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Georgia Tech Student Wiki for Introductory Physics.

This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

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Source Material

All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).

• A physics resource written by experts for an expert audience Physics Portal
• A wiki written for students by a physics expert MSU Physics Wiki
• A wiki book on modern physics Modern Physics Wiki
• A collection of 26 volumes of lecture notes by Prof. Wheeler of Reed College [1]
• The MIT open courseware for intro physics MITOCW Wiki
• An online concept map of intro physics HyperPhysics
• Interactive physics simulations PhET
• OpenStax intro physics textbooks: Vol1, Vol2, Vol3
• The Open Source Physics project is a collection of online physics resources OSP
• A resource guide compiled by the AAPT for educators ComPADRE
• The Feynman lectures on physics are free to read Feynman
• Final Study Guide for Modern Physics II created by a lab TA Modern Physics II Final Study Guide

Resources

• Commonly used wiki commands Wiki Cheatsheet
• A guide to representing equations in math mode Wiki Math Mode
• A page to keep track of all the physics Constants
• A listing of Notable Scientist with links to their individual pages

Physics 1

Week 1

GlowScript 101

• Python Syntax
• GlowScript

VPython

• VPython
• VPython basics
• VPython Common Errors and Troubleshooting
• VPython Functions
• VPython Lists
• VPython Loops
• VPython Multithreading
• VPython Animation
• VPython Objects
• VPython 3D Objects
• VPython Reference
• VPython MapReduceFilter
• VPython GUIs

Vectors and Units

• Vectors
• SI Units

Interactions

• Types of Interactions and How to Detect Them

Velocity and Momentum

• Newton's First Law of Motion
• Mass
• Velocity
• Speed
• Speed vs Velocity
• Relative Velocity
• Derivation of Average Velocity
• 2-Dimensional Motion
• 3-Dimensional Position and Motion

Week 2

Momentum and the Momentum Principle

• Linear Momentum
• Newton's Second Law: the Momentum Principle
• Impulse and Momentum
• Net Force
• Inertia
• Acceleration
• Relativistic Momentum

Iterative Prediction with a Constant Force

• Iterative Prediction

Week 3

Analytic Prediction with a Constant Force

• Kinematics
• Projectile Motion

Iterative Prediction with a Varying Force

• Fundamentals of Iterative Prediction with Varying Force
• Spring_Force
• Simple Harmonic Motion
• Iterative Prediction of Spring-Mass System
• Terminal Speed
• Predicting Change in multiple dimensions
• Two Dimensional Harmonic Motion
• Determinism

Week 4

Fundamental Interactions

• Gravitational Force
• Gravitational Force Near Earth
• Gravitational Force in Space and Other Applications
• 3 or More Body Interactions
• Electric Force
• Introduction to Magnetic Force
• Strong and Weak Force
• Reciprocity
• Conservation of Momentum

Week 5

Properties of Matter

• Kinds of Matter
• Ball and Spring Model of Matter
• Density
• Length and Stiffness of an Interatomic Bond
• Young's Modulus
• Speed of Sound in Solids
• Malleability
• Ductility
• Weight
• Hardness
• Boiling Point
• Melting Point
• Change of State

Week 6

Identifying Forces

• Free Body Diagram
• Inclined Plane
• Compression or Normal Force
• Tension

Curving Motion

• Curving Motion
• Centripetal Force and Curving Motion
• Perpetual Freefall (Orbit)

Week 7

Jeet Bhatkar

Energy Principle

The Energy Principle is a fundamental concept in physics that describes the relationship between different forms of energy and their conservation within a system. Understanding the Energy Principle is crucial for analyzing the motion and interactions of objects in various physical scenarios.

• Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion.

• Work/Energy

Potential energy arises from the position of an object relative to its surroundings. Common forms of potential energy include gravitational potential energy and elastic potential energy.

• The Energy Principle

Work and energy are closely related concepts. Work ( 𝑊) done on an object is defined as the force ( 𝐹) applied to the object multiplied by the displacement ( 𝑑) of the object in the direction of the force: The Energy Principle states that the total mechanical energy of a system remains constant if only conservative forces (forces that depend only on the positions of the objects) are acting on the system.

