Physics Book - User contributions [en]

Potential Energy

2016-04-18T02:23:41Z

Wxia33: /* The Main Idea */

Author: Matthew Lewine (mlewine3)

Added material by:

-Brittney Vidal (bvidal3) *did not create the page but I added information as well as videos and additional reading*

-William Xia (wxia33)

Potential energy is stored energy which results from position or configuration. It is often contrasted with [[Kinetic Energy|kinetic energy]].

[[File:Rubberband2.jpg|thumb|The energy stored in a stretched rubber band is a form of elastic potential energy.]]

==The Main Idea==

Potential energy is intimately related to kinetic energy. Potential energy is defined as the capacity for an object to do work; in terms of gravity, potential energy is related to the distance of an object to the center of mass of an object, and in terms of electric energy, potential energy is related to the distance a charged object has to another charged object.

The change in work is translated to changes in other forms of energy. For example, if a rock is on top of a cliff, it has zero kinetic energy because it is not moving, but it has plenty of potential energy. Once the rock is dropped, the potential energy is decreasing and the kinetic energy is increasing. Mathematically, the sign of the change of the potential energy is negative, while the change in kinetic energy is positive.

In terms of potential energy, its capacity for doing [[work]] is a result of its position in a gravitational field (gravitational potential energy), an [[Electric Field|electric field]] (electric potential energy), or a [[magnetic field]] (magnetic potential energy). It may have elastic potential energy due to a stretched spring or other elastic deformation.

It is interesting to note, that the universe naturally prefers lower potential configuration of systems. This peculiarity is partly why balancing a pencil on one finger is so hard; the pencil contains potential energy that can be released easily.

===A Mathematical Model===

A force is considered conservative if it is acting on an object as a function of position only.

We can relate work to potential energy using the equation

<math>U = -\int \vec{F}\cdot\vec{dr}</math>

This says that the potential energy U is equal to the [[work]] you must do to move an object from an arbitrary reference point <math>U=0</math> to the position <math>r</math>. We can take the derivative of both sides of this equation and obtain:

<math>\frac{-dU}{dx} = F(x)</math>

Which means that the force on an object is the negative of the derivative of the potential energy function U. Therefore, the force on an object is the negative of the slope of the potential energy curve. Plots of potential functions are valuable aids to visualizing the change of the force in a given region of space.

Let's apply this relationship. If the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential. Let's consider gravitational potential and elastic potential.

The potential energy function U of gravitational potential is <math>mgh</math>, where <math>m</math> is mass, <math>g</math> is the gravitational constant, and <math>h</math> is some distance away from the reference point at which U = 0. Then the force is

<math>F = \frac{-d}{dh}mgh = -mg</math>

We can go the other way as well. We know the force of gravity is <math>-mg</math>, and integrating with respect to h we obtain <math>U = mgh</math>.

This process can be done with elastic potential as well, where the force <math>F = -kx</math> and the potential energy function is <math>U = \frac{1}{2}k^{2}</math>

Potential energy can also be seen in the Energy Principle Equation. In words, the Energy Principle equation is "Energy change in a system=external energy input". The mathematical model of this equation is <math>deltaK=Wsurr + Wint</math>. As stated above, <math>-Wint=deltaU</math>, meaning that negative work internal is equal to the change in potential energy. Putting this all into the Energy Principle equation makes <math>deltaK+(-Wint)=Wsurr</math> which makes <math>deltaK+deltaU=Wsurr</math>. Simply stated, this equation means that the total work done on a given system by forces that are external is equal to the change in kinetic energy and the change in potential energy.

Here are the potential energy functions for all forms:

{| class="wikitable"
| '''Type''' || '''Equation''' || '''Variables'''
|-
| Gravitational Potential || <math>U = \frac{GMm}{r}</math> <br><math>U = mgh</math> close to Earth's surface || <math>G</math> is the gravitational constant, <math>M</math> and <math>m</math>, and <math>r</math> is distance
|-
| Elastic Potential || <math>U = \frac{1}{2}k^{2}</math> || <math>k</math> is the spring constant
|-
| Electric Potential || <math>U = k\frac{Qq}{r}</math> || <math>k</math> is Coulomb's constant, <math>Q</math> and <math>q</math> are point charges, <math>r</math> is distance
|-
| Magnetic Potential || <math>U = -μ \cdot B</math> || <math>μ</math> is the dipole moment and <math>μ = IA</math> in a current loop and <math>I</math> is the current and <math>A</math> is the area
|-
|}

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

An object of mass 5 kg is held 10 meters above the Earth's surface. Relative to the surface, how much potential energy does this object have?

Solution:
Using the equation <math>U = mgh</math> we can say <math>U = 5*9.8*10 = 490</math> J.

===Middling===

If it takes 4J of work to stretch a Hooke's law spring 10 cm from its unstretched length, determine the extra work required to stretch it an additional 10 cm.

Solution:
The work done in stretching or compressing a spring is proportional to the square of the displacement. If we double the displacement, we do 4 times as much work. It takes 16 J to stretch the spring 20 cm from its unstretched length, so it takes 12 J to stretch it from 10 cm to 20 cm.

