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- 1 Mathematical Foundations of Physics ›
- 2 Part I: Classical Mechanics ›
- 3 Part II: Oscillations, Waves, and Fluids ›
- 4 Part III: Thermodynamics ›
- 5 Part IV: Electricity and Magnetism ›
- 6 Part V: Optics ›
- 7 Part VI: Modern Physics ›
- 8 Part VII: Nuclear and Particle Physics ›
- 9 Part VIII: Condensed Matter and Applied Physics ›
- 10 Part IX: Astrophysics and Cosmology ›
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2.4.4.5 Two-Dimensional Collisions
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2.4 Momentum and Collisions
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2.4.5.1 Center of Mass of Particles
2.4.5 Center of Mass
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- ☰ 1 Mathematical Foundations of Physics
- ☰ 1.1 Physical Quantities and Units
- ☰ 1.1.1 Physical Quantities
- ☰ 1.1.2 SI Base Units
- ☰ 1.1.3 Derived Units
- ☰ 1.1.4 Unit Conversions
- ☰ 1.1.5 Scientific Notation
- ☰ 1.1.6 Orders of Magnitude
- ☰ 1.1.7 Dimensional Analysis
- ☰ 1.1.8 Significant Figures
- ☰ 1.1.9 Measurement Uncertainty
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- ☰ 1.2 Scalars and Vectors
- ☰ 1.2.1 Scalars and Vectors
- ☰ 1.2.2 Vector Notation
- ☰ 1.2.3 Vector Addition and Subtraction
- ☰ 1.2.4 Vector Components
- ☰ 1.2.5 Unit Vectors
- ☰ 1.2.6 Dot Product
- ☰ 1.2.7 Cross Product
- ☰ 1.2.8 Applications of Vectors in Physics
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- ☰ 1.3 Coordinate Systems
- ☰ 1.3.1 Cartesian Coordinates
- ☰ 1.3.2 Polar Coordinates
- ☰ 1.3.3 Cylindrical Coordinates
- ☰ 1.3.4 Spherical Coordinates
- ☰ 1.3.5 Coordinate Transformations
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- ☰ 1.4 Calculus for Physics
- ☰ 1.4.1 Functions and Graphs
- ☰ 1.4.2 Derivatives
- ☰ 1.4.3 Physical Meaning of Derivatives
- ☰ 1.4.4 Partial Derivatives
- ☰ 1.4.5 Integrals
- ☰ 1.4.6 Physical Meaning of Integrals
- ☰ 1.4.7 Differential Equations
- ☰ 1.4.8 Taylor Series and Approximations
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- ☰ 2 Part I: Classical Mechanics
- ☰ 2.1 Kinematics
- ☰ 2.1.1 Motion in One Dimension
- ☰ 2.1.1.1 Position
- ☰ 2.1.1.2 Distance and Displacement
- ☰ 2.1.1.3 Speed and Velocity
- ☰ 2.1.1.4 Average Velocity
- ☰ 2.1.1.5 Instantaneous Velocity
- ☰ 2.1.1.6 Acceleration
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- ☰ 2.1.2 Motion with Constant Acceleration
- ☰ 2.1.2.1 Kinematic Equations
- ☰ 2.1.2.2 Free Fall
- ☰ 2.1.2.3 Vertical Motion
- ☰ 2.1.2.4 Position-Time Graphs
- ☰ 2.1.2.5 Velocity-Time Graphs
- ☰ 2.1.2.6 Acceleration-Time Graphs
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- ☰ 2.1.3 Motion in Two and Three Dimensions
- ☰ 2.1.3.1 Position Vectors
- ☰ 2.1.3.2 Velocity Vectors
- ☰ 2.1.3.3 Acceleration Vectors
- ☰ 2.1.3.4 Relative Motion
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- ☰ 2.1.4 Projectile Motion
- ☰ 2.1.4.1 Horizontal Projection
- ☰ 2.1.4.2 Oblique Projection
- ☰ 2.1.4.3 Maximum Height
- ☰ 2.1.4.4 Time of Flight
- ☰ 2.1.4.5 Projectile Range
- ☰ 2.1.4.6 Trajectory Equation
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- ☰ 2.1.5 Circular Motion
- ☰ 2.1.5.1 Angular Position
- ☰ 2.1.5.2 Angular Velocity
- ☰ 2.1.5.3 Angular Acceleration
- ☰ 2.1.5.4 Uniform Circular Motion
- ☰ 2.1.5.5 Centripetal Acceleration
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- ☰ 2.2 Newton's Laws of Motion
- ☰ 2.2.1 Force
- ☰ 2.2.1.1 Concept of Force
- ☰ 2.2.1.2 Fundamental Forces
- ☰ 2.2.1.3 Contact Forces
- ☰ 2.2.1.4 Free-Body Diagrams
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- ☰ 2.2.2 Newton's First Law
- ☰ 2.2.2.1 Inertia
- ☰ 2.2.2.2 Inertial Reference Frames
- ☰ 2.2.2.3 Equilibrium
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- ☰ 2.2.3 Newton's Second Law
- ☰ 2.2.3.1 Force, Mass, and Acceleration
- ☰ 2.2.3.2 Net Force
- ☰ 2.2.3.3 Applications of F = ma
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- ☰ 2.2.4 Newton's Third Law
