Main Page

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!

Looking to make a contribution?

1. Pick one of the topics from intro physics listed below
2. Add content to that topic or improve the quality of what is already there.
3. Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default Template into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

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
• 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 page for review of Vectors and vector operations
• A listing of Notable Scientist with links to their individual pages

Physics 1

Week 1

Expand

Help with VPython

• Python Syntax

Expand

Vectors and Units

• Vectors
• SI Units

Expand

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

Expand

Vectors and Units

• Vectors
• SI Units

Expand

Interactions

• Types of Interactions and How to Detect Them

Expand

Velocity and Momentum

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

Week 2

Expand

Momentum and the Momentum Principle

• Momentum Principle
• Inertia
• Net Force
• Derivation of the Momentum Principle
• Impulse Momentum
• Acceleration
• Momentum with respect to external Forces
• Relativistic Momentum

Expand

Iterative Prediction with a Constant Force

• Newton’s Second Law of Motion
• Iterative Prediction
• Kinematics
• Newton’s Laws and Linear Momentum
• Projectile Motion

Week 3

Expand

Analytic Prediction with a Constant Force

• Analytical Prediction

Expand

Iterative Prediction with a Varying Force

• Predicting Change in multiple dimensions
• Spring Force
• Hooke's Law
• Simple Harmonic Motion
• Iterative Prediction of Spring-Mass System
• Terminal Speed
• Determinism

Week 4

Expand

Fundamental Interactions

Main Idea

• Gravitational Force
• Fluid Mechanics
• An Application of Gravitational Potential
• Electric Force
• Reciprocity

Week 5

Expand

Conservation of Momentum

• Conservation of Momentum

Expand

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

Expand

Identifying Forces

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

Expand

Curving Motion

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

Week 7

Expand

Energy Principle

• The Energy Principle
• Conservation of Energy
• Kinetic Energy
• Work
• Power (Mechanical)

Week 8

Expand

Work by Non-Constant Forces

• Work Done By A Nonconstant Force

Expand

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

Expand

Multiparticle Systems

• Center of Mass
• Multi-particle analysis of Momentum
• Momentum with respect to external Forces
• 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

Expand

Choice of System

• System & Surroundings

Expand

Thermal Energy, Dissipation, and Transfer of Energy

• Thermal Energy
• Specific Heat
• Heat Capacity
• Calorific Value(Heat of combustion)
• Specific Heat Capacity
• First Law of Thermodynamics
• Second Law of Thermodynamics and Entropy
• Temperature
• Predicting Change
• Energy Transfer due to a Temperature Difference
• Transformation of Energy
• The Maxwell-Boltzmann Distribution
• Air Resistance

Expand

Rotational and Vibrational Energy

• Translational, Rotational and Vibrational Energy

Week 11

Expand

Different Models of a System

• Point Particle Systems
• Real Systems

Expand

Models of Friction

• Friction
• Static Friction

Week 12

Expand

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

Expand

Rotations

• Rotation
• Angular Velocity
• Eulerian Angles

Expand

Angular Momentum

• Total Angular Momentum
• Translational Angular Momentum
• Rotational Angular Momentum
• The Angular Momentum Principle
• Angular Momentum Compared to Linear Momentum
• Angular Impulse
• Predicting the Position of a Rotating System
• Angular Momentum of Multiparticle Systems
• The Moments of Inertia
• Moment of Inertia for a cylinder
• Right Hand Rule

Week 14

Expand

Analyzing Motion with and without Torque

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

Week 15

Expand

Introduction to Quantum Concepts

• Bohr Model
• Energy graphs and the Bohr model
• Quantized energy levels
• Quantized energy levels part II
• Entropy

Physics 2

Week 1

Expand

3D Vectors

• Vectors
• Right-Hand Rule
• Right Hand Rule

Expand

Electric field

• Electric Field
• Electric Field and Electric Potential

Expand

Electric force

• Electric Force
• Lorentz Force

Expand

Electric field of a point particle

• Point Charge

Expand

Superposition

• Superposition Principle
• Superposition principle

Expand

Dipoles

• Electric Dipole
• Magnetic Dipole

Week 2

Expand

Interactions of charged objects

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

Expand

Tape experiments

• Polarization
• Electric Polarization

Expand

Polarization

• Polarization
• Electric Polarization
• Polarization of an Atom

Week 3

Expand

Insulators

• Insulators
• Potential Difference in an Insulator
• Charged Conductor and Charged Insulator
• Charged conductor and charged insulator