Formally:
<math>W = \frac{1}{2}kx^{2}.</math> Given W and x we find k.<br>
<math>4 J = \frac{1}{2}k(0.1)^{2}</math><br><br>
<math>k =\frac{8}{0.1^{2}} = 800</math> N/m.<br><br>
Using <math>x = 0.2</math> m, <math>W = \frac{1}{2}(800)(0.2)^{2} = 16</math> J<br><br>
Extra work: 16 J - 4 J = 12 J.

===Difficult===

We have a point charge A of charge +Q at the origin. Let's say we want to move another charge B of +q, located 10m away from particle A, to a location 5m away from particle B. How much work does it require to move the particle B 5m closer to particle A?

Solution:
We have a nonuniform electric field, so we need to integrate the potential energy function to find the amount of work needed.
<math>W = \int_{10}^{5} \frac{-kQq}{r^2}dr= -kQq\int_{10}^{5}\frac{1}{r^2}dr = \frac{kQq}{10} </math>

==Connectedness==
Potential energy is the driving force behind voltage, or the electric potential difference, expressed in volts. As a computer science major, I recognize the importance of this concept, as without potential difference we would not have transistors or circuits to power our machines.

Nuclear potential energy also exists, and is the potential energy of the particles inside an atomic nucleus. Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them have less mass than if they were individually free, and this mass difference is liberated as heat and radiation in nuclear reactions.

==History==

The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality.

== See also ==

[[Kinetic Energy]]<br>
[[Potential Energy for a Magnetic Dipole]]<br>
[[Potential Energy of a Multiparticle System]]<br>
[[Work]]
===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepe.html

===External links===
[http://www.scientificamerican.com/article/bring-science-home-rubber-bands-energy/]
[https://www.youtube.com/watch?v=elJUghWSVh4]
[https://www.youtube.com/watch?v=Y3xv-Oz68jQ]
[https://www.youtube.com/watch?v=zM7Cz1sQj9c]

==References==

"Potential Energy." HyperPhysics. Georgia State University, n.d. Web. 04 Dec. 2015.<br>
Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Hoboken, NJ: Wiley, 2011. Print.

"Electric Potential Energy." HyperPhysics. Georgia State University, n.d. Web. 16 Apr. 2016.<br>

[[Category:Which Category did you place this in?]]

Potential Energy

2016-04-17T21:46:57Z

Wxia33:

Author: Matthew Lewine (mlewine3)

Added material by:

-Brittney Vidal (bvidal3) *did not create the page but I added information as well as videos and additional reading*

-William Xia (wxia33)

Potential energy is stored energy which results from position or configuration. It is often contrasted with [[Kinetic Energy|kinetic energy]].

[[File:Rubberband2.jpg|thumb|The energy stored in a stretched rubber band is a form of elastic potential energy.]]

==The Main Idea==

Potential energy is intimately related to kinetic energy. Potential energy is defined as the capacity for an object to do work; in terms of gravity, potential energy is related to the distance of an object to the center of mass of an object, and in terms of electric energy, potential energy is related to the distance a charged object has to another charged object.

The change in work is translated to changes in other forms of energy. For example, if a rock is on top of a cliff, it has zero kinetic energy because it is not moving, but it has plenty of potential energy. Once the rock is dropped, the potential energy is decreasing and the kinetic energy is increasing. Mathematically, the sign of the change of the potential energy is negative, while the change in kinetic energy is positive.

In terms of potential energy, its capacity for doing [[work]] is a result of its position in a gravitational field (gravitational potential energy), an [[Electric Field|electric field]] (electric potential energy), or a [[magnetic field]] (magnetic potential energy). It may have elastic potential energy due to a stretched spring or other elastic deformation.

Negative work of done by internal forces of a system equates to the change in potential energy.

The unit for energy in SI is the joule, which has the symbol J.

The universe's matter flows towards the minimum total potential energy. This cosmic flow is time.

===A Mathematical Model===

A force is considered conservative if it is acting on an object as a function of position only.

We can relate work to potential energy using the equation

<math>U = -\int \vec{F}\cdot\vec{dr}</math>

This says that the potential energy U is equal to the [[work]] you must do to move an object from an arbitrary reference point <math>U=0</math> to the position <math>r</math>. We can take the derivative of both sides of this equation and obtain:

<math>\frac{-dU}{dx} = F(x)</math>

This says that the force on an object is the negative of the derivative of the potential energy function U. This means it is the negative of the slope of the potential energy curve. Plots of potential functions are valuable aids to visualizing the change of the force in a given region of space.

Let's apply this relationship. If the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential. Let's consider gravitational potential and elastic potential.

The potential energy function U of gravitational potential is <math>mgh</math>, where <math>m</math> is mass, <math>g</math> is the gravitational constant, and <math>h</math> is some distance away from the reference point at which U = 0. Then the force is

<math>F = \frac{-d}{dh}mgh = -mg</math>

We can go the other way as well. We know the force of gravity is <math>-mg</math>, and integrating with respect to h we obtain <math>U = mgh</math>.