- ☰ 2.2.4.1 Action-Reaction Pairs
- ☰ 2.2.4.2 Interaction Forces
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- ☰ 2.2.5 Common Forces
- ☰ 2.2.5.1 Weight
- ☰ 2.2.5.2 Normal Force
- ☰ 2.2.5.3 Tension
- ☰ 2.2.5.4 Spring Force
- ☰ 2.2.5.5 Static Friction
- ☰ 2.2.5.6 Kinetic Friction
- ☰ 2.2.5.7 Drag Force
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- ☰ 2.2.6 Applications of Newton's Laws
- ☰ 2.2.6.1 Connected Objects
- ☰ 2.2.6.2 Pulley Systems
- ☰ 2.2.6.3 Inclined Planes
- ☰ 2.2.6.4 Elevators
- ☰ 2.2.6.5 Circular Motion
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- ☰ 2.3 Work and Energy
- ☰ 2.3.1 Work
- ☰ 2.3.1.1 Work Done by a Constant Force
- ☰ 2.3.1.2 Work Done by a Variable Force
- ☰ 2.3.1.3 Work from Force-Position Graphs
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- ☰ 2.3.2 Kinetic Energy
- ☰ 2.3.2.1 Translational Kinetic Energy
- ☰ 2.3.2.2 Work-Energy Theorem
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- ☰ 2.3.3 Potential Energy
- ☰ 2.3.3.1 Gravitational Potential Energy
- ☰ 2.3.3.2 Elastic Potential Energy
- ☰ 2.3.3.3 Potential-Energy Curves
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- ☰ 2.3.4 Conservation of Energy
- ☰ 2.3.4.1 Mechanical Energy
- ☰ 2.3.4.2 Conservative Forces
- ☰ 2.3.4.3 Non-Conservative Forces
- ☰ 2.3.4.4 Conservation of Mechanical Energy
- ☰ 2.3.4.5 Energy Dissipation
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- ☰ 2.3.5 Power
- ☰ 2.3.5.1 Average Power
- ☰ 2.3.5.2 Instantaneous Power
- ☰ 2.3.5.3 Efficiency
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- ☰ 2.4 Momentum and Collisions
- ☰ 2.4.1 Linear Momentum
- ☰ 2.4.1.1 Momentum
- ☰ 2.4.1.2 Momentum and Force
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- ☰ 2.4.2 Impulse
- ☰ 2.4.2.1 Impulse
- ☰ 2.4.2.2 Impulse-Momentum Theorem
- ☰ 2.4.2.3 Force-Time Graphs
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- ☰ 2.4.3 Conservation of Momentum
- ☰ 2.4.3.1 Isolated Systems
- ☰ 2.4.3.2 Center-of-Mass Motion
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- ☰ 2.4.4 Collisions
- ☰ 2.4.4.1 Elastic Collisions
- ☰ 2.4.4.2 Inelastic Collisions
- ☰ 2.4.4.3 Perfectly Inelastic Collisions
- ☰ 2.4.4.4 One-Dimensional Collisions
- ☰ 2.4.4.5 Two-Dimensional Collisions
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- ☰ 2.4.5 Center of Mass
- ☰ 2.4.5.1 Center of Mass of Particles
- ☰ 2.4.5.2 Center of Mass of Continuous Objects
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- ☰ 2.4.6 Rocket Motion
- ☰ 2.4.6.1 Variable-Mass Systems
- ☰ 2.4.6.2 Rocket Equation
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- ☰ 2.5 Rotational Motion
- ☰ 2.5.1 Rotational Kinematics
- ☰ 2.5.1.1 Angular Displacement
- ☰ 2.5.1.2 Angular Velocity
- ☰ 2.5.1.3 Angular Acceleration
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- ☰ 2.5.2 Torque
- ☰ 2.5.2.1 Torque
- ☰ 2.5.2.2 Lever Arm
- ☰ 2.5.2.3 Vector Definition of Torque
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- ☰ 2.5.3 Moment of Inertia
- ☰ 2.5.3.1 Rotational Inertia
- ☰ 2.5.3.2 Common Moments of Inertia
- ☰ 2.5.3.3 Parallel-Axis Theorem
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- ☰ 2.5.4 Rotational Dynamics
- ☰ 2.5.4.1 Newton's Second Law for Rotation
- ☰ 2.5.4.2 Rotational Kinetic Energy
- ☰ 2.5.4.3 Work and Power in Rotation
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- ☰ 2.5.5 Angular Momentum
- ☰ 2.5.5.1 Angular Momentum
- ☰ 2.5.5.2 Conservation of Angular Momentum
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- ☰ 2.5.6 Rolling Motion
- ☰ 2.5.6.1 Rolling Without Slipping
- ☰ 2.5.6.2 Translational and Rotational Energy
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- ☰ 2.5.7 Static Equilibrium
- ☰ 2.5.7.1 Conditions for Equilibrium
- ☰ 2.5.7.2 Center of Gravity
- ☰ 2.5.7.3 Stability
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- ☰ 2.6 Gravitation
- ☰ 2.6.1 Newton's Law of Gravitation
- ☰ 2.6.1.1 Universal Gravitation
