance of a String
14.6
Wave Speed and Medium
14.6
Exercises
14.7
Wave Functions
14.7.1
Plane Waves
14.7.2
Spherical Waves
14.7.3
Wave Pulses
14.7.4
Exercises
14.8
Energy, Power, and Intensity
14.8.1
Energy Transported by Plane Wave
14.8.2
Intensity of a Spherical Wave
14.8.3
Exercises
14.9
Superposition of Waves
14.10
Interference of Waves
14.10.1
Mixing Two Waves of Equal Amplitude
14.10.2
Simplification for Large
\(L\)
14.10.3
Exercises
14.11
Beats
14.11
Exercises
14.12
Reflection and Transmission
14.12.1
(Calculus) Boundary Conditions
14.12.2
Reflection and Transmission Amplitudes
14.12.3
Perfect Reflection
14.12.4
Perfect Termination and Impedance Matching
14.13
Diffraction
14.13.1
Diffraction Through a Single Slit
14.14
Vibrations and Waves Bootcamp
14.14
Exercises
15
Sound
15.1
Characteristics of Sound Wave
15.1.1
Sound through Solid Media
15.1.2
Exercises
15.2
Planar Sound Wave
15.2
Exercises
15.3
Intensity of Sound
15.3.1
Decibels and Sound Level
15.3.2
Perception of Sound Level
15.3.3
Exercises
15.4
Quality of Sound
15.5
Musical Instruments
15.5.1
Stringed Instruments
15.5.2
Wind Instruments
15.6
Doppler Effect
15.6.1
Doppler Effect When Detector is Moving and Source is Stationary
15.6.2
Doppler Effect When Detector is Stationary and Source is Moving
15.6.3
Doppler Effect when Both Source and Detector Moving
15.6.4
Exercises
15.7
Sound Bootcamp
15.7
Exercises
16
Stress and Strain
16.1
Static Equilibrium
16.1.1
Internal and External Forces
16.1.2
Static Equilibrium of Rigid Bodies
16.1.3
Deformable Objects and Static Equilibrium
16.1.4
Exercises
16.2
Elasticity and Stress
16.2.1
Elasticity
16.2.2
Strain
16.2.3
Stress
16.2.4
General Hooke’s Law
16.2.5
Exercises
16.3
Types of Stress and Strain
16.3.1
Tensile and Compressive Stresses
16.3.2
Shear Stress
16.3.3
Ultimate Strength
16.3.4
Pressure
16.3.5
Exercises
16.4
Energy in Strained Material
16.4
Exercises
16.5
Stress and Strain Bootcamp
16.5
Exercises
17
Static Fluids
17.1
Density
17.2
Pressure
17.2.1
Pressure in a Fluid
17.2.2
Units of Pressure
17.2.3
Range of Pressure
17.2.4
Exercises
17.3
Pressure in Fluid near Earth
17.3.1
Atmospheric Pressure
17.3.2
Pressure in a Fluid with Surface Open to Atmosphere
17.3.3
Atmospheric Pressure Above Sea Level
17.3.4
(Calculus) Variation of Atmospheric Pressure with Height
17.3.5
Exercises
17.4
Pressure Measurements
17.4.1
Mercury Barometer
17.4.2
Closed-tube Manometer
17.4.3
Open-end Manometer
17.4.4
Exercises
17.5
Pascal’s Principles
17.5.1
Pascal’s First Principle
17.5.2
Pascal’s Second Principle
17.5.3
Pascal’s Third Principle
17.5.4
Exercises
17.6
Archimedes’ Principle
17.6
Exercises
17.7
Surface Tension
17.7.1
Surface Energy and Surface Tension
17.7.2
Surface Tension in Stretching a Planar Film
17.7.3
Exercises - Surface Tension
17.7.4
Capillary Action
17.7.5
Exercises - Capilary Action
17.8
Static Fluid Bootcamp
17.8
Exercises
18
Dynamic Fluid
18.1
Fluid Flow
18.1.1
Flow in a Pipe
18.1.2
Incompressibility and Steady Flow
18.1.3
(Calculus) Current Density
18.1.4
(Calculus) Laminar Flow in a Cylindrical Tube
18.1.5
Exercises
18.2
Bernoulli’s Equation
18.2
Exercises
18.3
Applications of Bernoulli’s Equation
18.3.1
Bernoulli for Static Fluid or Same Speed at Two Ends
18.3.2
Same Pressure at Two ends
18.3.3
Bernoulli for no Change in Height
18.3.4
Exercises
18.4
Viscosity
18.4.1
Cohesive Forces and Laminar Flow
18.4.2
Laminar Flow
18.4.3
Units of Coefficient of Viscosity
18.4.4
(Calculus) Velocity of the Layers in Laminar Flow - Rectangular Geometry
18.5
Stoke’s Law
18.6
Poiseuilli’s Law
18.6.1
(Calculus) Velocity Profile in a Flow Through a Cylidrical Pipe
18.6.2
(Calculus) Derivation of Poiseuilli’s Law
18.6.3
Exercises
18.7
Turbulence
18.7
Exercises
18.8
Dynamic Fluid Bootcamp
18.8
Exercises
III
Thermodynamics
19
Heat and Temperature
19.1
The Thermodynamic State
19.1.1
Thermodynamic Systems
19.2
Nature of Heat
19.2.1
Unit of Heat
19.2.2
Thermal Contact
19.2.3
Microscopic Picture of Heat Flow
19.3
Temperature
19.3.1
Thermal Equilibrium
19.3.2
Zeroth Law of Thermodynamics
19.3.3
Temperature Scales
19.3.4
Calibration Using The Triple Point of Water
19.3.5
Change in Temperature in Different Scales
19.3.6
Exercises
19.4
Thermometers
19.4.1
Thermometric Property
19.4.2
Calibration Using The Triple Point of Water
19.4.3
Constant Volume Gas Thermometer
19.4.4
Important Fixed Points for Standard Thermal Baths
19.4.5
Calibration With Two Fixed Points
19.4.6
Exercises
19.5
Heat and Temperature Bootcamp
19.5
Exercises
20
Thermal Expansion
20.1
Thermal Length Expansion
20.1.1
Thermal Expansion Applications
20.1.1.1
Bimetal Strip