This process can be done with elastic potential as well, where the force <math>F = -kx</math> and the potential energy function is <math>U = \frac{1}{2}k^{2}</math>

Potential energy can also be seen in the Energy Principle Equation. In words, the Energy Principle equation is "Energy change in a system=external energy input". The mathematical model of this equation is <math>deltaK=Wsurr + Wint</math>. As stated above, <math>-Wint=deltaU</math>, meaning that negative work internal is equal to the change in potential energy. Putting this all into the Energy Principle equation makes <math>deltaK+(-Wint)=Wsurr</math> which makes <math>deltaK+deltaU=Wsurr</math>. Simply stated, this equation means that the total work done on a given system by forces that are external is equal to the change in kinetic energy and the change in potential energy.

Here are the potential energy functions for all forms:

{| class="wikitable"
| '''Type''' || '''Equation''' || '''Variables'''
|-
| Gravitational Potential || <math>U = \frac{GMm}{r}</math> <br><math>U = mgh</math> close to Earth's surface || <math>G</math> is the gravitational constant, <math>M</math> and <math>m</math>, and <math>r</math> is distance
|-
| Elastic Potential || <math>U = \frac{1}{2}k^{2}</math> || <math>k</math> is the spring constant
|-
| Electric Potential || <math>U = k\frac{Qq}{r}</math> || <math>k</math> is Coulomb's constant, <math>Q</math> and <math>q</math> are point charges, <math>r</math> is distance
|-
| Magnetic Potential || <math>U = -μ \cdot B</math> || <math>μ</math> is the dipole moment and <math>μ = IA</math> in a current loop and <math>I</math> is the current and <math>A</math> is the area
|-
|}

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

An object of mass 5 kg is held 10 meters above the Earth's surface. Relative to the surface, how much potential energy does this object have?

Solution:
Using the equation <math>U = mgh</math> we can say <math>U = 5*9.8*10 = 490</math> J.

===Middling===

If it takes 4J of work to stretch a Hooke's law spring 10 cm from its unstretched length, determine the extra work required to stretch it an additional 10 cm.

Solution:
The work done in stretching or compressing a spring is proportional to the square of the displacement. If we double the displacement, we do 4 times as much work. It takes 16 J to stretch the spring 20 cm from its unstretched length, so it takes 12 J to stretch it from 10 cm to 20 cm.

Formally:
<math>W = \frac{1}{2}kx^{2}.</math> Given W and x we find k.<br>
<math>4 J = \frac{1}{2}k(0.1)^{2}</math><br><br>
<math>k =\frac{8}{0.1^{2}} = 800</math> N/m.<br><br>
Using <math>x = 0.2</math> m, <math>W = \frac{1}{2}(800)(0.2)^{2} = 16</math> J<br><br>
Extra work: 16 J - 4 J = 12 J.

===Difficult===

We have a point charge A of charge +Q at the origin. Let's say we want to move another charge B of +q, located 10m away from particle A, to a location 5m away from particle B. How much work does it require to move the particle B 5m closer to particle A?

Solution:
We have a nonuniform electric field, so we need to integrate the potential energy function to find the amount of work needed.
<math>W = \int_{10}^{5} \frac{-kQq}{r^2}dr= -kQq\int_{10}^{5}\frac{1}{r^2}dr = \frac{kQq}{10} </math>

==Connectedness==
Potential energy is the driving force behind voltage, or the electric potential difference, expressed in volts. As a computer science major, I recognize the importance of this concept, as without potential difference we would not have transistors or circuits to power our machines.

Nuclear potential energy also exists, and is the potential energy of the particles inside an atomic nucleus. Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them have less mass than if they were individually free, and this mass difference is liberated as heat and radiation in nuclear reactions.

==History==

The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality.

== See also ==

[[Kinetic Energy]]<br>
[[Potential Energy for a Magnetic Dipole]]<br>
[[Potential Energy of a Multiparticle System]]<br>
[[Work]]
===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepe.html

===External links===
[http://www.scientificamerican.com/article/bring-science-home-rubber-bands-energy/]
[https://www.youtube.com/watch?v=elJUghWSVh4]
[https://www.youtube.com/watch?v=Y3xv-Oz68jQ]
[https://www.youtube.com/watch?v=zM7Cz1sQj9c]

==References==

"Potential Energy." HyperPhysics. Georgia State University, n.d. Web. 04 Dec. 2015.<br>
Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Hoboken, NJ: Wiley, 2011. Print.

"Electric Potential Energy." HyperPhysics. Georgia State University, n.d. Web. 16 Apr. 2016.<br>

[[Category:Which Category did you place this in?]]

Potential Energy

2016-04-17T21:39:13Z

Wxia33:

Author: Matthew Lewine (mlewine3)

Added material by:
-Brittney Vidal (bvidal3) *did not create the page but I added information as well as videos and additional reading*
-William Xia (wxia33)

Potential energy is stored energy which results from position or configuration. It is often contrasted with [[Kinetic Energy|kinetic energy]].

[[File:Rubberband2.jpg|thumb|The energy stored in a stretched rubber band is a form of elastic potential energy.]]

==The Main Idea==

In terms of potential energy, its capacity for doing [[work]] is a result of its position in a gravitational field (gravitational potential energy), an [[Electric Field|electric field]] (electric potential energy), or a [[magnetic field]] (magnetic potential energy). It may have elastic potential energy due to a stretched spring or other elastic deformation.