• Conservation of Energy

The principle of conservation of energy states that the total energy of an isolated system remains constant over time. In other words, energy cannot be created or destroyed, only transformed from one form to another. This principle is a fundamental concept in physics and has wide-ranging applications in mechanics, thermodynamics, and other branches of science.

Week 8

Work by Non-Constant Forces

• Work Done By A Nonconstant Force

Potential Energy

• Potential Energy
• Potential Energy of Macroscopic Springs
• Spring Potential Energy
• Ball and Spring Model
• Gravitational Potential Energy
• Energy Graphs
• Escape Velocity

Week 9

Multiparticle Systems

• Center of Mass
• Multi-particle analysis of Momentum
• Potential Energy of a Multiparticle System
• Work and Energy for an Extended System
• Internal Energy
  • Potential Energy of a Pair of Neutral Atoms

Week 10

Choice of System

• System & Surroundings

Thermal Energy, Dissipation, and Transfer of Energy

• Thermal Energy
• Specific Heat
• Calorific Value(Heat of combustion)
• First Law of Thermodynamics
• Second Law of Thermodynamics and Entropy
• Temperature
• Transformation of Energy
• The Maxwell-Boltzmann Distribution
• Air Resistance
• The Third Law of Thermodynamics

Rotational and Vibrational Energy

• Translational, Rotational and Vibrational Energy
• Rolling Motion

Week 11

Different Models of a System

• Point Particle Systems
• Real Systems

Friction

• Friction
• Static Friction
• Kinetic Friction

Week 12

Conservation of Momentum

• Conservation of Momentum

Collisions

• Newton's Third Law of Motion
• Collisions
• Elastic Collisions
• Inelastic Collisions
• Maximally Inelastic Collision
• Head-on Collision of Equal Masses
• Head-on Collision of Unequal Masses
• Scattering: Collisions in 2D and 3D
• Rutherford Experiment and Atomic Collisions
• Coefficient of Restitution

Week 13

Rotations

• Rotational Kinematics
• Eulerian Angles

Angular Momentum

• Total Angular Momentum
• Translational Angular Momentum
• Rotational Angular Momentum
• The Angular Momentum Principle
• Angular Impulse
• Predicting the Position of a Rotating System
• The Moments of Inertia
• Right Hand Rule

Week 14

Analyzing Motion with and without Torque

• Torque
• Torque 2
• Systems with Zero Torque
• Systems with Nonzero Torque
• Torque vs Work
• Gyroscopes

Week 15

Introduction to Quantum Concepts

• Bohr Model
• Energy graphs and the Bohr model
• Quantized energy levels
• Electron transitions
• Entropy

Physics 2

Week 1

3D Vectors

• Vectors
• Right-Hand Rule
• Right Hand Rule

Electric field

• Electric Field
• Electric Field and Electric Potential

Electric force

Jeet Bhatkar – Fall 2025

Big Idea

Electric force is the interaction between objects that have electric charge. It is:

• Long-range: acts even when charges do not touch
• Vector-valued: has magnitude and direction
• Superposable: forces from many charges add as vectors

At the intro level, the electric force between two point charges is described by Coulomb’s law, the electrostatic analog of the gravitational force between masses.

Key Equations

Coulomb’s Law (magnitude)

[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math]

• [math]\displaystyle{F}[/math] = magnitude of the electric force
• [math]\displaystyle{k \approx 8.99 \times 10^9\ \text{N·m}^2/\text{C}^2}[/math]
• [math]\displaystyle{q_1, q_2}[/math] = charges (C)
• [math]\displaystyle{r}[/math] = separation between the charges (m)

Coulomb’s Law (vector form)

[math]\displaystyle{ \vec{F}_{2 \leftarrow 1} = k \dfrac{q_1 q_2}{r^2} \,\hat{r}_{2 \leftarrow 1} }[/math]

• [math]\displaystyle{\vec{F}_{2 \leftarrow 1}}[/math] = force on charge 2 due to charge 1
• [math]\displaystyle{\hat{r}_{2 \leftarrow 1}}[/math] = unit vector from 1 to 2

Relation to Electric Field

[math]\displaystyle{ \vec{F} = q \vec{E} }[/math]

Once you know [math]\displaystyle{\vec{E}}[/math] at a point, you can find the force on any charge [math]\displaystyle{q}[/math] placed there.