20.1.1.2
Preventing Rail Tracks from Stress
20.2
Thermal Area Expansion
20.2
Exercises
20.3
Thermal Volume Expansion
20.3.1
Volume Expansion of Solids and Liquids
20.3.2
Volume Expansion Gases
20.4
Thermal Stress
20.4.1
Thermal Stress in Solids
20.4.2
Thermal Stress in Liquids and Gas
20.4.3
(Calculus) Pressure Change in Ideal Gas at Constant Volume
20.4.4
Exercises
20.5
Compressibility
20.6
Thermal Expansion Bootcamp
20.6
Exercises
21
Ideal Gas
21.1
Ideal Gas Law
21.1.1
Specifying Thermodynamic State of Ideal Gas
21.1.2
Exercises
21.2
Thermodynamic Processes
21.2.1
Quasi-static Processes
21.2.2
Isothermal Process
21.2.3
Isobaric and Isochoric Processes
21.2.4
Adiabatic Process
21.3
Mechanical Work by Gas
21.3.1
Mechanical Work
21.3.2
(Calculus) Mechanical Work by Ideal Gas
21.3.2.1
(Calculus) Work by Gas in an Isothermal Process
21.3.2.2
(Calculus) Work by Gas in an Adiabatic Process
21.3.3
Exercises
21.4
Real Gases
21.4.1
Virial Expansion
21.4.2
Exercises
21.5
Ideal Gas Bootcamp
21.5
Exercises
22
Thermal Properties
22.1
Specific Heat
22.1.1
Molar Specific Heat
22.1.2
Process-Dependence of Specific Heat
22.1.3
Quantifying Heat
22.1.4
(Calculus) Quantifying Heat
22.1.5
Exercises
22.2
States of Matter
22.2.1
Phases of Matter
22.2.2
Phases Diagram
22.2.3
Heat of Transformation
22.2.4
Exercises
22.3
Calorimetry
22.3
Exercises
22.4
Thermal Properties Bootcamp
22.4
Exercises
23
Heat Transfer
23.1
Thermal Conduction
23.1.1
(Calculus) Thermal Conduction
23.1.2
Exercises
23.2
Convection
23.3
Radiation
23.3.1
(Calculus) Black Body Radiation
23.3.2
Exercises
23.4
Thermal Equilibration Process
23.4.1
Newton’s Law of Cooling
23.4.2
(Calculus) By Conduction and Convection
23.4.3
(Calculus) Heating and Cooling by Radiation
23.5
Thermal Energy Balance
23.6
Heat Transfer Bootcamp
23.6
Exercises
24
First Law of Thermodynamics
24.1
First Law of Thermodynamics
24.1.1
Energy Change of a Thermally Insualted System
24.1.2
Energy Change for a Fixed-Volume System
24.1.3
First Law of Thermodynamics
24.1.4
First Law of Thermodynamics and Internal Energy
24.1.5
Other Forms of Energy
24.1.6
Adiabatic Work and Internal Energy
24.1.7
(Calculus) Infinitesimal First law of thermodynamics
24.2
Energy Conservation in Calorimetry
24.2.1
Exercises
24.3
Quasistatic Adiabatic Process
24.3
Exercises
24.4
Enthalpy
24.4.1
Change in Enthalpy
24.4.2
Exercises
24.5
Joule-Thomson Effect
24.5
Exercises
24.6
First Law of Thermodynamics Bootcamp
24.6
Exercises
25
Second Law of Thermodynamics
25.1
Second Law of Thermodynamics
25.2
The Heat Engine
25.2
Exercises
25.3
The Carnot Engine
25.3.1
Proof of
\(Q_C/Q_H = T_C/T_H\)
in Carnot Cycle
25.3.2
Exercises
25.4
The Carnot Refrigerator
25.4.1
Is a Perfect Refrigerator Possible?
25.4.2
Exercises
25.5
Real Engines
25.5.1
The Efficiency of a Real Heat Engine
25.5.2
Exercises
25.5.3
Internal Combustion Engine
25.5.4
Steam Engine
25.6
Second Law Bootcamp
25.6
Exercises
26
Entropy
26.1
Reversible Process
26.2
Entropy
26.2.1
(Calculus) Entropy Change for an Ideal Gas in an Isochoric Process
26.2.2
(Calculus) Entropy Change for an Ideal Gas in an Isobaric Process
26.2.3
(Calculus) Entropy Change for an Ideal Gas in an Isothermal Process
26.2.4
Exercises
26.3
The Third Law of Thermodynamics
26.4
Entropy Change in Irreversible Processes
26.4
Exercises
26.5
The Second Law and Entropy
26.5.1
(Calculus) Entropy Change of Universe
26.6
Entropy and Disorder
26.7
The Fundamental Thermodynamic Identity
26.8
Clausius’s Theorem
26.9
Entropy Bootcamp
26.9
Exercises
27
Kinetic Theory of Gases
27.1
Pressure of an Ideal Gas
27.1.1
Simple Model
27.1.2
Less Simple Model
27.1.3
Exercises
27.2
Maxwell’s Distribution of Molecular Speeds
27.2.1
(Calculus) Maxwell’s distribution
27.3
Mean Free Path
27.3
Exercises
27.4
Internal Energy of Ideal Gases
27.4.1
Internal Energy and Degrees of Freedom
27.5
Effusion
27.6
Vapor Pressure
27.7
Water Vapor and Humidity
27.7
Exercises
27.8
Kinetic Theory Bootcamp
27.8
Exercises
IV
Electricity and Magnetism
28
The Electric Charge
28.1
Electrification by Friction
28.1.1
Two types of charges
28.2
Microscopic Origin of Electricity
28.3
Principle of Conservation of Charge
28.4
Conduction of Electricity
28.5
Electroscope and Electrostatic Induction
28.6
Quantization of Electric Charge
28.7
Electric Charge Bootcamp
28.7
Exercises
29
Coulomb’s Law
29.1
Coulomb’s Force
29.1.1
Coulomb’s Law
29.1.2
Coulomb’s Force in Vector Form
29.1.3
Exercises
29.2
Superposition of Forces
29.2
Exercises
29.3
Electric Field
29.3.1
Definition of Electric Field
29.3.2
How Electric Field Solves the Action-at-a-Distance Problem?