- ☰ 2.6.1.2 Gravitational Constant
- ☰ 2.6.1.3 Superposition
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- ☰ 2.6.2 Gravitational Field
- ☰ 2.6.2.1 Gravitational Field Strength
- ☰ 2.6.2.2 Field of Spherical Bodies
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- ☰ 2.6.3 Gravitational Potential
- ☰ 2.6.3.1 Gravitational Potential Energy
- ☰ 2.6.3.2 Gravitational Potential
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- ☰ 2.6.4 Planetary Motion
- ☰ 2.6.4.1 Kepler's Laws
- ☰ 2.6.4.2 Circular Orbits
- ☰ 2.6.4.3 Orbital Velocity
- ☰ 2.6.4.4 Orbital Period
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- ☰ 2.6.5 Satellites and Spaceflight
- ☰ 2.6.5.1 Geostationary Satellites
- ☰ 2.6.5.2 Escape Velocity
- ☰ 2.6.5.3 Orbital Energy
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- ☰ 3 Part II: Oscillations, Waves, and Fluids
- ☰ 3.1 Oscillations
- ☰ 3.1.1 Simple Harmonic Motion
- ☰ 3.1.1.1 Periodic Motion
- ☰ 3.1.1.2 Amplitude
- ☰ 3.1.1.3 Frequency and Period
- ☰ 3.1.1.4 Angular Frequency
- ☰ 3.1.1.5 SHM Equation
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- ☰ 3.1.2 Mass-Spring Systems
- ☰ 3.1.2.1 Hooke's Law
- ☰ 3.1.2.2 Spring Oscillations
- ☰ 3.1.2.3 Energy in SHM
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- ☰ 3.1.3 Pendulums
- ☰ 3.1.3.1 Simple Pendulum
- ☰ 3.1.3.2 Physical Pendulum
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- ☰ 3.1.4 Damped Oscillations
- ☰ 3.1.4.1 Damping
- ☰ 3.1.4.2 Critical Damping
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- ☰ 3.1.5 Forced Oscillations and Resonance
- ☰ 3.1.5.1 Driving Force
- ☰ 3.1.5.2 Resonance
- ☰ 3.1.5.3 Natural Frequency
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- ☰ 3.2 Mechanical Waves
- ☰ 3.2.1 Fundamentals of Waves
- ☰ 3.2.1.1 Transverse Waves
- ☰ 3.2.1.2 Longitudinal Waves
- ☰ 3.2.1.3 Wavelength
- ☰ 3.2.1.4 Frequency
- ☰ 3.2.1.5 Wave Speed
- ☰ 3.2.1.6 Amplitude
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- ☰ 3.2.2 Mathematical Description of Waves
- ☰ 3.2.2.1 Wave Function
- ☰ 3.2.2.2 Phase
- ☰ 3.2.2.3 Wave Equation
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- ☰ 3.2.3 Superposition
- ☰ 3.2.3.1 Interference
- ☰ 3.2.3.2 Constructive Interference
- ☰ 3.2.3.3 Destructive Interference
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- ☰ 3.2.4 Standing Waves
- ☰ 3.2.4.1 Nodes and Antinodes
- ☰ 3.2.4.2 Strings
- ☰ 3.2.4.3 Pipes
- ☰ 3.2.4.4 Harmonics
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- ☰ 3.2.5 Sound Waves
- ☰ 3.2.5.1 Speed of Sound
- ☰ 3.2.5.2 Sound Intensity
- ☰ 3.2.5.3 Decibels
- ☰ 3.2.5.4 Beats
- ☰ 3.2.5.5 Doppler Effect
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- ☰ 3.3 Fluid Mechanics
- ☰ 3.3.1 Properties of Fluids
- ☰ 3.3.1.1 Density
- ☰ 3.3.1.2 Pressure
- ☰ 3.3.1.3 Compressibility
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- ☰ 3.3.2 Fluid Statics
- ☰ 3.3.2.1 Hydrostatic Pressure
- ☰ 3.3.2.2 Pascal's Principle
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- ☰ 3.3.3 Buoyancy
- ☰ 3.3.3.1 Archimedes' Principle
- ☰ 3.3.3.2 Floating and Sinking
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- ☰ 3.3.4 Fluid Dynamics
- ☰ 3.3.4.1 Flow Rate
- ☰ 3.3.4.2 Continuity Equation
- ☰ 3.3.4.3 Bernoulli's Equation
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- ☰ 3.3.5 Viscosity
- ☰ 3.3.5.1 Laminar Flow
- ☰ 3.3.5.2 Turbulent Flow
- ☰ 3.3.5.3 Poiseuille's Law
- ☰ 3.3.5.4 Reynolds Number
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- ☰ 4 Part III: Thermodynamics
- ☰ 4.1 Temperature and Heat
- ☰ 4.1.1 Temperature and Thermal Equilibrium
- ☰ 4.1.2 Zeroth Law of Thermodynamics
- ☰ 4.1.3 Temperature Scales
- ☰ 4.1.4 Thermal Expansion
- ☰ 4.1.5 Heat and Internal Energy
- ☰ 4.1.6 Specific Heat Capacity
- ☰ 4.1.7 Calorimetry
- ☰ 4.1.8 Phase Changes
- ☰ 4.1.9 Latent Heat
- ☰ 4.1.10 Heat Transfer
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- ☰ 4.2 Kinetic Theory of Gases
- ☰ 4.2.1 Ideal Gas Law