Expand

Conductors

• Conductivity
• Charge Transfer
• Resistivity
• Polarization of a conductor
• Charged Conductor and Charged Insulator
• Charged conductor and charged insulator

Expand

Charging and Discharging

• Charge Transfer
• Electrostatic Discharge
• Charged Conductor and Charged Insulator
• Charged conductor and charged insulator

Week 4

Expand

Field of a Charged Rod

This entire page and all its contents were created by Lukas Yoder, PHYS 2212 Class of Fall 2018

The Main Idea

Previously, we've learned about the electric field of a point particle. Often, when analyzing physical systems, it is the case that we're unable to analyze each individual particle that composes an object and need to therefore generalize collections of particles into shapes (in this case, a rod) whereby the mathematics corresponding to electric field calculations can be simplified. This can essentially be done by adding up the contributions to the electric field made by parts of an object, approximating each part of an object as a point charge.

The System in Question

As discussed in the previous section, we're considering a system abstracted from the particle model we're familiar with, therefore we will make the generalization that our rod of length L has a total charge of quantity Q. For this generalization, we will need to assume that the rod is so thin that we can ignore its thickness.

Since the electric field produced by a charge at any given location is proportional to the distance from the charge to that location, we will need to relate the observation location to the source of the charge, which we will consider the origin of the rod. To do that, we will need to divide the rod into pieces of length \delta y each containing a charge \delta Q. In the image below, you can see what this looks like and the relation that can be found between the observation location and the source, forming the distance vector \vect{r}.

By the pythagorean theorem, we can find the vector \vect{r} as follows:

And to find the unit vector in the direction of \vect{r}, \hat{r}, we do as follows:

Finding the Contribution of Each Piece to the Electric Field

Now that we've set up a model for the system, with the rod broken down into pieces, we can find the contribution of each piece to the electric field of the system. We will start from the electric field equation you learned for a point particle but plug in the parameters for the rod system into the equation.

By mathematically simplifying, we then get the following equation:

Finding the Net Contribution of all Pieces

In the previous section, we found out the contribution to the electric field at a given location of only one of the pieces constituting the rod. In order to figure out the net field at any particular location, we need to add up the electric fields produced by individual pieces along the length of the rod.

We will switch from vector notation for the electric field to the scalar notation for the x- and y-components. (From the vector in the equation above, we can see that the z-component of the electric field at any point is always 0.) The x-component of the electric field is the sum of the x-components of every \delta{y} along the rod, and the y-component of the electric field is the sum of the y-components of every \delta{y} along the rod. We can show this mathematically:

To make use of this relation, because we don't know \delta{Q}, we need to relate it to parameters that we already know about the rod system we're analyzing. We can express \delta{Q} as the charge density of the rod (which is Q/L) times the \delta{y} we've chosen for the system. Thus,

By plugging the above equation into our equations for the x- and y-components of the electric field at a point, we can find the electric field at any point in the system. This technique is called numerical integration and is typically done by computers because the computational complexity is dependant upon the size of \delta{y} with respect to L.

Simplifying

Using calculus, we can simplify a lot of the math required to compute the electric field at any given point. Notationally, all we're doing is switching from the discretely-sized \delta{y} to \textit{dy} and from the sigma notation to an integral starting from -L/2 (the lower end of the rod) and ending at L/2 (the upper end of the rod) as follows:

By evaluating the integral, we can determine that the x-component of the electric field at any point is:

Without evaluating the integral for the y-component of the electric field, we can use symmetry to determine that the y-component of the electric field at any given point is 0. Let's consider the contributions to the electric field from the top and bottom halves of the rod at any observation point.

Since the y-components of E_top and E_bottom are of equal magnitude and opposite direction, they cancel each other out, and therefore the y-component of teh electric field at any given point due to the rod is 0.

Finally, because the rod is round and can be rotated, as a convenience, we'll use d (distance from the rod) as opposed to x (distance along the x-direction) to refer to the electric field.

Thus we can simplify electric field calculations for a rod into a form that we can readily use:

Further Simplification

By noting the contributions of each variable to the equation for the electric field, we can make approximations to simplify our math by simply declaring one variable as insignificant.

For example, if we have a system in which the length of a rod is much greater than the magnitude of the distance from the rod (denoted L>>d), we can neglect some of the instances in which d is taken into account as follows:

Finding the Electric Field from a Rod with Code

Here is some code that you can run which shows the electric field vector at a given distance from the rod along its length. The rod is shown as a series of green balls to help emphasize that when using the numerical integrations mentioned on this page, you are measuring the field produced by discrete parts of the rod being analyzed.