Negative work of done by internal forces of a system equates to the change in potential energy.

The unit for energy in SI is the joule, which has the symbol J.

The universe's matter flows towards the minimum total potential energy. This cosmic flow is time.

===A Mathematical Model===

A force is considered conservative if it is acting on an object as a function of position only.

We can relate work to potential energy using the equation

<math>U = -\int \vec{F}\cdot\vec{dr}</math>

This says that the potential energy U is equal to the [[work]] you must do to move an object from an arbitrary reference point <math>U=0</math> to the position <math>r</math>. We can take the derivative of both sides of this equation and obtain:

<math>\frac{-dU}{dx} = F(x)</math>

This says that the force on an object is the negative of the derivative of the potential energy function U. This means it is the negative of the slope of the potential energy curve. Plots of potential functions are valuable aids to visualizing the change of the force in a given region of space.

Let's apply this relationship. If the potential energy function U is known, the force at any point can be obtained by taking the derivative of the potential. Let's consider gravitational potential and elastic potential.

The potential energy function U of gravitational potential is <math>mgh</math>, where <math>m</math> is mass, <math>g</math> is the gravitational constant, and <math>h</math> is some distance away from the reference point at which U = 0. Then the force is

<math>F = \frac{-d}{dh}mgh = -mg</math>

We can go the other way as well. We know the force of gravity is <math>-mg</math>, and integrating with respect to h we obtain <math>U = mgh</math>.

This process can be done with elastic potential as well, where the force <math>F = -kx</math> and the potential energy function is <math>U = \frac{1}{2}k^{2}</math>

Potential energy can also be seen in the Energy Principle Equation. In words, the Energy Principle equation is "Energy change in a system=external energy input". The mathematical model of this equation is <math>deltaK=Wsurr + Wint</math>. As stated above, <math>-Wint=deltaU</math>, meaning that negative work internal is equal to the change in potential energy. Putting this all into the Energy Principle equation makes <math>deltaK+(-Wint)=Wsurr</math> which makes <math>deltaK+deltaU=Wsurr</math>. Simply stated, this equation means that the total work done on a given system by forces that are external is equal to the change in kinetic energy and the change in potential energy.

Here are the potential energy functions for all forms:

{| class="wikitable"
| '''Type''' || '''Equation''' || '''Variables'''
|-
| Gravitational Potential || <math>U = \frac{GMm}{r}</math> <br><math>U = mgh</math> close to Earth's surface || <math>G</math> is the gravitational constant, <math>M</math> and <math>m</math>, and <math>r</math> is distance
|-
| Elastic Potential || <math>U = \frac{1}{2}k^{2}</math> || <math>k</math> is the spring constant
|-
| Electric Potential || <math>U = k\frac{Qq}{r}</math> || <math>k</math> is Coulomb's constant, <math>Q</math> and <math>q</math> are point charges, <math>r</math> is distance
|-
| Magnetic Potential || <math>U = -μ \cdot B</math> || <math>μ</math> is the dipole moment and <math>μ = IA</math> in a current loop and <math>I</math> is the current and <math>A</math> is the area
|-
|}

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===

An object of mass 5 kg is held 10 meters above the Earth's surface. Relative to the surface, how much potential energy does this object have?

Solution:
Using the equation <math>U = mgh</math> we can say <math>U = 5*9.8*10 = 490</math> J.

===Middling===

If it takes 4J of work to stretch a Hooke's law spring 10 cm from its unstretched length, determine the extra work required to stretch it an additional 10 cm.

Solution:
The work done in stretching or compressing a spring is proportional to the square of the displacement. If we double the displacement, we do 4 times as much work. It takes 16 J to stretch the spring 20 cm from its unstretched length, so it takes 12 J to stretch it from 10 cm to 20 cm.

Formally:
<math>W = \frac{1}{2}kx^{2}.</math> Given W and x we find k.<br>
<math>4 J = \frac{1}{2}k(0.1)^{2}</math><br><br>
<math>k =\frac{8}{0.1^{2}} = 800</math> N/m.<br><br>
Using <math>x = 0.2</math> m, <math>W = \frac{1}{2}(800)(0.2)^{2} = 16</math> J<br><br>
Extra work: 16 J - 4 J = 12 J.

===Difficult===

We have a point charge A of charge +Q at the origin. Let's say we want to move another charge B of +q, located 10m away from particle A, to a location 5m away from particle B. How much work does it require to move the particle B 5m closer to particle A?

Solution:
We have a nonuniform electric field, so we need to integrate the potential energy function to find the amount of work needed.
<math>W = \int_{10}^{5} \frac{-kQq}{r^2}dr= -kQq\int_{10}^{5}\frac{1}{r^2}dr = \frac{kQq}{10} </math>

==Connectedness==
Potential energy is the driving force behind voltage, or the electric potential difference, expressed in volts. As a computer science major, I recognize the importance of this concept, as without potential difference we would not have transistors or circuits to power our machines.

Nuclear potential energy also exists, and is the potential energy of the particles inside an atomic nucleus. Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them have less mass than if they were individually free, and this mass difference is liberated as heat and radiation in nuclear reactions.