Conceptual Picture

Sign of charges

• Like charges (both positive or both negative) → repel
• Unlike charges (one positive, one negative) → attract

Distance dependence

• Force falls off as [math]\displaystyle{1/r^2}[/math], so doubling the distance makes the force 4 times smaller.

Superposition principle If there are many charges, the net force on a given charge is the vector sum of the forces from each individual charge: [math]\displaystyle{ \vec{F}_\text{net} = \sum_i \vec{F}_i }[/math].

Electric vs. gravitational force

• Both follow inverse-square laws
• Gravity is always attractive; electric force can be attractive or repulsive
• Electric forces are usually much stronger at the particle scale

Worked Example 1: Two Point Charges on a Line

Problem. Two charges are placed on the x-axis:

• [math]\displaystyle{q_1 = +3.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.00\ \text{m}}[/math]
• [math]\displaystyle{q_2 = -2.0\ \mu\text{C}}[/math] at [math]\displaystyle{x = 0.40\ \text{m}}[/math]

What is the magnitude and direction of the force on [math]\displaystyle{q_2}[/math]?

Solution (outline).

1. Distance between charges:

[math]\displaystyle{ r = 0.40\ \text{m} }[/math].

1. Magnitude using Coulomb’s law:

[math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} = (8.99 \times 10^9)\,\dfrac{(3.0 \times 10^{-6})(2.0 \times 10^{-6})}{(0.40)^2} }[/math]

1. Sign and direction:

• [math]\displaystyle{q_1}[/math] is positive, [math]\displaystyle{q_2}[/math] is negative → force is attractive
• On [math]\displaystyle{q_2}[/math], the force points toward [math]\displaystyle{q_1}[/math]
• Since [math]\displaystyle{q_1}[/math] is at smaller x, the force on [math]\displaystyle{q_2}[/math] points in the −x direction

You can finish by computing the numerical value and writing it as a vector, e.g. [math]\displaystyle{\vec{F}_{2 \leftarrow 1} = -F\,\hat{x}}[/math].

Worked Example 2: Superposition with Three Charges

Problem. Three equal charges [math]\displaystyle{q}[/math] are at the corners of an equilateral triangle of side [math]\displaystyle{a}[/math]. What is the net force on one of the charges?

Idea (no full algebra).

• Each of the other two charges exerts a force of magnitude

 [math]\displaystyle{ F = k \dfrac{q^2}{a^2} }[/math]  

• The angle between these two forces is [math]\displaystyle{60^\circ}[/math]
• Use vector addition:

 * Add components along the symmetry axis  
 * Perpendicular components cancel by symmetry  

This shows how symmetry plus superposition simplify the vector addition.

Computational Model (GlowScript)

Below is a simple GlowScript (VPython) model that computes and visualizes the electric force between two point charges in 3D.

You can:

• Paste this into a new GlowScript Trinket (Python / VPython),
• Get the embed code from Trinket,
• Embed that code into this page so it runs directly here.

<syntaxhighlight lang="python"> from vpython import *

1. constant

k = 8.99e9 # N·m^2/C^2

1. scene setup

scene.caption = "Drag the red charge to see how the force on the blue charge changes.\n"

1. charges (positions in meters, charges in coulombs)

q1 = 2e-6 # C (blue, fixed) q2 = -3e-6 # C (red, movable)

charge1 = sphere(pos=vector(-0.5, 0, 0), radius=0.05, color=color.blue) charge2 = sphere(pos=vector(0.5, 0, 0), radius=0.05, color=color.red, make_trail=True)