- ☰ 4.2.2 Molecular Interpretation of Pressure
- ☰ 4.2.3 Temperature and Molecular Kinetic Energy
- ☰ 4.2.4 RMS Molecular Speed
- ☰ 4.2.5 Maxwell-Boltzmann Distribution
- ☰ 4.2.6 Mean Free Path
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- ☰ 4.3 Thermodynamics
- ☰ 4.3.1 Thermodynamic Systems
- ☰ 4.3.2 First Law of Thermodynamics
- ☰ 4.3.3 Isothermal Processes
- ☰ 4.3.4 Isobaric Processes
- ☰ 4.3.5 Isochoric Processes
- ☰ 4.3.6 Adiabatic Processes
- ☰ 4.3.7 Heat Engines
- ☰ 4.3.8 Carnot Cycle
- ☰ 4.3.9 Refrigerators
- ☰ 4.3.10 Second Law of Thermodynamics
- ☰ 4.3.11 Entropy
- ☰ 4.3.12 Reversible and Irreversible Processes
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- ☰ 5 Part IV: Electricity and Magnetism
- ☰ 5.1 Electric Charge and Electric Field
- ☰ 5.1.1 Electric Charge
- ☰ 5.1.2 Conductors and Insulators
- ☰ 5.1.3 Coulomb's Law
- ☰ 5.1.4 Superposition
- ☰ 5.1.5 Electric Field
- ☰ 5.1.6 Electric Field Lines
- ☰ 5.1.7 Electric Dipoles
- ☰ 5.1.8 Electric Flux
- ☰ 5.1.9 Gauss's Law
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- ☰ 5.2 Electric Potential
- ☰ 5.2.1 Electric Potential Energy
- ☰ 5.2.2 Electric Potential
- ☰ 5.2.3 Equipotential Surfaces
- ☰ 5.2.4 Relationship Between Potential and Field
- ☰ 5.2.5 Potential of Continuous Charge Distributions
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- ☰ 5.3 Capacitance
- ☰ 5.3.1 Capacitors
- ☰ 5.3.2 Parallel-Plate Capacitor
- ☰ 5.3.3 Series and Parallel Capacitors
- ☰ 5.3.4 Energy Stored in Capacitors
- ☰ 5.3.5 Dielectrics
- ☰ 5.3.6 Polarization
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- ☰ 5.4 Electric Current and Resistance
- ☰ 5.4.1 Electric Current
- ☰ 5.4.2 Current Density
- ☰ 5.4.3 Drift Velocity
- ☰ 5.4.4 Resistance
- ☰ 5.4.5 Ohm's Law
- ☰ 5.4.6 Resistivity
- ☰ 5.4.7 Electrical Energy
- ☰ 5.4.8 Electric Power
- ☰ 5.4.9 Electromotive Force
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- ☰ 5.5 DC Circuits
- ☰ 5.5.1 Kirchhoff's Laws
- ☰ 5.5.2 Multi-Loop Circuits
- ☰ 5.5.3 RC Circuits
- ☰ 5.5.4 Measuring Instruments
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- ☰ 5.6 Magnetism
- ☰ 5.6.1 Magnetic Fields
- ☰ 5.6.2 Lorentz Force
- ☰ 5.6.3 Motion of Charged Particles
- ☰ 5.6.4 Force on Current-Carrying Wires
- ☰ 5.6.5 Torque on Current Loops
- ☰ 5.6.6 Biot-Savart Law
- ☰ 5.6.7 Ampère's Law
- ☰ 5.6.8 Solenoids
- ☰ 5.6.9 Magnetic Materials
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- ☰ 5.7 Electromagnetic Induction
- ☰ 5.7.1 Magnetic Flux
- ☰ 5.7.2 Faraday's Law
- ☰ 5.7.3 Lenz's Law
- ☰ 5.7.4 Motional EMF
- ☰ 5.7.5 Self-Inductance
- ☰ 5.7.6 Mutual Inductance
- ☰ 5.7.7 RL Circuits
- ☰ 5.7.8 LC Oscillations
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- ☰ 5.8 Alternating Current
- ☰ 5.8.1 AC Voltage and Current
- ☰ 5.8.2 RMS Quantities
- ☰ 5.8.3 Resistors in AC Circuits
- ☰ 5.8.4 Capacitors in AC Circuits
- ☰ 5.8.5 Inductors in AC Circuits
- ☰ 5.8.6 RLC Circuits
- ☰ 5.8.7 Impedance
- ☰ 5.8.8 Resonance
- ☰ 5.8.9 Transformers
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- ☰ 5.9 Maxwell's Equations and Electromagnetic Waves
- ☰ 5.9.1 Gauss's Law for Electricity
- ☰ 5.9.2 Gauss's Law for Magnetism
- ☰ 5.9.3 Faraday's Law
- ☰ 5.9.4 Ampère-Maxwell Law
- ☰ 5.9.5 Electromagnetic Waves
- ☰ 5.9.6 Speed of Light
- ☰ 5.9.7 Electromagnetic Spectrum
- ☰ 5.9.8 Poynting Vector
- ☰ 5.9.9 Radiation Pressure
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- ☰ 6 Part V: Optics
- ☰ 6.1 Geometrical Optics
- ☰ 6.1.1 Nature of Light
- ☰ 6.1.2 Reflection
- ☰ 6.1.3 Plane Mirrors
- ☰ 6.1.4 Refraction
- ☰ 6.1.5 Snell's Law
- ☰ 6.1.6 Total Internal Reflection
- ☰ 6.1.7 Spherical Mirrors
- ☰ 6.1.8 Thin Lenses
- ☰ 6.1.9 Mirror Equation
- ☰ 6.1.10 Lens Equation
- ☰ 6.1.11 Magnification
- ☰ 6.1.12 Ray Diagrams
- ☰ 6.1.13 Optical Instruments
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- ☰ 6.2 Wave Optics
- ☰ 6.2.1 Interference
- ☰ 6.2.2 Young's Double-Slit Experiment