29.3.3
Electric Field of a Point Charge at Origin
29.3.4
Electric Field Lines of a Single Charge
29.3.5
Exercises
29.4
Superposition of Electric Fields
29.4
Exercises
29.5
Electric Field Lines
29.5.1
Graphical Definition of Electric Field
29.6
Continuous Charge Distributions
29.6.1
Electric Field of Continuous Charges
29.6.1.1
Electric Field of a Charged Rod
29.6.1.2
Electric Field of a Charged Ring
29.6.1.3
Electric Field of a Charged Disk
29.6.1.4
Electric Field Near a Large Uniformly Charged Sheet
29.6.1.5
Electric Field of Two Oppositely Charged Sheets Facing Each Other
29.6.2
Exercises
29.7
Charged Particles in Electric Field
29.8
Coulomb’s Law Bootcamp
29.8
Exercises
30
Gauss’s Law
30.1
Flux of Electric Field
30.1.1
Flux of Particles
30.1.2
Flux of Electric Field
30.1.3
(Calculus) Flux of Electric Field
30.2
Gauss’s Law
30.2.1
Statement of Gauss’s Law
30.2.2
(Calculus) Statement of Gauss’s Law
30.2.3
(Calculus) Divergence of Electric Field
30.2.4
Applying Gauss’s Law to Find Electric Field
30.3
Electric Field for Spherical Symmetry
30.3.1
Spherical Symmetry of Charge Distribution
30.3.2
Consequences of Symmetry
30.3.3
Electric Field of a Uniformly Charged Sphere
30.3.3.1
Electric Field at an Outside Point by Gauss’s Law
30.3.3.2
Electric Field at an Inside Point by Gauss’s Law
30.3.4
Exercises
30.4
Electric Field for Cylindrical Symmetry
30.4.1
Cylindrical Symmetry
30.4.2
Consequences of Cylindrical Symmetry
30.4.3
Electric Field of a Uniformly Charged Cylinder
30.4.3.1
Deriving Electric Field at an Outside Point by Gauss’s Law
30.4.3.2
Deriving Electric Field at an Inside Point by Gauss’s Law
30.4.4
Exercises
30.5
Electric Field for Planar Symmetry
30.5.1
Planar Symmetry
30.5.2
Consequences of Planar Symmetry
30.5.3
Electric Field of a Uniformly Charged Plane Sheet
30.5.4
Derivation of Electric Field by Gauss’s Law
30.5.5
Exercises
30.6
Gauss’s Law Bootcamp
30.6
Exercises
31
Electric Potential
31.1
Electric Potential
31.1.1
Electric Potential in a Constant Electric Field Region
31.1.2
Exercises
31.2
Electric Potential Map
31.3
Electric Potential of Point Charge
31.3.1
(Calculus) Derivation of the Formula for Electric Potential for Point Charge
31.3.2
Exercises
31.4
Superposition of Electric Potential
31.5
Electrostatic Energy
31.5.1
(Calculus) Electrostatic Energy of a Continuous Charge System
31.5.2
Exercises
31.6
Electric Potential of Charge Distributions
31.6.1
(Calculus) Electric Potential of a Charge Distribution
31.7
Electric Potential and Electric Field
31.7.1
(Calculus) Electric Potential From Electric Field
31.7.2
(Calculus) Gradient of Potential and Curl of Electric Field
31.7.3
(Calculus) Laplace’s Equation
31.7.4
Electric Potential in Constant Electric Field Region
31.7.5
Exercises
31.8
Conservation of Energy of Moving Charges
31.9
Electric Potential Bootcamp
31.9
Exercises
32
Conductors
32.1
Conductors and Insulators
32.1.1
Electric Field inside a Conductor
32.2
Charged Metal
32.2.1
Conduction Electrons
32.2.2
Polarization of Metal Near an External Charge
32.2.3
Charging a Metal
32.2.4
Distribution of Charges on the Metal Surfaces
32.3
Electric Field Inside Conductors
32.4
Electric Potential of Charged Conductors
32.4.1
An Isolated Charged Metallic Sphere
32.4.2
An Isolated Charged Long Metallic Wire
32.4.3
Exercises
32.5
Capacitors
32.5.1
Capacitance
32.5.2
(Calculus) Energy Stored in a Charged Capacitor
32.6
Parallel Plate Capacitor
32.6.1
Capacitor with a Dielectric between Plates
32.6.2
Exercises
32.7
Spherical Capacitor
32.7
Exercises
32.8
Cylindrical Capacitor
32.8
Exercises
32.9
Conductors as Boundaries
32.10
Method of Images
32.10.1
(Calculus) Electric Field for a Charge Near a Grounded Cunductor
32.10.2
(Calculus) Distribution of Induced Charges on Metal Plate near a Point Charge
32.10.3
Exercises
32.11
Conductors Bootcamp
32.11
Exercises
33
Dielectrics
33.1
Electric Dipoles
33.1.1
Electric Dipoles and Electric Dipole Moment
33.1.2
Induced Dipoles
33.1.3
Permanent Dipole Moments
33.1.4
Exercises
33.2
Force and Torque on an Electric Dipole
33.2.1
An Electric Dipole in a Constant Electric Field
33.2.2
(Calculus) Dipole in a Non-Uniform Electric Field
33.2.3
Exercises
33.3
Potential Energy of an Electric Dipole
33.3.1
(Calculus) Derivation of Potential Energy Formula
33.3.2
Exercises
33.4
Electric Potential of a Dipole
33.4.1
Derivation of Dipole Potential