1. arrow to show force on q2 due to q1

F_arrow = arrow(pos=charge2.pos, axis=vector(0.2, 0, 0))

def electric_force(q1, q2, r1, r2):

   r_vec = r2 - r1
   r = mag(r_vec)
   if r == 0:
       return vector(0, 0, 0)
   F_mag = k * q1 * q2 / r**2
   return F_mag * norm(r_vec)

dragging = False

def down():

   global dragging
   if scene.mouse.pick is charge2:
       dragging = True

def up():

   global dragging
   dragging = False

scene.bind("mousedown", lambda evt: down()) scene.bind("mouseup", lambda evt: up())

while True:

   rate(60)

   if dragging:
       # move the red charge with the mouse in the x-y plane
       m = scene.mouse.pos
       charge2.pos = vector(m.x, m.y, 0)

   F = electric_force(q1, q2, charge1.pos, charge2.pos)

   # update arrow to show force on q2
   F_arrow.pos = charge2.pos
   # scale arrow length for visibility (purely visual)
   F_arrow.axis = F * 1e7

</syntaxhighlight>

You can extend this model to include more charges or show the net force on a test charge at different locations.

Common Mistakes and How to Avoid Them

• Forgetting that force is a vector.

 Always draw a diagram and keep track of directions. Use components in 2D/3D.

• Dropping the absolute value in the magnitude formula.

 [math]\displaystyle{ F = k \dfrac{|q_1 q_2|}{r^2} }[/math] is a positive magnitude. Decide direction separately.

• Mixing up [math]\displaystyle{r}[/math] and [math]\displaystyle{r^2}[/math].

 The force goes like [math]\displaystyle{1/r^2}[/math], not [math]\displaystyle{1/r}[/math].

• Using wrong units.

 Convert microcoulombs to coulombs, centimeters to meters, etc.  
 [math]\displaystyle{1\ \mu\text{C} = 1 \times 10^{-6}\ \text{C}}[/math].

• Trying to memorize instead of understand.

 Focus on inverse-square behavior, sign of charges, and superposition.

Connections to Other Topics

• Electric Field – Electric force per unit charge is the electric field:

 [math]\displaystyle{ \vec{E} = \dfrac{\vec{F}}{q} }[/math].

• Potential Energy and Electric Potential – Work done by electric forces leads to electric potential energy and voltage.
• Lorentz Force – The full force on a moving charge also includes magnetic fields:

 [math]\displaystyle{ \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) }[/math].  
 This page focuses on the electric part.

Practice Problems

You can add your own numerical values and solve them. Consider including full solutions in a collapsible section.

1. Two charges of [math]\displaystyle{+2.0\ \mu\text{C}}[/math] and [math]\displaystyle{+5.0\ \mu\text{C}}[/math] are 0.30 m apart.

  * (a) Find the magnitude of the force on each charge.  
  * (b) Is the force attractive or repulsive? Explain.

1. A charge [math]\displaystyle{q_1 = +4.0\ \mu\text{C}}[/math] is at the origin and [math]\displaystyle{q_2 = -1.0\ \mu\text{C}}[/math] is at [math]\displaystyle{x = 0.20\ \text{m}}[/math].

  * Find the electric force on [math]\displaystyle{q_1}[/math] (magnitude and direction).  
  * Verify that Newton’s third law holds (forces are equal and opposite).

1. Three equal positive charges are placed at the corners of a square of side [math]\displaystyle{a}[/math].

  * Find the net force on one of the corner charges.  
  * Use symmetry to simplify the vector addition.

1. A particle with charge [math]\displaystyle{q = -1.6 \times 10^{-19}\ \text{C}}[/math] experiences an electric force of [math]\displaystyle{3.2 \times 10^{-14}\ \text{N}}[/math] in the +y direction.

  * (a) What is the electric field at that point (magnitude and direction)?  
  * (b) If the charge were positive instead, what would the force direction be?