- ☰ 6.2.3 Diffraction
- ☰ 6.2.4 Single-Slit Diffraction
- ☰ 6.2.5 Diffraction Gratings
- ☰ 6.2.6 Polarization
- ☰ 6.2.7 Malus's Law
- ☰ 6.2.8 Brewster's Angle
- ☰ 6.2.9 Rayleigh Criterion
- ☰ 6.2.10 Optical Resolution
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- ☰ 7 Part VI: Modern Physics
- ☰ 7.1 Special Relativity
- ☰ 7.1.1 Galilean Relativity
- ☰ 7.1.2 Michelson-Morley Experiment
- ☰ 7.1.3 Einstein's Postulates
- ☰ 7.1.4 Lorentz Transformations
- ☰ 7.1.5 Relativity of Simultaneity
- ☰ 7.1.6 Time Dilation
- ☰ 7.1.7 Length Contraction
- ☰ 7.1.8 Relativistic Velocity Addition
- ☰ 7.1.9 Relativistic Momentum
- ☰ 7.1.10 Relativistic Energy
- ☰ 7.1.11 Mass-Energy Equivalence
- ☰ 7.1.12 Energy-Momentum Relation
- ☰ 7.1.13 Spacetime Diagrams
- ☰ 7.1.14 Light Cones
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- ☰ 7.2 Introduction to Quantum Physics
- ☰ 7.2.1 Blackbody Radiation
- ☰ 7.2.2 Planck's Hypothesis
- ☰ 7.2.3 Photoelectric Effect
- ☰ 7.2.4 Photon Energy
- ☰ 7.2.5 Photon Momentum
- ☰ 7.2.6 Compton Scattering
- ☰ 7.2.7 de Broglie Wavelength
- ☰ 7.2.8 Matter Waves
- ☰ 7.2.9 Wave-Particle Duality
- ☰ 7.2.10 Double-Slit Experiment
- ☰ 7.2.11 Heisenberg Uncertainty Principle
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- ☰ 7.3 Quantum Mechanics
- ☰ 7.3.1 Wave Function
- ☰ 7.3.2 Probability Interpretation
- ☰ 7.3.3 Normalization
- ☰ 7.3.4 Schrödinger Equation
- ☰ 7.3.5 Operators and Observables
- ☰ 7.3.6 Expectation Values
- ☰ 7.3.7 Particle in a Box
- ☰ 7.3.8 Finite Potential Wells
- ☰ 7.3.9 Quantum Tunneling
- ☰ 7.3.10 Quantum Harmonic Oscillator
- ☰ 7.3.11 Hydrogen Atom
- ☰ 7.3.12 Quantum Numbers
- ☰ 7.3.13 Angular Momentum
- ☰ 7.3.14 Spin
- ☰ 7.3.15 Stern-Gerlach Experiment
- ☰ 7.3.16 Pauli Exclusion Principle
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- ☰ 7.4 Atomic Physics
- ☰ 7.4.1 Thomson Atomic Model
- ☰ 7.4.2 Rutherford Atomic Model
- ☰ 7.4.3 Bohr Model
- ☰ 7.4.4 Atomic Spectra
- ☰ 7.4.5 Hydrogen Spectrum
- ☰ 7.4.6 Electron Shells
- ☰ 7.4.7 Orbitals
- ☰ 7.4.8 Electron Configurations
- ☰ 7.4.9 X-Ray Spectra
- ☰ 7.4.10 Atomic Transitions
- ☰ 7.4.11 Lasers
- ☰ 7.4.12 Stimulated Emission
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- ☰ 8 Part VII: Nuclear and Particle Physics
- ☰ 8.1 Nuclear Structure
- ☰ 8.1.1 The Atomic Nucleus
- ☰ 8.1.1.1 Protons and Neutrons
- ☰ 8.1.1.2 Atomic Number
- ☰ 8.1.1.3 Mass Number
- ☰ 8.1.1.4 Isotopes
- ☰ 8.1.1.5 Isotones
- ☰ 8.1.1.6 Isobars
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- ☰ 8.1.2 Nuclear Size and Density
- ☰ 8.1.2.1 Nuclear Radius
- ☰ 8.1.2.2 Nuclear Density
- ☰ 8.1.2.3 Nuclear Charge Distribution
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- ☰ 8.1.3 Nuclear Forces
- ☰ 8.1.3.1 Strong Nuclear Force
- ☰ 8.1.3.2 Properties of Nuclear Forces
- ☰ 8.1.3.3 Proton-Neutron Interaction
- ☰ 8.1.3.4 Nuclear Stability
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- ☰ 8.1.4 Mass and Binding Energy
- ☰ 8.1.4.1 Atomic Mass Units
- ☰ 8.1.4.2 Mass Defect
- ☰ 8.1.4.3 Binding Energy
- ☰ 8.1.4.4 Binding Energy per Nucleon
- ☰ 8.1.4.5 Binding-Energy Curve
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- ☰ 8.1.5 Nuclear Models
- ☰ 8.1.5.1 Liquid-Drop Model
- ☰ 8.1.5.2 Semi-Empirical Mass Formula
- ☰ 8.1.5.3 Nuclear Shell Model
- ☰ 8.1.5.4 Magic Numbers
- ☰ 8.1.5.5 Collective Model
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- ☰ 8.1.6 Nuclear Spin and Magnetic Moments
- ☰ 8.1.6.1 Nuclear Angular Momentum
- ☰ 8.1.6.2 Nuclear Spin
- ☰ 8.1.6.3 Nuclear Magnetic Moment
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- ☰ 8.2 Radioactivity and Nuclear Decay
- ☰ 8.2.1 Radioactive Decay
- ☰ 8.2.1.1 Nuclear Instability
- ☰ 8.2.1.2 Random Nature of Decay
- ☰ 8.2.1.3 Decay Constant
-
- ☰ 8.2.2 Radioactive Decay Law
- ☰ 8.2.2.1 Exponential Decay
- ☰ 8.2.2.2 Activity
- ☰ 8.2.2.3 Half-Life
- ☰ 8.2.2.4 Mean Lifetime
-
- ☰ 8.2.3 Alpha Decay
- ☰ 8.2.3.1 Alpha Particles
- ☰ 8.2.3.2 Energy of Alpha Decay