Notice the edge-effects of the electric field of the rod. For reasons discussed above, if we used the long rod approximation (L>>d), these effects would be negligible.

Click Here to Run the Code

The Main Idea

Previously, we've learned about the electric field of a point particle. Often, when analyzing physical systems, it is the case that we're unable to analyze each individual particle that composes an object and need to therefore generalize collections of particles into shapes (in this case, a rod) whereby the mathematics corresponding to electric field calculations can be simplified. This can essentially be done by adding up the contributions to the electric field made by parts of an object, approximating each part of an object as a point charge.

The System in Question

As discussed in the previous section, we're considering a system abstracted from the particle model we're familiar with, therefore we will make the generalization that our rod of length L has a total charge of quantity Q. For this generalization, we will need to assume that the rod is so thin that we can ignore its thickness.

[image 1]

Since the electric field produced by a charge at any given location is proportional to the distance from the charge to that location, we will need to relate the observation location to the source of the charge, which we will consider the origin of the rod. To do that, we will need to divide the rod into pieces of length \delta y each containing a charge \delta Q. In the image below, you can see what this looks like and the relation that can be found between the observation location and the source, forming the distance vector \vect{r}.

[image 2]

By the pythagorean theorem, we can find the vector \vect{r} as follows:

[image 3]

And to find the unit vector in the direction of \vect{r}, \hat{r}, we do as follows:

[image 4]

Finding the Contribution of Each Piece to the Electric Field

Now that we've set up a model for the system, with the rod broken down into pieces, we can find the contribution of each piece to the electric field of the system. We will start from the electric field equation you learned for a point particle but plug in the parameters for the rod system into the equation.

[image 5]

By mathematically simplifying, we then get the following equation:

[image 6]

Finding the Net Contribution of all Pieces

In the previous section, we found out the contribution to the electric field at a given location of only one of the pieces constituting the rod. In order to figure out the net field at any particular location, we need to add up the electric fields produced by individual pieces along the length of the rod.

We will switch from vector notation for the electric field to the scalar notation for the x- and y-components. (From the vector in the equation above, we can see that the z-component of the electric field at any point is always 0.) The x-component of the electric field is the sum of the x-components of every \delta{y} along the rod, and the y-component of the electric field is the sum of the y-components of every \delta{y} along the rod. We can show this mathematically:

[image 7]

To make use of this relation, because we don't know \delta{Q}, we need to relate it to parameters that we already know about the rod system we're analyzing. We can express \delta{Q} as the charge density of the rod (which is Q/L) times the \delta{y} we've chosen for the system. Thus,

[image 8]

By plugging the above equation into our equations for the x- and y-components of the electric field at a point, we can find the electric field at any point in the system. This technique is called numerical integration and is typically done by computers because the computational complexity is dependant upon the size of \delta{y} with respect to L.

Simplifying

Using calculus, we can simplify a lot of the math required to compute the electric field at any given point. Notationally, all we're doing is switching from the discretely-sized \delta{y} to \textit{dy} and from the sigma notation to an integral starting from -L/2 (the lower end of the rod) and ending at L/2 (the upper end of the rod) as follows:

[image 9] [image 10]

By evaluating the integral, we can determine that the x-component of the electric field at any point is:

[image 11]

Without evaluating the integral for the y-component of the electric field, we can use symmetry to determine that the y-component of the electric field at any given point is 0. Let's consider the contributions to the electric field from the top and bottom halves of the rod at any observation point.

[image 12]

Since the y-components of E_top and E_bottom are of equal magnitude and opposite direction, they cancel each other out, and therefore the y-component of teh electric field at any given point due to the rod is 0.

[image 13]

Finally, because the rod is round and can be rotated, as a convenience, we'll use d (distance from the rod) as opposed to x (distance along the x-direction) to refer to the electric field.

Thus we can simplify electric field calculations for a rod into a form that we can readily use:

[image 14]

Further Simplification

By noting the contributions of each variable to the equation for the electric field, we can make approximations to simplify our math by simply declaring one variable as insignificant.

For example, if we have a system in which the length of a rod is much greater than the magnitude of the distance from the rod (denoted L>>d), we can neglect some of the instances in which d is taken into account as follows:

[image 15]

The Main Idea

Previously, we've learned about the electric field of a point particle. Often, when analyzing physical systems, it is the case that we're unable to analyze each individual particle that composes an object and need to therefore generalize collections of particles into shapes (in this case, a rod) whereby the mathematics corresponding to electric field calculations can be simplified. This can essentially be done by adding up the contributions to the electric field made by parts of an object, approximating each part of an object as a point charge.