What to Review Before an Exam

• Determine force direction from a diagram, not just from algebra
• Practice vector addition of multiple forces
• Do quick estimates: “If I double the distance, what happens to the force?”
• Know the difference between:

 * Force between charges (Coulomb’s law)  
 * Electric field  
 * Electric potential energy

Electric field of a point particle

• Point Charge

Superposition

• Superposition Principle
• Superposition principle

Dipoles

• Electric Dipole
• Magnetic Dipole

Week 2

Interactions of charged objects

• Electric Field
• Electric Potential
• Electric Force
• Lorentz Force

Tape experiments

• Polarization
• Electric Polarization

Polarization

• Polarization
• Electric Polarization
• Polarization of an Atom

Week 3

Conductors and Insulators

• Conductivity and Resistivity
• Insulators
• Potential Difference in an Insulator
• Conductors
• Polarization of a conductor

Charging and Discharging

• Charge Transfer
• Electrostatic Discharge
• Charged Conductor and Charged Insulator

Week 4

Field of a charged rod

• Charged Rod

Field of a charged ring/disk/capacitor

• Charged Ring
• Charged Disk
• Charged Capacitor

Field of a charged sphere

• Charged Spherical Shell
• Field of a Charged Ball

Week 5

Potential energy

• Potential Energy

Electric potential

• Electric Potential
• Path Independence of Electric Potential
• Potential Difference Path Independence, claimed by Aditya Mohile
• Potential Difference in a Uniform Field
• Potential Difference of Point Charge in a Non-Uniform Field

Sign of a potential difference

• Sign of a Potential Difference

Potential at a single location

• Electric Potential
• Potential Difference at One Location

Path independence and round trip potential

• Path Independence of Electric Potential
• Potential Difference Path Independence, claimed by Aditya Mohile

Week 6

Electric field and potential in an insulator

• Potential Difference in an Insulator
• Electric Field in an Insulator

Moving charges in a magnetic field

• Magnetic Field
• Magnetic Force
• Lorentz Force

Biot-Savart Law

• Biot-Savart Law
• Biot-Savart Law for Currents

Moving charges, electron current, and conventional current

• Moving Point Charge

A moving point charge creates both electric and magnetic fields. As the charge accelerates or changes position, it alters the surrounding electromagnetic field, which can influence other charges nearby. This is the fundamental concept behind electromagnetic radiation and wave propagation. When many charges move collectively—such as electrons in a wire—this flow is referred to as electric current. This perfectly segues us into the next section of this page.

• Current

Current is typically measured in amperes and represents the rate at which charge flows through a surface. Although electrons carry the charge and move from negative to positive, conventional current is defined in the opposite direction: from positive to negative. This convention dates back to early scientific assumptions and remains standard in circuit diagrams and equations today.

Week 7

Magnetic field of a wire

• Magnetic Field of a Long Straight Wire
• Magnetic Field of a Curved Wire

Magnetic field of a current-carrying loop

• Magnetic Field of a Loop

Magnetic field of a Charged Disk

• Magnetic Field of a Disk

Magnetic dipoles

• Magnetic Dipole Moment
• Bar Magnet

Atomic structure of magnets

• Atomic Structure of Magnets

Week 8

Circuitry Basics

• Understanding Fundamentals of Current, Voltage, and Resistance

Steady state current

• Steady State
• Non Steady State

Kirchoff's Laws

• Loop Rule
• Node Rule

Electric fields and energy in circuits

• Electric Potential Difference

Macroscopic analysis of circuits

• Series Circuits
• Parallel Circuits
• Parallel Circuits vs. Series Circuits*
• Loop Rule
• Node Rule
• Fundamentals of Resistance
• Problem Solving

Week 9

Electric field and potential in circuits with capacitors

• Charging and Discharging a Capacitor
• RC Circuit
• R Circuit
• AC and DC

Magnetic forces on charges and currents

• Magnetic Force
• Lorentz Force
• Motors and Generators
• Applying Magnetic Force to Currents
• Magnetic Force in a Moving Reference Frame
• Right-Hand Rule
• Analysis of Railgun vs Coil gun technologies

Electric and magnetic forces

• Electric Force
• Magnetic Force
• Lorentz Force
• VPython Modelling of Electric and Magnetic Forces