-
- ☰ 8.2.4 Beta Decay
- ☰ 8.2.4.1 Beta-Minus Decay
- ☰ 8.2.4.2 Beta-Plus Decay
- ☰ 8.2.4.3 Electron Capture
- ☰ 8.2.4.4 Neutrinos
- ☰ 8.2.4.5 Energy Spectrum
-
- ☰ 8.2.5 Gamma Decay
- ☰ 8.2.5.1 Nuclear Excited States
- ☰ 8.2.5.2 Gamma-Ray Emission
- ☰ 8.2.5.3 Internal Conversion
-
- ☰ 8.2.6 Decay Chains
- ☰ 8.2.6.1 Parent and Daughter Nuclei
- ☰ 8.2.6.2 Secular Equilibrium
- ☰ 8.2.6.3 Natural Radioactive Series
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- ☰ 8.3 Interaction of Radiation with Matter
- ☰ 8.3.1 Charged Particle Interactions
- ☰ 8.3.1.1 Ionization
- ☰ 8.3.1.2 Excitation
- ☰ 8.3.1.3 Energy Loss
- ☰ 8.3.1.4 Stopping Power
- ☰ 8.3.1.5 Range
-
- ☰ 8.3.2 Heavy Charged Particles
- ☰ 8.3.2.1 Alpha Particles
- ☰ 8.3.2.2 Bragg Curve
- ☰ 8.3.2.3 Bragg Peak
-
- ☰ 8.3.3 Electron Interactions
- ☰ 8.3.3.1 Collisional Energy Loss
- ☰ 8.3.3.2 Bremsstrahlung
- ☰ 8.3.3.3 Electron Range
-
- ☰ 8.3.4 Photon Interactions
- ☰ 8.3.4.1 Pair Production
- ☰ 8.3.4.2 Rayleigh Scattering
-
- ☰ 8.3.5 Attenuation of Radiation
- ☰ 8.3.5.1 Linear Attenuation Coefficient
- ☰ 8.3.5.2 Mass Attenuation Coefficient
- ☰ 8.3.5.3 Exponential Attenuation
- ☰ 8.3.5.4 Half-Value Layer
-
- ☰ 8.3.6 Neutron Interactions
- ☰ 8.3.6.1 Elastic Scattering
- ☰ 8.3.6.2 Inelastic Scattering
- ☰ 8.3.6.3 Neutron Capture
- ☰ 8.3.6.4 Neutron Moderation
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- ☰ 8.4 Radiation Detection and Measurement
- ☰ 8.4.1 Principles of Radiation Detection
- ☰ 8.4.1.1 Energy Deposition
- ☰ 8.4.1.2 Detector Efficiency
- ☰ 8.4.1.3 Energy Resolution
- ☰ 8.4.1.4 Timing Resolution
- ☰ 8.4.1.5 Dead Time
-
- ☰ 8.4.2 Gas-Filled Detectors
- ☰ 8.4.2.1 Ionization Chambers
- ☰ 8.4.2.2 Proportional Counters
- ☰ 8.4.2.3 Geiger-Müller Counters
-
- ☰ 8.4.3 Scintillation Detectors
- ☰ 8.4.3.1 Scintillation Process
- ☰ 8.4.3.2 Organic Scintillators
- ☰ 8.4.3.3 Inorganic Scintillators
- ☰ 8.4.3.4 Photomultiplier Tubes
- ☰ 8.4.3.5 Silicon Photomultipliers
-
- ☰ 8.4.4 Semiconductor Detectors
- ☰ 8.4.4.1 Silicon Detectors
- ☰ 8.4.4.2 Germanium Detectors
- ☰ 8.4.4.3 Electron-Hole Pair Creation
-
- ☰ 8.4.5 Gamma-Ray Spectroscopy
- ☰ 8.4.5.1 Photopeak
- ☰ 8.4.5.2 Compton Continuum
- ☰ 8.4.5.3 Compton Edge
- ☰ 8.4.5.4 Escape Peaks
-
- ☰ 8.4.6 Coincidence Measurements
- ☰ 8.4.6.1 Coincidence Detection
- ☰ 8.4.6.2 Timing Windows
- ☰ 8.4.6.3 True Coincidences
- ☰ 8.4.6.4 Random Coincidences
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- ☰ 8.5 Nuclear Reactions
- ☰ 8.5.1 Principles of Nuclear Reactions
- ☰ 8.5.1.1 Reaction Notation
- ☰ 8.5.1.2 Conservation Laws
- ☰ 8.5.1.3 Reaction Energetics
-
- ☰ 8.5.2 Q-Value
- ☰ 8.5.2.1 Exothermic Reactions
- ☰ 8.5.2.2 Endothermic Reactions
- ☰ 8.5.2.3 Reaction Thresholds
-
- ☰ 8.5.3 Reaction Cross Section
- ☰ 8.5.3.1 Cross Section
- ☰ 8.5.3.2 Reaction Probability
- ☰ 8.5.3.3 Energy Dependence
-
- ☰ 8.5.4 Types of Nuclear Reactions
- ☰ 8.5.4.1 Elastic Scattering
- ☰ 8.5.4.2 Inelastic Scattering
- ☰ 8.5.4.3 Capture Reactions
- ☰ 8.5.4.4 Transfer Reactions
- ☰ 8.5.4.5 Charge-Exchange Reactions
-
- ☰ 8.5.5 Compound Nucleus
- ☰ 8.5.5.1 Formation
- ☰ 8.5.5.2 Decay Channels
- ☰ 8.5.5.3 Resonances
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- ☰ 8.6 Nuclear Fission and Fusion
- ☰ 8.6.1 Nuclear Fission
- ☰ 8.6.1.1 Fission Process
- ☰ 8.6.1.2 Fission Fragments
- ☰ 8.6.1.3 Energy Release
- ☰ 8.6.1.4 Neutron Production
-
- ☰ 8.6.2 Chain Reactions
- ☰ 8.6.2.1 Criticality
- ☰ 8.6.2.2 Multiplication Factor
- ☰ 8.6.2.3 Critical Mass
-
- ☰ 8.6.3 Nuclear Reactors
- ☰ 8.6.3.1 Reactor Components
- ☰ 8.6.3.2 Fuel
- ☰ 8.6.3.3 Moderator
- ☰ 8.6.3.4 Control Rods
- ☰ 8.6.3.5 Coolant
-
- ☰ 8.6.4 Nuclear Fusion
- ☰ 8.6.4.1 Fusion Reactions
- ☰ 8.6.4.2 Coulomb Barrier
-
- ☰ 8.6.5 Stellar Fusion
- ☰ 8.6.5.1 Proton-Proton Chain
- ☰ 8.6.5.2 CNO Cycle
- ☰ 8.6.5.3 Nucleosynthesis
-
- ☰ 8.6.6 Controlled Fusion
- ☰ 8.6.6.1 Magnetic Confinement
- ☰ 8.6.6.2 Tokamaks
- ☰ 8.6.6.3 Inertial Confinement