33.4.2
(Calculus) Derivation of Dipole Electric Field
33.5
Linear Dielectrics
33.5.1
Polarization
33.5.2
Electric Field Inside a Dielectric
33.5.3
Electric Field Inside a Dielectric
33.5.4
Linear Dielectrics
33.5.5
Dielectric Breakdown
33.5.6
Exercises
33.6
Forces on Dielectrics
33.7
Dielectrics Bootcamp
33.7
Exercises
34
Current and DC Circuit
34.1
Electric Current
34.1.1
Electric Current in a Metal Wire
34.1.2
Current Density
34.1.3
Surface Current Density
34.1.4
Vector Current Density
34.1.5
Exercises
34.2
Electromotive Force
34.2.1
Van der Graaff Generator
34.2.2
(Calculus) EMF from Electric Field
34.3
Ohm’s Law
34.3.1
Conductivity and Resistivity
34.3.2
Conductance and Resistance
34.3.3
Current Through a Junction of Two Materials
34.3.4
Exercises
34.4
Power Dissipation
34.4
Exercises
34.5
Simple DC Circuits
34.5.1
A Simple DC Circuit
34.6
Resistors in Series
34.6.1
Current and Voltages in Series
34.6.2
Equivalent Resistance of Resitors in Series
34.6.3
Potential Drops Across Each Resistor in Series
34.6.4
Exercises
34.7
Resistors in Parallel
34.7.1
Potential Drop Across Resistors in Parallel
34.7.2
Currents in Resitors in Parallel
34.7.3
Equivalent Resistor of Resistors in Parallel
34.7.4
Exercises
34.8
Series-Parallel Method
34.8
Exercises
34.9
Kirchhoff’s Rules
34.9.1
Sign Conventions for Voltage in Loop Equation
34.9.2
Applying KCL and KVL
34.9.3
Exercises
34.10
The Wheatstone Bridge
34.11
Capacitor Discharging Circuit
34.11.1
(Calculus) Equation of Motion for Discharging a Capacitor
34.11.2
Exercises
34.12
Capacitor Charging Circuit
34.12.1
(Calculus) Equation of Motion for Charging a Capacitor
34.12.2
Exercises
34.13
Energy in Capacitors
34.14
Capacitors in Series
34.15
Capacitors in Parallel
34.16
Current and DC Circuits Bootcamp
34.16
Exercises
35
Magnetism
35.1
Magnets
35.2
Permanent and Temporary Magnets
35.2.1
Electromagnets
35.3
Existence of Magnetic Field
35.3.1
Magnetic Field of Current Carrying Wire
35.4
Magnetic Force on Moving Charges
35.4.1
Operational Definition of Magnetic Field
35.4.2
Lorentz Force on Electric Charges
35.4.3
Exercises
35.5
Force and Torque on Magnetic Dipole
35.5.1
(Calculus) Force on a Magnetic Dipole
35.6
Motion in a Magnetic Field
35.6.1
(Calculus) Equation of Motion of a Particle in Uniform Magnetic Field
35.6.2
Exercises
35.7
The Hall Effect
35.7
Exercises
35.8
Force on Current Carrying Wire
35.8.1
Derivation of Force on Current in Straight Wire
35.8.2
Effective Force on the Wire vs Magnetic Force on the Current
35.8.3
Force on a Wire with Multiple Straight Segments
35.8.4
(Calculus) Magnetic Force on Arbitrary Wire
35.8.5
Exercises
35.9
Torque on Current Carrying Wire
35.9.1
Magnetic Dipole Moment of Current Loop
35.9.2
Modeling Magnetic Dipoles as Current Loops
35.9.3
Exercises
35.10
Magnetism Bootcamp
35.10
Exercises
36
Magnetic Field
36.1
Magnetic Field of Steady Current
36.1.1
(Calculus) Biot-Savart Law
36.1.2
(Calculus) Strategy for Setting Up Biot-Savart Problems
36.1.3
Exercises
36.2
Magnetic Dipole Field
36.3
Circulation of Magnetic Field
36.3.1
(Calculus) General Definition of Circulation
36.3.2
Exercises
36.4
Ampere’s Law
36.4.1
(Calculus) Strategy for Using Ampere’s Law
36.4.2
(Calculus) Steps in Solving Ampere’s Law Problems
36.4.3
Exercises
36.5
Gauss’s Law for Magnetic Field
36.6
Magnetic Field Bootcamp
36.6
Exercises
37
Magnetic Materials
37.1
Magnetic Dipoles
37.1.1
Force on a Magnetic Dipole in a Uniform Magnetic Field
37.1.2
Torque on a Magnetic Dipole in a Uniform Magnetic Field
37.1.3
(Calculus) Force on a Magnetic Dipole in a Nonuniform Magnetic Field
37.1.4
Energy of a Magnetic Dipole in External Field
37.1.5
Exercises
37.2
Microscopic View of Magnetic Materials
37.2.1
Orbital Angular Momentum and Magnetic Dipole Moment
37.2.2
Spin Magnetic Dipole Moment
37.2.2.1
Total Angular Momentum
37.2.2.2
Pairing of Spins
37.3
Induced Magnetic Dipoles
37.4
Magnetization of Materials
37.4.1
Diamagnets, Paramagnets, and Ferromagnets
37.4.2
Nuclear Magnetization
37.4.3
Exercises
37.5
Magnetic Field of Magnets
37.5.1
(Calculus) A Uniformly Magnetized Thin Bar Magnet
37.5.2
(Calculus) A Uniformly Magnetized Sphere
37.6
Magnetization and Magnetic Field
37.6.1
Field in Paramagnets and Diamagnets
37.6.2
(Calculus) Ampere’s Law for Auxiliary Field
37.6.3
Field in Ferromagnets
37.6.4
Exercises
37.7
Magnetic Materials Bootcamp