==History==

The term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotle's concept of potentiality.

== See also ==

[[Kinetic Energy]]<br>
[[Potential Energy for a Magnetic Dipole]]<br>
[[Potential Energy of a Multiparticle System]]<br>
[[Work]]
===Further reading===

http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepe.html

===External links===
[http://www.scientificamerican.com/article/bring-science-home-rubber-bands-energy/]
[https://www.youtube.com/watch?v=elJUghWSVh4]
[https://www.youtube.com/watch?v=Y3xv-Oz68jQ]
[https://www.youtube.com/watch?v=zM7Cz1sQj9c]

==References==

"Potential Energy." HyperPhysics. Georgia State University, n.d. Web. 04 Dec. 2015.<br>
Chabay, Ruth W., and Bruce A. Sherwood. Matter & Interactions. Hoboken, NJ: Wiley, 2011. Print.

"Electric Potential Energy." HyperPhysics. Georgia State University, n.d. Web. 16 Apr. 2016.<br>

[[Category:Which Category did you place this in?]]

Main Page

2016-04-14T12:38:03Z

Wxia33:

__NOTOC__
Welcome to the Georgia Tech Wiki for Introductory Physics. This resources 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?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#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 [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in three semester of introductory physics. You can add subcategories as needed but a single topic should direct readers to a page in one of these categories.

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula 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

<div style="float:left; width:30%; padding:1%;">
==Physics 1==
===Week 1===

====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Help with VPython=====
<div class=“mw-collapsible-content”>
*[[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]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Vectors and Units=====
<div class=“mw-collapsible-content”>
*[[Vectors]]
*[[SI units]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>

=====Interactions=====
<div class=“mw-collapsible-content”>
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Velocity and Momentum=====
<div class=“mw-collapsible-content”>
*[[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]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:vpython_resources Software for Projects]

</div>

===Week 2===
====Student Content====
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Momentum and the Momentum Principle=====
<div class=“mw-collapsible-content”>
*[[Momentum Principle]]
*[[Inertia]]
*[[Net Force]]
*[[Derivation of the Momentum Principle]]
*[[Impulse Momentum]]
*[[Acceleration]]
*[[Momentum with respect to external Forces]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Constant Force=====
<div class=“mw-collapsible-content”>
*[[Newton’s Second Law of Motion]]
*[[Iterative Prediction]]
*[[Kinematics]]
*[[Newton’s Laws and Linear Momentum]]
*[[Projectile Motion]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:scalars_and_vectors Scalars and Vectors]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:displacement_and_velocity Displacement and Velocity]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:modeling_with_vpython Modeling Motion with VPython]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:relative_motion Relative Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:graphing_motion Graphing Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:momentum_principle The Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:acceleration Acceleration & The Change in Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:motionPredict Applying the Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:constantF Constant Force Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:iterativePredict Iterative Prediction of Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>

===Week 3===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Analytic Prediction with a Constant Force=====
<div \
class=“mw-collapsible-content”>
*[[Analytical Prediction]]
</div>
</div>

<div class=“toccolours mw-collapsible mw-collapsed”>
=====Iterative Prediction with a Varying Force=====
<div \
class=“mw-collapsible-content”>
*[[Predicting Change in multiple dimensions]]
*[[Spring Force]]
*[[Hooke’s Law]]
*[[Simple Harmonic Motion]]
*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Determinism]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:drag Drag]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:impulseGraphs Impulse Graphs]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:springMotion Non-constant Force: Springs & Spring-like Interactions]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:friction Contact Interactions: The Normal Force & Friction]

</div>

===Week 4===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Fundamental Interactions=====
<div class=“mw-collapsible-content”>
*[[Gravitational Force]]
*[[Electric Force]]
*[[Reciprocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]

</div>

===Week 5===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Conservation of Momentum=====
<div class=“mw-collapsible-content”>
*[[Conservation of Momentum]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Properties of Matter=====
<div class=“mw-collapsible-content”>
*[[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]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:model_of_a_wire Modeling a Solid Wire: springs in series and parallel]

</div>

===Week 6===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Identifying Forces=====
<div class=“mw-collapsible-content”>
*[[Free Body Diagram]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Curving Motion=====
<div class=“mw-collapsible-content”>
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:gravitation Non-constant Force: Newtonian Gravitation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_accel Gravitational Acceleration]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ucm Uniform Circular Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:freebodydiagrams Free Body Diagrams]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:curving_motion Curved Motion]

</div>

===Week 7===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Energy Principle=====
<div class=“mw-collapsible-content”>
*[[The Energy Principle]]
*[[Conservation of Energy]]
*[[Kinetic Energy]]
*[[Work]]
*[[Power (Mechanical)]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:define_energy What is Energy?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:point_particle The Simplest System: A Single Particle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work Work: Mechanical Energy Transfer]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_cons Conservation of Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]

</div>

===Week 8===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Work by Non-Constant Forces=====
<div \
class=“mw-collapsible-content”>
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Potential Energy=====
<div class=“mw-collapsible-content”>
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:work_by_nc_forces Work Done by Non-Constant Forces]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:potential_energy Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:force_and_PE Force and Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:power Power: The Rate of Energy Change]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 9===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Multiparticle Systems=====
<div class=“mw-collapsible-content”>
*[[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]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:mp_multi The Momentum Principle in Multi-particle Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_sep Separating Energy in Multi-Particle Systems]