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- ☰ 8.7 Particle Physics Foundations
- ☰ 8.7.1 From Atoms to Elementary Particles
- ☰ 8.7.1.1 Discovery of the Electron
- ☰ 8.7.1.2 Discovery of the Nucleus
- ☰ 8.7.1.3 Discovery of the Neutron
- ☰ 8.7.1.4 Discovery of Antimatter
-
- ☰ 8.7.2 Classification of Particles
- ☰ 8.7.2.1 Elementary Particles
- ☰ 8.7.2.2 Composite Particles
- ☰ 8.7.2.3 Fermions
- ☰ 8.7.2.4 Bosons
-
- ☰ 8.7.3 Antiparticles
- ☰ 8.7.3.1 Matter and Antimatter
- ☰ 8.7.3.2 Pair Production
- ☰ 8.7.3.3 Annihilation
-
- ☰ 8.7.4 Relativistic Particle Kinematics
- ☰ 8.7.4.1 Four-Momentum
- ☰ 8.7.4.2 Invariant Mass
-
- ☰ 8.7.5 Particle Decays
- ☰ 8.7.5.1 Decay Width
- ☰ 8.7.5.2 Lifetime
- ☰ 8.7.5.3 Branching Ratio
- ☰ 8.7.5.4 Conservation Laws
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- ☰ 8.8 Quarks and Hadrons
- ☰ 8.8.1 Quarks
- ☰ 8.8.1.1 Up Quark
- ☰ 8.8.1.2 Down Quark
- ☰ 8.8.1.3 Strange Quark
- ☰ 8.8.1.4 Charm Quark
- ☰ 8.8.1.5 Top Quark
- ☰ 8.8.1.6 Bottom Quark
-
- ☰ 8.8.2 Quark Properties
- ☰ 8.8.2.1 Mass
- ☰ 8.8.2.2 Flavor
- ☰ 8.8.2.3 Color Charge
-
- ☰ 8.8.3 Hadrons
- ☰ 8.8.3.1 Baryons
- ☰ 8.8.3.2 Mesons
-
- ☰ 8.8.4 Baryon Structure
- ☰ 8.8.4.1 Proton Quark Structure
- ☰ 8.8.4.2 Neutron Quark Structure
- ☰ 8.8.4.3 Other Baryons
-
- ☰ 8.8.5 Meson Structure
- ☰ 8.8.5.1 Pions
- ☰ 8.8.5.2 Kaons
- ☰ 8.8.5.3 Heavy Mesons
-
- ☰ 8.8.6 Confinement
- ☰ 8.8.6.1 Color Confinement
- ☰ 8.8.6.2 Hadronization
- ☰ 8.8.6.3 Jets
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- ☰ 8.9 Leptons and Neutrinos
- ☰ 8.9.1 Charged Leptons
- ☰ 8.9.1.1 Electron
- ☰ 8.9.1.2 Muon
- ☰ 8.9.1.3 Tau
-
- ☰ 8.9.2 Neutrinos
- ☰ 8.9.2.1 Electron Neutrino
- ☰ 8.9.2.2 Muon Neutrino
- ☰ 8.9.2.3 Tau Neutrino
-
- ☰ 8.9.3 Neutrino Interactions
- ☰ 8.9.3.1 Weak Interactions
- ☰ 8.9.3.2 Neutrino Detection
-
- ☰ 8.9.4 Neutrino Oscillations
- ☰ 8.9.4.1 Neutrino Flavor
- ☰ 8.9.4.2 Flavor Oscillation
- ☰ 8.9.4.3 Neutrino Mass
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- ☰ 8.10 Fundamental Interactions
- ☰ 8.10.1 Four Fundamental Interactions
- ☰ 8.10.1.1 Electromagnetism
- ☰ 8.10.1.2 Strong Interaction
- ☰ 8.10.1.3 Weak Interaction
-
- ☰ 8.10.2 Exchange Particles
- ☰ 8.10.2.1 Photons
- ☰ 8.10.2.2 Gluons
- ☰ 8.10.2.3 W Bosons
- ☰ 8.10.2.4 Z Boson
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- ☰ 8.10.3 Electromagnetic Interaction
- ☰ 8.10.3.1 Photon Exchange
-
- ☰ 8.10.4 Strong Interaction
- ☰ 8.10.4.1 Color Charge
- ☰ 8.10.4.2 Gluons
- ☰ 8.10.4.3 Quantum Chromodynamics
-
- ☰ 8.10.5 Weak Interaction
- ☰ 8.10.5.1 Beta Decay
- ☰ 8.10.5.2 W and Z Bosons
- ☰ 8.10.5.3 Flavor-Changing Processes
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- ☰ 8.11 The Standard Model
- ☰ 8.11.1 Overview of the Standard Model
- ☰ 8.11.1.1 Matter Particles
- ☰ 8.11.1.2 Force Carriers
- ☰ 8.11.1.3 Particle Generations
-
- ☰ 8.11.2 Fermions
- ☰ 8.11.2.1 Quarks
- ☰ 8.11.2.2 Leptons
-
- ☰ 8.11.3 Gauge Bosons
- ☰ 8.11.3.1 Photon
- ☰ 8.11.3.2 Gluons
- ☰ 8.11.3.3 W Bosons
- ☰ 8.11.3.4 Z Boson
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- ☰ 8.11.4 Higgs Field and Higgs Boson
- ☰ 8.11.4.1 Higgs Field
- ☰ 8.11.4.2 Spontaneous Symmetry Breaking
- ☰ 8.11.4.3 Particle Masses
- ☰ 8.11.4.4 Higgs Boson
-
- ☰ 8.11.5 Standard Model Interactions
- ☰ 8.11.5.1 Electroweak Theory
- ☰ 8.11.5.2 Quantum Chromodynamics
-
- ☰ 8.11.6 Limitations of the Standard Model
- ☰ 8.11.6.1 Gravity
- ☰ 8.11.6.2 Dark Matter
- ☰ 8.11.6.3 Neutrino Masses
- ☰ 8.11.6.4 Matter-Antimatter Asymmetry
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- ☰ 8.12 Symmetries and Conservation Laws
- ☰ 8.12.1 Conservation Laws
- ☰ 8.12.1.1 Energy
-
- ☰ 8.12.2 Particle Quantum Numbers
- ☰ 8.12.2.1 Baryon Number
- ☰ 8.12.2.2 Lepton Number
- ☰ 8.12.2.3 Strangeness
- ☰ 8.12.2.4 Charm
- ☰ 8.12.2.5 Isospin
-
- ☰ 8.12.3 Symmetries
- ☰ 8.12.3.1 Charge Conjugation
- ☰ 8.12.3.2 Parity
- ☰ 8.12.3.3 Time Reversal
-
- ☰ 8.12.4 CP Symmetry