37.7
Exercises
38
The Electromagnetic Effect
38.1
Faraday’s Experiments
38.2
Magnetic Flux
38.3
Faraday’s Flux Rule and Lenz’s Law
38.3.1
Moving Conductors
38.3.2
Changing Magnetic Field
38.3.3
Faraday’s Flux Rule
38.3.3.1
Case of Uniform Magnetic Field
38.3.4
Flux Rule and Stacking Loops
38.3.5
Lenz’s Law
38.3.6
Faraday’s Paradox
38.3.7
Exercises
38.4
Motional EMF
38.4.1
Moving Conductor in a Magnetic Field
38.4.2
Moving Metal Bar on a U-Shaped Metal
38.4.3
Energy Dissipation by Induced Current
38.4.4
Exercises
38.5
Motional EMF from Rotation
38.5.1
(Calculus) Energy Required for Rotation of Loop in Magnetic Field
38.6
Eddy’s Current
38.7
Faraday’s Law
38.7.1
(Calculus) Faraday’s Law
38.7.2
Analogy Between Faraday’s law and Ampere’s law
38.7.3
Exercises
38.8
Nonconservative Electric Field
38.9
Electromagnetic Effect Bootcamp
38.9
Exercises
39
Inductance
39.1
Mutual Inductance
39.1.1
Symmetry of Mutual Inductance
39.2
Self-Inductance
39.3
Inductance in Circuits
39.3.1
Energy Dissipation in RL-circuit
39.3.2
(Calculus) Current After Closing Switch in an Inductive Circuit
39.3.3
Inductors in Series and Parallel
39.3.4
Exercises
39.4
Energy in an Inductor
39.4.1
Energy in Magnetic Field
39.4.2
Energy in Interacting Inductors
39.5
Inductance Bootcamp
39.5
Exercises
40
Electromagnetic Oscillations
40.1
LC Circuits
40.1.1
(Calculus) Equation of Motion of LC circuit
40.1.1.1
Solution of Equation of Motion
40.1.2
Analogy Between Simple Harmonic Oscillator and LC Circuit
40.1.3
Energy in an LC-Circuit
40.2
Damping by Resistance
40.2.1
Meaning of
\(\gamma\)
40.2.2
Quality Factor Q of an Oscillator
40.2.3
(Calculus) Equation of Motion of RLC circuit
40.2.4
(Calculus) Solution of Equation of Motion of RLC circuit
40.2.4.1
Underdamping Case with
\(q(0)=Q_0\)
and
\(I(0)=0\)
40.2.5
Exercises
40.3
Driven Oscillations
40.3.1
(Calculus) Equation of Motion of Driven RLC Circuit
40.3.2
(Calculus) Solution of Equation of Motion of Driven RLC Circuit
40.3.3
Power Delivered to the Circuit by the EMF Source
40.4
Resonance in Driven Circuits
40.4.1
Resonance of Voltage Across Capacitor
40.4.2
Dependence of Phase on the Driving Frequency
40.4.3
Resonance of Current
40.4.4
Exercises
40.5
Power Delivered by the Source
40.5
Exercises
40.6
EM-Oscillations Bootcamp
40.6
Exercises
41
AC Circuits
41.1
AC Source
41.1.1
Phases of Power Lines
41.1.2
Phases of Currents and voltages
41.1.3
(Calculus) The Ideal AC Generator
41.2
Passive Circuit Elements
41.3
Inductive AC Circuits
41.3.1
Series RL Circuit
41.3.2
Exercises
41.4
Capacitative AC Circuits
41.4.1
Series RC Circuit
41.4.2
Exercises
41.5
RLC Circuits
41.5.1
Resonance of Current in Driven RLC Circuits
41.5.2
Exercises
41.6
Power in AC Circuits
41.6.1
Power of an AC Source Driving an RLC Circuit
41.6.2
Exercises
41.7
Circuit Analysis Using Complex Numbers
41.7.1
Rectangular and Polar Forms of Complex Numbers
41.7.2
Complex Impedance of a Resistor
41.7.3
Complex Impedance of an Inductor
41.7.4
Complex Impedance of a Capacitor
41.7.5
AC Circuit Problems
41.7.6
Exercises
41.8
Coupled Circuits
41.8.1
Transformers
41.8.2
Exercises
41.9
AC Circuits Bootcamp
41.9
Exercises
42
Maxwell’s Equations
42.1
Displacement Current
42.1
Exercises
42.2
Maxwell’s Equations in Point Form
42.2.1
Maxwell’s Equations
42.2.2
Exercises
42.3
Conservation of Charge
42.4
Electromagnetic Waves
42.4.1
Hertz’s Experiment For Production And Detection Of EM Waves
42.4.2
Plane Electromagnetic Waves
42.4.3
Wavelength and Wavenumber
42.4.4
Time Period and Frequency
42.4.5
Transverse Nature of Electromagnetic Waves in Vacuum
42.4.6
The Electromagnetic Spectrum
42.4.7
Energy and Intensity of EM Waves
42.4.8
Momentum of EM Wave and Radiation Pressure
42.4.9
Exercises
42.5
Maxwell’s Equations Bootcamp
42.5
Exercises
V
Optics
43
Fundamentals of Optics
43.1
Spectrum and Photons
43.2
Ray Optics versus Wave Optics
43.2
Exercises
43.3
Speed of Light
43.3.1
SI Unit of Length
43.3.2
Exercises
43.4
Radiometry
43.5
Photometry
43.5
Exercises
43.6
Optical Media
43.6.1
Transparent Medium
43.6.2
Dispersion of Media
43.6.3
Exercises
43.7
Reflection and Refraction
43.7.1
Law of reflection
43.7.2
Law of Refraction or Snell’s Law
43.7.3
Exercises
43.8
Bending of Light at Plane Interface
43.8.1
Total Internal Reflection and Critical Angle
43.8.2
Total Internal Reflections in Fiber Optics
43.8.3
Bending of Light Through a Prism