Velocity selector

• Lorentz Force
• Combining Electric and Magnetic Forces

Week 10

Hall Effect

• Hall Effect
• Right-Hand Rule
• Motional Emf
• Magnetic Force
• Magnetic Torque

Magnetic force

• Magnetic Force
• Lorentz Force

Magnetic torque

• Magnetic Torque
• Right-Hand Rule

Week 12

Gauss's Law

• Gauss's Flux Theorem
• Gauss's Law
• Magnetic Flux

Ampere's Law

• Ampere's Law
• Ampere-Maxwell Law
• Magnetic Field of Coaxial Cable Using Ampere's Law
• Magnetic Field of a Long Thick Wire Using Ampere's Law
• Magnetic Field of a Toroid Using Ampere's Law
• Magnetic Field of a Solenoid Using Ampere's Law
• The Differential Form of Ampere's Law

Week 13

Semiconductors

• Semiconductor Devices

Faraday's Law

• Faraday's Law
• Motional Emf using Faraday's Law
• Lenz's Law

Maxwell's equations

• Gauss's Law
• Magnetic Flux
• Ampere's Law
• Faraday's Law
• Maxwell's Electromagnetic Theory

Week 14

Circuits revisited

Inductors

• Inductors
• Current in an LC Circuit
• Current in an RL Circuit

Week 15

Electromagnetic Radiation

• Electromagnetic Radiation

Sparks in the air

• Sparks in Air
• Spark Plugs

Superconductors

• Superconducters
• Superconductors
• Meissner effect

Physics 3

Week 1

Classical Physics

• Classical Physics

Weeks 2 and 3

Special Relativity and the Lorentz Transformation

• Frame of Reference

• Einstein's Theory of Special Relativity
• Time Dilation
• Twin Paradox
• Lorentz Transformations
• Relativistic Doppler Effect
• Einstein's Theory of General Relativity
• Albert A. Micheleson & Edward W. Morley
• Magnetic Force in a Moving Reference Frame

Week 4

Photons and the Photoelectric Effect

• Spontaneous Photon Emission
• Light Scattering
• Lasers
• Electronic Energy Levels and Photons
• Quantum Properties of Light
• The Photoelectric Effect

Weeks 5 and 6

Matter Waves and Wave-Particle Duality

• Wave-Particle Duality
• Particle in a 1-Dimensional box
• Heisenberg Uncertainty Principle

Week 7

Wave Mechanics

• Standing Waves
• Wavelength
• Wavelength and Frequency
• Mechanical Waves
• Transverse and Longitudinal Waves
• Fourier Series and Transform

Week 8

Schrödinger Equation

• The Born Rule
• Solution for a Single Free Particle
• Solution for a Single Particle in an Infinite Quantum Well - Darin
• Solution for a Single Particle in a Semi-Infinite Quantum Well
• Quantum Harmonic Oscillator
• Solution for Simple Harmonic Oscillator

Week 9

Quantum Mechanics

• Quantum Tunneling through Potential Barriers

The Hydrogen Atom

• Quantum Theory
• Atomic Theory

Week 10

Rutherford-Bohr Model

• Rutherford Experiment and Atomic Collisions
• Bohr Model
• Quantized energy levels
• Energy graphs and the Bohr model

Week 11

Many-Electron Atoms

• Quantum Theory
• Atomic Theory
• Pauli exclusion principle

Week 12

The Nucleus

• Nucleus

Week 13

Molecules

• Molecules
• Covalent Bonds

Week 14

Statistical Physics

• Application of Statistics in Physics

Week 15

Statistical Physics

• Temperature & Entropy

Additional Topics

Thermodynamics

• Maxwell Relations
• Brownian Motion

Nuclear Physics

• Nuclear Fission
• Nuclear Energy from Fission and Fusion
• Radioactive Decay Processes

Particle Physics

• Elementary Particles and Particle Physics Theory
• String Theory

Solid-State/Condensed Matter Physics

• What is Condensed Matter
• Crystalline Structures
• Electric-Band Structure