- ☰ 8.12.4.1 CP Conservation
- ☰ 8.12.4.2 CP Violation
- ☰ 8.12.4.3 Matter-Antimatter Asymmetry
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- ☰ 8.13 Particle Accelerators
- ☰ 8.13.1 Principles of Acceleration
- ☰ 8.13.1.1 Electric-Field Acceleration
- ☰ 8.13.1.2 Magnetic-Field Steering
-
- ☰ 8.13.2 Linear Accelerators
- ☰ 8.13.2.1 LINACs
- ☰ 8.13.2.2 Radio-Frequency Acceleration
-
- ☰ 8.13.3 Cyclotrons
- ☰ 8.13.3.1 Cyclotron Principle
- ☰ 8.13.3.2 Cyclotron Frequency
- ☰ 8.13.3.3 Limitations
-
- ☰ 8.13.4 Synchrotrons
- ☰ 8.13.4.1 Circular Accelerators
- ☰ 8.13.4.2 Magnetic Focusing
- ☰ 8.13.4.3 RF Cavities
-
- ☰ 8.13.5 Colliders
- ☰ 8.13.5.1 Fixed-Target Experiments
- ☰ 8.13.5.2 Collider Experiments
- ☰ 8.13.5.3 Center-of-Mass Energy
-
- ☰ 8.13.6 Major Particle Accelerators
- ☰ 8.13.6.1 Large Hadron Collider
- ☰ 8.13.6.2 Electron-Positron Colliders
- ☰ 8.13.6.3 Heavy-Ion Colliders
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- ☰ 8.14 Particle Detectors
- ☰ 8.14.1 Principles of Particle Detection
- ☰ 8.14.1.1 Ionization
- ☰ 8.14.1.2 Excitation
- ☰ 8.14.1.3 Energy Deposition
- ☰ 8.14.1.4 Particle Identification
-
- ☰ 8.14.2 Tracking Detectors
- ☰ 8.14.2.1 Cloud Chambers
- ☰ 8.14.2.2 Bubble Chambers
- ☰ 8.14.2.3 Wire Chambers
- ☰ 8.14.2.4 Silicon Trackers
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- ☰ 8.14.3 Calorimeters
- ☰ 8.14.3.1 Electromagnetic Calorimeters
- ☰ 8.14.3.2 Hadronic Calorimeters
- ☰ 8.14.3.3 Shower Development
-
- ☰ 8.14.4 Cherenkov Detectors
- ☰ 8.14.4.1 Cherenkov Radiation
- ☰ 8.14.4.2 Particle Velocity Measurement
-
- ☰ 8.14.5 Time-of-Flight Detectors
- ☰ 8.14.5.1 Timing Measurements
- ☰ 8.14.5.2 Particle Identification
-
- ☰ 8.14.6 Modern Detector Systems
- ☰ 8.14.6.1 Tracking
- ☰ 8.14.6.2 Muon Systems
- ☰ 8.14.6.3 Trigger Systems
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- ☰ 9 Part VIII: Condensed Matter and Applied Physics
- ☰ 9.1 Solid-State Physics
- ☰ 9.1.1 Crystal Structure
- ☰ 9.1.1.1 Crystal Lattices
- ☰ 9.1.1.2 Unit Cells
- ☰ 9.1.1.3 Bravais Lattices
-
- ☰ 9.1.2 Electronic Properties
- ☰ 9.1.2.1 Energy Bands
- ☰ 9.1.2.2 Conductors
- ☰ 9.1.2.3 Insulators
- ☰ 9.1.2.4 Semiconductors
-
- ☰ 9.1.3 Semiconductor Physics
- ☰ 9.1.3.1 Intrinsic Semiconductors
- ☰ 9.1.3.2 Doping
- ☰ 9.1.3.3 p-Type Materials
- ☰ 9.1.3.4 n-Type Materials
- ☰ 9.1.3.5 p-n Junctions
-
- ☰ 9.1.4 Superconductivity
- ☰ 9.1.4.1 Zero Resistance
- ☰ 9.1.4.2 Meissner Effect
- ☰ 9.1.4.3 Critical Temperature
-
-
- ☰ 9.2 Electronics
- ☰ 9.2.1 Semiconductor Diodes
- ☰ 9.2.1.1 p-n Junction
- ☰ 9.2.1.2 Diode Characteristics
- ☰ 9.2.1.3 Rectifiers
-
- ☰ 9.2.2 Transistors
- ☰ 9.2.2.1 Bipolar Junction Transistors
- ☰ 9.2.2.2 Field-Effect Transistors
-
- ☰ 9.2.3 Operational Amplifiers
- ☰ 9.2.3.1 Ideal Op-Amp
- ☰ 9.2.3.2 Amplifiers
- ☰ 9.2.3.3 Comparators
-
- ☰ 9.2.4 Digital Electronics
- ☰ 9.2.4.1 Binary Numbers
- ☰ 9.2.4.2 Logic Gates
- ☰ 9.2.4.3 Boolean Algebra
- ☰ 9.2.4.4 Basic Digital Circuits
-
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- ☰ 10 Part IX: Astrophysics and Cosmology
- ☰ 10.1 Astrophysics
- ☰ 10.1.1 Measuring the Universe
- ☰ 10.1.1.1 Astronomical Distances
- ☰ 10.1.1.2 Parallax
- ☰ 10.1.1.3 Luminosity
- ☰ 10.1.1.4 Apparent Brightness
-
- ☰ 10.1.2 Stars
- ☰ 10.1.2.1 Stellar Spectra
- ☰ 10.1.2.2 Hertzsprung-Russell Diagram
- ☰ 10.1.2.3 Stellar Evolution
-
- ☰ 10.1.3 Stellar Remnants
- ☰ 10.1.3.1 White Dwarfs
- ☰ 10.1.3.2 Neutron Stars
- ☰ 10.1.3.3 Black Holes
-
- ☰ 10.1.4 Galaxies
- ☰ 10.1.4.1 Structure of Galaxies
- ☰ 10.1.4.2 Milky Way
- ☰ 10.1.4.3 Galaxy Classification
-
-
- ☰ 10.2 Cosmology
- ☰ 10.2.1 Expanding Universe
- ☰ 10.2.1.1 Hubble's Law
- ☰ 10.2.1.2 Cosmological Redshift
-
- ☰ 10.2.2 Big Bang Cosmology
- ☰ 10.2.2.1 Early Universe
- ☰ 10.2.2.2 Cosmic Microwave Background
- ☰ 10.2.2.3 Primordial Nucleosynthesis
-
- ☰ 10.2.3 Dark Matter
- ☰ 10.2.3.1 Evidence for Dark Matter
-
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