43.8.4
Exercises
43.9
Fermat’s Principle
43.9.1
(Calculus) Law of Reflection from Fermat’s Principle
43.9.2
(Calculus) Law of Refraction from Fermat’s Principle
43.9.3
Fermal’s Principle is Fundamental
43.9.4
Exercises
43.10
Fundamentals of Optics Bootcamp
43.10
Exercises
44
Image Formation
44.1
Image Formation by Reflection
44.1.1
Image in a Plane Mirror
44.1.2
Multiple Images
44.1.3
Exercises
44.2
Curved Mirrors
44.2.1
Image by Convex Mirror
44.2.1.1
Locating Image of an Arbitrary Point Object By a Convex Mirror
44.2.2
Image by Concave Mirror
44.2.2.1
Object Within Focal Length of Concave Mirror
44.2.2.2
Object Farther than Focal Length of Concave Mirror
44.2.3
Exercises
44.3
Image Formation by Reflection - Algebraic Methods
44.3.1
Concave Mirror Equation
44.3.2
Size and Orientation of Image
44.3.3
Virtual Image by a Concave Mirror
44.3.4
Convex Mirror Equation
44.3.4.1
Sign Convention
44.3.4.2
Size and Orientation of Image by Convex Mirror
44.3.5
Summary
44.3.6
Exercises
44.4
Image Formation by Refraction
44.4.1
Refraction at a Convex Surface
44.4.1.1
Image of an Off-Axis Point
44.4.1.2
First and Second Focal Points
44.4.2
Refraction at a Concave Surface
44.4.3
Transverse Magnification of Image by Refraction at Spherical Surface
44.4.4
Apparent Depth Behind Curved Surface
44.4.5
Exercises
44.5
Lenses
44.5.1
Special Rays Through a Thin Converging Lens
44.5.2
Special Rays Through a Thin Diverging Lens
44.5.3
Focal Length and Power of Lens
44.6
Image Formation by Thin Lens
44.6.1
Real Image by a Convex Lens
44.6.2
Virtual Image by a Convex Lens
44.6.3
Image by a Concave Lens
44.6.4
Exercises
44.7
Lens-Maker Equation
44.8
Image in Two-lens Systems
44.8.1
Ray Tracing in a Two-Lens System
44.8.2
Algebraic Method for Two-Lens System
44.8.3
Exercises
44.9
Image Formation Bootcamp
44.9
Exercises
45
Optical Instruments
45.1
Basics of Optical Instruments
45.1.1
Focal Length, Optical Equation, Magnifications
45.1.2
Aperture, Aperture Stop, Marginal Ray, Numerical Aperture
45.1.3
F/Number and F-Stops
45.1.4
Power of Stacked Lenses
45.1.5
Exercises
45.2
The Human Eye
45.2.1
Accomodation and Near Point
45.2.2
Common Eye Defects
45.2.3
Optical Power of Eye
45.2.4
Eye as an Optical Instrument
45.2.5
Exercises
45.3
Magnifying Glass
45.3.1
Role of Near Point of Eye
45.3.1.1
Placing the Viewing Object
45.3.1.2
Role of Eye in the Angular Magnification
45.3.2
Exercises
45.4
Compound Microscope
45.4.1
Magnification of a Compound Microscope
45.4.2
Exercises
45.5
Pinhole Camera
45.5.1
F/# of a Pinhole Camera
45.6
Telescope
45.6.1
Refracting Telescope
45.6.2
Reflecting Telescope
45.6.3
Resolving Power of a Telescope
45.6.4
Exercises
45.7
Optical Aberrations
45.7.1
Spherical Aberration
45.7.2
Coma
45.7.3
Astigmatism
45.7.4
Curvature of Field
45.7.5
Distortion
45.7.6
Chromatic Aberration
45.8
Optical Instruments Bootcamp
45.8
Exercises
46
Wave Descrition of Light
46.1
Electromagnetic Wave
46.2
Intensity of Light
46.2.1
Power Flow Through Slanted Surface
46.2.2
Intensity of an Isotropic Source
46.2.3
Exercises
46.3
Radiation Pressure
46.3
Exercises
46.4
Reflection and Refraction
46.4.1
Fresnel’s Equations
46.4.1.1
Plane of Incidence and Polarizations
46.4.1.2
Reflection and Transmission Coefficients
46.4.1.3
Fresnel Equations for S Polarized Waves
46.4.1.4
Fresnel Equations for P Polarized Waves
46.4.2
Reflection Coefficient, Brewster’s and Critical Angles
46.4.3
Reflectance and Transmittance
46.4.4
Reflection at Normal Incidence
46.4.5
Exercises
46.5
Polarization of Light
46.5.1
Linear Polarization
46.5.2
Circular Polarization
46.5.3
Malus’s Law
46.5.4
Polarizers
46.5.5
Linear Polarizers
46.5.6
Circularly Polarizer
46.5.7
Exercises
46.6
Birefrengence
46.7
Light Wave Bootcamp
46.7
Exercises
47
Interference of Light
47.1
Superposition Principle and Interference
47.2
Young’s Double-Slit Experiment
47.2.1
Intensity on the Screen
47.2.1.1
Conditions for Constructive and Destrucive Interferences
47.2.1.2
Conditions Near Center of Screen
47.2.1.3
Maximum Number of Fringes
47.2.2
Exercises
47.3
Interference from Dielectric Films
47.3.1
Derivation of Interference Conditions for Dielectric Film
47.3.2
Reflected Waves from a Wedge-shaped Film
47.3.2.1
Newton’s Rings
47.3.3
Exercises
47.4
Interferometers
47.5
Michelson Interferometer
47.6
Fabry-Perot Interferometer
47.6.1
Interference Condition in Fabry-Perot Interferometer