</div>

===Week 10===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Choice of System=====
<div class=“mw-collapsible-content”>
*[[System & Surroundings]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Thermal Energy, Dissipation and Transfer of Energy=====
<div \
class=“mw-collapsible-content”>
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Heat Capacity]]
*[[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]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Rotational and Vibrational Energy=====
<div \
class=“mw-collapsible-content”>
*[[Translational, Rotational and Vibrational Energy]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_and_spring_PE (Near Earth) Gravitational and Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rest_mass Changes of Rest Mass Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:newton_grav_pe Newtonian Gravitational Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:grav_pe_graphs Graphing Energy for Gravitationally Interacting Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:escape_speed Escape Speed]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:spring_PE Spring Potential Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:internal_energy Internal Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 11===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Different Models of a System=====
<div \
class=“mw-collapsible-content”>
*[[Real Systems]]
*[[Point Particle Systems]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>

=====Models of Friction=====
<div class=“mw-collapsible-content”>
*[[Friction]]
*[[Static Friction]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:system_choice Choosing a System Matters]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:energy_dissipation Dissipation of Energy]

</div>

===Week 12===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Collisions=====
<div class=“mw-collapsible-content”>
*[[Newton’s Third Law of Motion]]
*[[Collisions]]
*[[Collisions 2]]
*[[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]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:collisions Colliding Objects]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:center_of_mass Center of Mass Motion]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:pp_vs_real Point Particle and Real Systems]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:colliding_systems Collisions]

</div>

===Week 13===
====Student Content====
<div class=“toccolours \
mw-collapsible mw-collapsed”>
=====Rotations=====
<div class=“mw-collapsible-content”>
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class=“toccolours mw-collapsible mw-collapsed”>
=====Angular Momentum=====
<div class=“mw-collapsible-content”>
*[[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]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:rot_KE Rotational Kinetic Energy]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:angular_motivation Why Angular Momentum?]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:ang_momentum Angular Momentum]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_conservation Angular Momentum Conservation]

</div>
===Week 14===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Analyzing Motion with and without Torque=====
<div \
class=“mw-collapsible-content”>
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:torque Torques Cause Changes in Rotation]
* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:L_principle Net Torque & The Angular Momentum Principle]

</div>

===Week 15===

====Student Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>
=====Introduction to Quantum Concepts=====
<div \class=“mw-collapsible-content”>
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
</div>
</div>

====Expert Content====
<div class=“toccolours mw-collapsible \
mw-collapsed”>

* [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes:discovery_of_the_nucleus Discovery of the Nucleus]

</div>

<div style=“float:left; width:30%; padding:1%;”>

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Page claimed by Laura Winalski]]*
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric force====
<div class="mw-collapsible-content">

*[[Electric Force]] Claimed by Amarachi Eze
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====

<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

'''Bold text'''====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[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]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of Potential Difference, claimed by Tyler Quill]]
</div>

== Claimed by Tyler Quill ==

</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
*[[Conventional Current]]*
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Series circuit]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel CIrcuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hall effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
*[[Right-Hand Rule]]
*[[Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Motional EMF====
<div class="mw-collapsible-content">
*[[Motional Emf]]
*[[Motional Emf using Faraday's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Ampere's Law====
<div class="mw-collapsible-content">
*[[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]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Inductors====
<div class="mw-collapsible-content">
*[[Inductors]]
*[[Current in an LC Circuit]]
*[[RL Circuits]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
<div class="mw-collapsible-content">
*[[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]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>

Category:Real Life Applications of Electromagnetic Principles

2016-04-14T12:33:42Z

Wxia33: Blanked the page

Category:Real Life Applications of Electromagnetic Principles

2016-04-14T12:33:19Z

Wxia33: Created page with "Coil Gun vs. Rail Gun Analysis"

Coil Gun vs. Rail Gun Analysis

Main Page

2016-02-08T04:25:36Z

Wxia33: /* Real Life Applications of Electromagnetic Principles */

__NOTOC__
Welcome to the Georgia Tech Wiki for Intro Physics. This resources 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!

Looking to make a contribution?
#Pick a specific topic from intro physics
#Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.
#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 [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]

== Organizing Categories ==
These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these categories.

<div class="toccolours mw-collapsible mw-collapsed">
===Classes===
<div class="mw-collapsible-content">

*[[Physics 1]]
*[[Physics 2]]
**[[Week 1—Vectors, Fields, and Superposition]]
**[[Week 2—Dipoles and Interactions]]
**[[Week 3—Insulators and Conductors]]
**[[Week 4—Electric Fields of Particular Shapes]]
**[[Week 5—Potential]]
**[[Week 6—Electrostatics in an Insulator and Magnetic Fields]]
**[[Week 7—Magnetic Fields of Particular Shapes]]
**[[Week 8—Introduction to Circuits]]
**[[Week 9—Capacitors and Lorentz Force]]
**[[Week 10—Hall Effect, Motional EMF, and Torque]]
**[[Week 12—Gauss's Law and Ampere's Law]]
**[[Week 13—Semiconductors and Faraday's Law]]
**[[Week 14—Inductors]]
**[[Week 15—Maxwell's Equations, Radiation, and Polarization]]
**[[Week 16—Sparks and Superconductors]]
*[[Physics 3]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">