The System in Question

Expand

Field of a charged ring/disk/capacitor

• Charged Ring
• Charged Disk
• Charged Capacitor

Expand

Field of a charged sphere

• Charged Spherical Shell
• Field of a Charged Ball

Week 5

Expand

Potential energy

Written by Lukas Yoder, PHYS 2212 Class of Fall 2018

• Potential Energy

The Main Idea

Potential energy is the energy that an object has because of its characteristics relative to other objects within the universe. In Physics 1

Expand

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

Expand

Sign of a potential difference

• Sign of a Potential Difference

Expand

Potential at a single location

• Electric Potential
• Potential Difference at One Location

Expand

Path independence and round trip potential

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

Week 6

Expand

Electric field and potential in an insulator

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

Expand

Moving charges in a magnetic field

• Magnetic Field
• Magnetic Force
• Lorentz Force

Expand

Biot-Savart Law

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

Expand

Moving charges, electron current, and conventional current

• Moving Point Charge
• Current

Week 7

Expand

Magnetic field of a wire

• Magnetic Field of a Long Straight Wire

Expand

Magnetic field of a current-carrying loop

• Magnetic Field of a Loop

Expand

Magnetic field of a Charged Disk

• Magnetic Field of a Disk

Expand

Magnetic dipoles

• Magnetic Dipole Moment
• Bar Magnet

Expand

Atomic structure of magnets

• Atomic Structure of Magnets

Week 8

Expand

Steady state current

• Steady State
• Non Steady State

Expand

Kirchoff's Laws

• Kirchoff's Laws

Expand

Electric fields and energy in circuits

• Series circuit
• Node Rule
• Loop Rule
• Electric Potential Difference

Expand

Macroscopic analysis of circuits

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

Week 9

Expand

Electric field and potential in circuits with capacitors

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

Expand

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

Expand

Electric and magnetic forces

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

Expand

Velocity selector

• Lorentz Force
• Combining Electric and Magnetic Forces

Week 10

Expand

Hall Effect

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

Expand

Motional EMF

• Motional Emf
• Motional Emf using Faraday's Law

Expand

Magnetic force

• Magnetic Force
• Lorentz Force

Expand

Magnetic torque

• Magnetic Torque
• Right-Hand Rule

Week 12

Expand

Gauss's Law

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

Expand

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

Expand

Semiconductors

• Semiconductor Devices

Expand

Faraday's Law

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

Expand

Maxwell's equations

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

Week 14

Expand

Circuits revisited

Expand

Inductors

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

Week 15

Expand

Electromagnetic Radiation

• Electromagnetic Radiation

Expand

Sparks in the air

• Sparks in Air
• Spark Plugs

Expand

Superconductors

• Superconducters
• Superconductors
• Meissner effect

Physics 3

Week 1

Expand

Classical Physics

Week 2

Expand

Special Relativity

• Frame of Reference
• Einstein's Theory of Special Relativity
• Time Dilation
• Einstein's Theory of General Relativity
• Albert A. Micheleson & Edward W. Morley
• Magnetic Force in a Moving Reference Frame

Week 3

Expand

Photons

• Spontaneous Photon Emission
• Light Scattering: Why is the Sky Blue
• Lasers
• Electronic Energy Levels and Photons
• Quantum Properties of Light

Week 4

Expand

Matter Waves

• Wave-Particle Duality

Week 5

Expand

Wave Mechanics

• Standing Waves
• Wavelength
• Wavelength and Frequency
• Mechanical Waves
• Transverse and Longitudinal Waves

Week 6

Expand

Rutherford-Bohr Model

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

Week 7

Expand

The Hydrogen Atom

• Quantum Theory
• Atomic Theory

Week 8

Expand

Many-Electron Atoms

• Quantum Theory
• Atomic Theory
• Pauli exclusion principle

Week 9

Expand

Molecules

Week 10

Expand

Statistical Physics

Week 11

Expand

Condensed Matter Physics

Week 12

Expand

The Nucleus

• Nucleus

Week 13

Expand

Nuclear Physics

• Nuclear Fission
• Nuclear Energy from Fission and Fusion

Week 14

Expand

Particle Physics

• Elementary Particles and Particle Physics Theory
• String Theory