47.6.2
Intensity of Trnasmitted Waves in Fabry Perot
47.6.3
Applications of Fabry-Perot Interferometer
47.6.4
Exercises
47.7
Interference of Light Bootcamp
47.7
Exercises
48
Diffraction of Light
48.1
The Diffraction Phenomenon
48.2
The Huygens-Fresnel Principle
48.3
Diffraction Through a Single Slit
48.3.1
Minima in a Single-slit Diffraction
48.4
Intensity in Diffraction Pattern
48.4.1
Diffraction Maxima and Minima
48.5
Diffraction Through a Double-Slit
48.5.1
Derivation of the Intensity Formula
48.6
Circular Aperture and Resolution
48.7
Diffraction Grating
48.7.1
Maxima and Minima Directions in a Transmission Grating
48.7.2
Half-Widths of Principal Peaks
48.7.3
Dispersion of a Diffraction Grating
48.7.4
Resolving Power of a Diffraction Grating
48.7.5
Exercises
48.8
Diffraction of Light Bootcamp
48.8
Exercises
VI
Modern Physics
49
Special Relativity INPROGRESS
49.1
Galilean Relativity
49.1.1
Events
49.1.2
The Galilean Transformations
49.2
The Michelson-Morley Experiment
49.2.1
Michelson-Moreley Experiment
49.3
Mach’s Critique of Newtonian Thought
49.4
Postulates of Special Relativity
49.5
Einstein’s Clock
49.5.1
Synchronizing Clocks in One Frame
49.6
Time Dilation
49.6.1
View From Frame S’
49.6.2
The Twin Paradox
49.7
Lorentz Transformations
49.7.1
Derivation of Lorentz transformations
49.8
Length Contraction
49.9
Simultaneity
49.9.1
Order of Events
49.10
Transformation of Velocity
49.11
Relativistic Doppler Effect
49.11.1
Doppler Effect and Aberration
49.11.2
Ives-Stilwell Experiment
49.12
Relativistic Momentum
49.12.1
Derivation of
\(\vec p = \gamma m_0 v\)
49.12.2
What happens to
\(\vec F =d\vec p/dt\text{?}\)
49.13
Relativistic Energy
49.13.1
The Equivalence of Mass and Energy
49.14
Massless Particles
49.15
Special Relativity Bootcamp
49.15
Exercises
50
Quantum Nature of Light INPROGRESS
50.1
Historical Background
50.2
Light as Electromagnetic Waves
50.2.1
Hertz’s Experiment
50.2.2
Electromagnetic Spectrum
50.3
The Blackbody Radiation
50.3.1
Planck’s Explanation
50.4
Photoelectric Effect
50.4.1
Lenard and Millikan’s Experiments
50.4.2
Einstein’s Theory of Photoelectric Effect
50.4.3
How does Einstein’s photoelectric equation explain experimental results?
50.5
Compton Effect
50.5.1
Compton’s Experiment
50.6
Single Photon as Wave
50.7
Quantum Nature of Light Bootcamp
50.7
Exercises
51
Matter Waves INPROGRESS
51.1
Matter Waves
51.2
Evidence for Matter Waves
51.2.1
The Davisson-Germer Experiment
51.2.2
G. P. Thomson’s Experiment
51.2.3
The Tonomura Experiment
51.3
Schrödinger’s Equation
51.3.1
Probability Amplitude and Probability Current
51.4
Heisenberg’s Uncertainty Principle
51.5
Particle in a Box
51.6
Reflection of Wave
51.7
Quantum Tunneling
51.7.1
Scanning Tunneling Microscope
51.8
Matter Waves Bootcamp
51.8
Exercises
52
Atomic Structures INPROGRESS
52.1
The Discovery of Electron
52.2
Charge of an Electron
52.2.1
Millikan’s Oil Drop Experiment
52.3
Nuclear Model
52.3.1
The Rutherford’s Experiment
52.3.2
Chadwick’s Experiment and Discovery of Neutron
52.4
Spectroscopy of Hydrogen
52.5
The Bohr Model
52.5.1
Bohr’s Assumptions
52.5.2
Bohr’s Orbits
52.5.3
Allowed Energies for a Hydrogen Atom
52.5.4
Bohr’s Derivation of Rydberg Formula
52.6
Hydrogen Atom According to Schrödinger Equation
52.6.1
Quantum Numbers of Energy States of H Atom
52.6.2
Low-Energy States of Hydrogen Atom
52.6.3
Emission Spectrum of Hydrogen Atom
52.6.4
Quantization of Energy and Angular Momentum
52.7
Angular Momentum
52.7.1
Orbital Angular Momentum
52.7.2
Normal Zeeman Effect
52.7.3
Spin Angular Momentum
52.7.4
The Spin-Orbit Interaction
52.8
Pauli’s Exclusion Principle
52.8.1
Fermions and Bosons
52.8.2
Pauli’s Exclusion principle
52.8.3
Applications of Pauli’s Principle
52.9
Ordering of elements
52.9.1
X Rays and the Nuclear Charge
52.9.2
The Madelung Rule and the Aufbau Principle
52.10
Atomic Structures Bootcamp
52.10
Exercises
53
Electronic Properties of Meterials INPROGRESS
53.1
Molecules
53.1.1
Binding Energy
53.1.2
Types of Bonds
53.1.2.1
Ionic Bond
53.1.2.2
Covalent Bond
53.1.2.3
Hydrogen Bond
53.1.2.4
van der Waals Bond
53.2
Structure of Solids
53.2.1
X ray Diffraction from Single Crystals
53.2.2
The Powder X ray Diffraction
53.3
Conduction in Metals
53.3.1
Microscopic View of Ohm’s Law
53.3.2
Wiedemann-Franz Law
53.3.3
Temperature-dependence of Resistivity
53.4