*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Escape Velocity]]
*[[Fundamental Interactions]]
*[[Determinism]]
*[[System & Surroundings]]
*[[Free Body Diagram]]
*[[Newton's First Law of Motion]]
*[[Newton's Second Law of Motion]]
*[[Newton's Third Law of Motion]]
*[[Gravitational Force]]
*[[Electric Force]]
*[[Conservation of Energy]]
*[[Conservation of Charge]]
*[[Terminal Speed]]
*[[Simple Harmonic Motion]]
*[[Speed and Velocity]]
*[[Derivation of Average Velocity]]
*[[Acceleration]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
*[[Center of Mass]]
*[[Spring Force]]
*[[Reaction Time]]
*[[Time Dilation]]
*[[Pauli exclusion principle]]
*[[Interactions of Momentum and Energy Principles]]
*[[Magnus Effect]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Modeling with VPython===
<div class="mw-collapsible-content">
*[[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]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Theory===
<div class="mw-collapsible-content">
*[[Einstein's Theory of Special Relativity]]
*[[Einstein's Theory of General Relativity]]
*[[Quantum Theory]]
*[[Maxwell's Electromagnetic Theory]]
*[[Atomic Theory]]
*[[String Theory]]
*[[Elementary Particles and Particle Physics Theory]]
*[[Law of Gravitation]]
*[[Newton's Laws]]
*[[Higgs field]]
*[[Supersymmetry]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Notable Scientists===
<div class="mw-collapsible-content">
*[[Alexei Alexeyevich Abrikosov]]
*[[Christian Doppler]]
*[[Albert Einstein]]
*[[Ernest Rutherford]]
*[[Joseph Henry]]
*[[Michael Faraday]]
*[[J.J. Thomson]]
*[[James Maxwell]]
*[[Robert Hooke]]
*[[Carl Friedrich Gauss]]
*[[Nikola Tesla]]
*[[Andre Marie Ampere]]
*[[Sir Isaac Newton]]
*[[J. Robert Oppenheimer]]
*[[Oliver Heaviside]]
*[[Rosalind Franklin]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[Leo Szilard]]
*[[Galileo Galilei]]
*[[Gustav Kirchhoff]]
*[[Max Planck]]
*[[Heinrich Hertz]]
*[[Edwin Hall]]
*[[James Watt]]
*[[Count Alessandro Volta]]
*[[Josiah Willard Gibbs]]
*[[Richard Phillips Feynman]]
*[[Sir David Brewster]]
*[[Daniel Bernoulli]]
*[[William Thomson]]
*[[Leonhard Euler]]
*[[Robert Fox Bacher]]
*[[Stephen Hawking]]
*[[Amedeo Avogadro]]
*[[Wilhelm Conrad Roentgen]]
*[[Pierre Laplace]]
*[[Thomas Edison]]
*[[Hendrik Lorentz]]
*[[Jean-Baptiste Biot]]
*[[Lise Meitner]]
*[[Lisa Randall]]
*[[Felix Savart]]
*[[Heinrich Lenz]]
*[[Max Born]]
*[[Archimedes]]
*[[Jean Baptiste Biot]]
*[[Carl Sagan]]
*[[Eugene Wigner]]
*[[Marie Curie]]
*[[Pierre Curie]]
*[[Werner Heisenberg]]
*[[Johannes Diderik van der Waals]]
*[[Louis de Broglie]]
*[[Aristotle]]
*[[Émilie du Châtelet]]
*[[Blaise Pascal]]
*[[Siméon Denis Poisson]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
*[[James Prescott Joule]]
*[[John Bardeen]]
*[[Leo Baekeland]]
*[[Alhazen]]
*[[Willebrord Snell]]
*[[Fritz Walther Meissner]]
*[[Johannes Kepler]]
*[[Johann Wilhelm Ritter]]
*[[Philipp Lenard]]
*[[Robert A. Millikan]]
*[[Joseph Louis Gay-Lussac]]
*[[Guglielmo Marconi]]
*[[William Lawrence Bragg]]
*[[Robert Goddard]]
*[[Léon Foucault]]
*[[Henri Poincaré]]
*[[Steven Weinberg]]
*[[Arthur Compton]]
*[[Pythagoras of Samos]]
*[[Subrahmanyan Chandrasekhar]]
*[[Wilhelm Eduard Weber]]
*[[Edmond Becquerel]]
*[[Joseph Rotblat]]
*[[Carl David Anderson]]
*[[Hermann von Helmholtz]]
*[[Nicolas Leonard Sadi Carnot]]
*[[Wallace Carothers]]
*[[David J. Wineland]]
*[[Rudolf Clausius]]
*[[Edward L. Norton]]
*[[Shuji Nakamura]]
*[[Pierre Laplace Pt. 2]]
*[[William B. Shockley]]
*[[Osborne Reynolds]]
*[[Christian Huygens]]
*[[Hans Bethe]]
*[[Erwin Schrodinger]]
*[[Wolfgang Pauli]]
*[[Paul Dirac]]
*[[Bill Nye]]
*[[Arnold Sommerfeld]]
*[[Ernest Lawrence]]
*[[James Franck]]
*[[Chen-Ning Yang]]
*[[Albert A. Michelson & Edward W. Morley]]
*[[George Paget Thomson]]
*[[Konstantin Tsiolkovsky]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Properties of Matter===
<div class="mw-collapsible-content">
*[[Mass]]
*[[Velocity]]
*[[Relative Velocity]]
*[[Density]]
*[[Charge]]
*[[Spin]]
*[[SI Units]]
*[[Heat Capacity]]
*[[Specific Heat]]
*[[Wavelength]]
*[[Electrical Conductivity/Resistivity]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Inertia]]
*[[Non-Newtonian Fluids]]
*[[Ferrofluids]]
*[[Color]]
*[[Temperature]]
*[[Plasma]]
*[[Electron Mobility]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[Friction]]
* [[Static Friction]]
* [[Tension]]
* [[Hooke's Law]]
*[[Centripetal Force and Curving Motion]]
*[[Compression or Normal Force]]
* [[Length and Stiffness of an Interatomic Bond]]
* [[Speed of Sound in Solids]]
* [[Iterative Prediction of Spring-Mass System]]
* [[Geneva Drives: An Interesting Method of Movement]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Momentum===
<div class="mw-collapsible-content">
* [[Vectors]]
* [[Kinematics]]
* [[Conservation of Momentum]]
* [[Predicting Change in multiple dimensions]]
* [[Derivation of the Momentum Principle]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving Motion]]
* [[Projectile Motion]]
* [[Multi-particle Analysis of Momentum]]
* [[Iterative Prediction]]
* [[Analytical Prediction]]
* [[Newton's Laws and Linear Momentum]]
* [[Net Force]]
* [[Center of Mass]]
* [[Momentum at High Speeds]]
* [[Momentum with respect to external Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Angular Momentum===
<div class="mw-collapsible-content">
* [[The Moments of Inertia]]
* [[Moment of Inertia for a cylinder]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
[[Systems with Zero Torque*]]
* [[Systems with Nonzero Torque]]
* [[Torque vs Work]]
* [[Angular Impulse]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Angular Momentum of Multiparticle Systems]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]
* [[Angular Momentum Compared to Linear Momentum]]
*[[Torque 2]]
* [[3 Fundamental Principles of Mechanics]]
* [[Eulerian Angles]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Energy===
<div class="mw-collapsible-content">
*[[The Photoelectric Effect]]
*[[Photons]]
*[[The Energy Principle]]
*[[Predicting Change]]
*[[Rest Mass Energy]]
*[[Kinetic Energy]]
*[[Potential Energy]]
**[[Potential Energy for a Magnetic Dipole]]
**[[Potential Energy of a Multiparticle System]]
**[[Potential Energy of Macroscopic Springs]]
**[[Graviational Potential Energy]]
*[[Work]]
**[[Work Done By A Nonconstant Force]]
*[[Work and Energy for an Extended System]]
*[[Thermal Energy]]
*[[Conservation of Energy]]
*[[Electric Potential]]
*[[Energy Transfer due to a Temperature Difference]]
*[[Gravitational Potential Energy]]
*[[Point Particle Systems]]
*[[Real Systems]]
*[[Spring Potential Energy]]
**[[Ball and Spring Model]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
*[[Translational, Rotational and Vibrational Energy]]
*[[Franck-Hertz Experiment]]
*[[Power (Mechanical)]]
*[[Transformation of Energy]]