Quantum Model of Conduction in Metals
53.4.1
Fermi Level
53.4.1.1
Free Electron Approximation
53.4.1.2
Fermi Energy
53.4.1.3
Density of States
53.4.1.4
Fermi-Dirac Distribution
53.4.2
Mean Free Path of Electrons in Metal
53.5
Band Structure
53.6
Semiconductors
53.6.1
Electron and Hole Carriers
53.6.2
Doped Semiconductors
53.6.3
The p-n Junction
53.6.4
The Light-Emitting Diode
53.6.5
The Diode Laser
53.7
Electronic Properties BootCamp
53.7
Exercises
54
Nuclear Physics INPROGRESS
54.1
Survey of Nuclear Properties
54.1.1
Nucleons
54.1.2
Charge, Mass, and Radius
54.1.3
Nuclear Stability and Binding Energy
54.1.3.1
\(N/Z\)
Ratio as a Measure of Stability
54.1.3.2
Evenness of
\(Z\text{,}\)
\(N\text{,}\)
and
\(A\)
as measures of stability
54.1.3.3
Binding energy as a measure of stability
54.1.4
Nuclear Spin and Magnetism
54.1.4.1
Nuclear Spin
54.1.4.2
Nuclear Magnetic Moment
54.1.4.3
Energy in a magnetic field
54.2
Radioactivity
54.2.1
Alpha, beta, and gamma rays
54.2.2
The Decay Dynamics
54.2.3
Radioactive Dating
54.2.4
Alpha Decay
54.2.5
Beta Decay
54.2.5.1
Electron Capture
54.2.6
Gamma Decay
54.2.7
Natural Radioactivity Series
54.3
Biological Effects of Radiation
54.3.1
Radiation Dose
54.3.1.1
Radiation Hazard
54.3.1.2
Medical Uses of Radiation
54.4
Nuclear Reactions
54.4.1
Nuclear Reaction Cross-section
54.4.2
Nuclear Reaction with Neutron
54.5
Nuclear Fission
54.5.1
Nuclear Chain Reaction
54.5.2
Harnessing energy from fission
54.5.2.1
Sustainable chain reaction
54.5.2.2
Moderator
54.5.2.3
Control Rods
54.5.2.4
Enrichment
54.5.2.5
Steam engine
54.6
Nuclear Fusion
54.6.1
Controlled Fusion
54.6.1.1
Magnetic Confinement
54.6.1.2
Inertial Confinement
54.7
Nuclear Physics Bootcamp
54.7
Exercises
55
Building Blocks of Nature INPROGRESS
55.1
Antiparticles
55.1.1
Other Antiparticles
55.2
The Fundamental Forces
55.2.1
Force Carriers
55.2.1.1
Yukawa Potential
55.3
Lepton, Hadrons, and Quarks
55.3.1
Leptons
55.3.1.1
Lepton Family Number Conservation
55.3.2
Hadrons, Baryons and Mesons
55.3.2.1
Baryon Number Conservation
55.3.2.2
Strange Conservation
55.3.3
Quarks
55.3.3.1
Eight-fold Way
55.3.3.2
Quark flavors
55.3.3.3
Quark Colors
55.3.3.4
Color force between quarks
55.3.3.5
Strong force between nucleons
55.4
The Standard Model of Particle Physics
55.5
Particle Production and Detection
55.5.1
Particle Production
55.5.1.1
Energy Required to Produce an Elementary Particle
55.5.2
Particle Detection
55.5.3
Counters
55.5.3.1
Ion chamber
55.5.3.2
Scintillation counter
55.5.4
Track Detectors
55.5.4.1
Nuclear emulsion
55.5.4.2
Cloud chamber
55.5.4.3
Bubble chamber
55.5.4.4
Wire chamber
55.6
Building Blocks Bootcamp
55.6
Exercises
56
Stars, Galaxies, and Universe INPROGRESS
56.1
Cosmic Distances
56.1.1
The Parallax Method
56.1.2
Limitations of the Parallax Method
56.1.3
Standard Candles for Distance
56.2
Luminosity and Temperature of Stars
56.2.1
Apparent Magnitude and Flux
56.2.2
Temperature of Stars
56.2.3
The Hertzsprung-Russell Diagram
56.3
Masses of Astronomical Objects
56.4
Energy Source of Sun
56.5
Life Cycles of Stars
56.5.1
Neutron Stars
56.5.2
Black Holes
56.6
The Milky Way and Other Galaxies
56.6.1
Active Galactic Nuclei
56.7
Hubble’s Law
56.7.1
Extragalactic Distances
56.7.1.1
Cepheids as standard candle
56.7.2
Recession Velocities
56.7.3
Hubble’s Law
56.8
Einstein’s Gravitation
56.8.1
Successes of Einstein’s Theory
56.8.2
Some Solutions of Einstein’s Equations
56.9
The Expanding Universe
56.9.1
Hubble’s Law and Big Bang Cosmology
56.9.2
Thermal History of Universe
56.10
Evidence for Big Bang
56.10.1
Dicovery of the Cosmic Background Radiation
56.10.2
The Origin of CMR
56.10.3
Nucleosynthesis of Light Elements
56.11
Dark Matter and Dark Energy
56.11.1
Critical Density
56.11.2
Amount of Matter in the Universe
56.11.3
Dark Energy and Acceleration of Universe
56.12
Stars and Galaxies Bootcamp
56.12
Exercises
Backmatter
Index
Colophon
Chapter
29
Coulomb’s Law
The electric force between charges is given Coulomb’s law which we will study in this chapter. If you have studied Newton’s law of gravitation, then a lot of the math in this chapter will be familiar to you.
29.1
Coulomb’s Force
29.2
Superposition of Forces
29.3
Electric Field
29.4
Superposition of Electric Fields
29.5
Electric Field Lines
29.6
Continuous Charge Distributions
29.7
Charged Particles in Electric Field
29.8
Coulomb’s Law Bootcamp