*[[Energy Graphs]]
**[[Energy graphs and the Bohr model]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
**[[Spontaneous Photon Emission]]
*[[Path Independence of Electric Potential]]
*[[Energy in a Circuit]]
*[[The Photovoltaic Effect]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Collisions===
<div class="mw-collapsible-content">
[[File:opener.png]]

*[[Collisions]]
Collisions are events that happen very frequently in our day-to-day world. In the realm of Physics, a collision is defined as any sort of process in which before and after a short time interval there is little interaction, but during that short time interval there are large interactions. When looking at collisions, it is first important to understand two very important principles: the Momentum Principle and the Energy Principle. Both principles serve use when talking of collisions because they provide a way in which to analyze these collisions. Collisions themselves can be categorized into 3 main different types: elastic collisions, inelastic collisions, maximally inelastic collisions. All 3 collisions will get touched on in more detail further on.
[[File:pe.png]]

*[[Elastic Collisions]]
A collision is deemed "elastic" when the internal energy of the objects in the system does not change (in other words, change in internal energy equals 0). Because in an elastic collision no kinetic energy is converted over to internal energy, in any elastic collision Kfinal always equals Kinitial.
[[File:Elco.png]]

*[[Inelastic Collisions]]
A collision is said to be "inelastic" when it is not elastic; therefore, an inelastic collision is an interaction in which some change in internal energy occurs between the colliding objects (in other words, change in internal energy does not equal 0). Examples of such changes that occur between colliding objects include, but are not limited to, things like they get hot, or they vibrate/rotate, or they deform. Because some of the kinetic energy is converted to internal energy during an inelastic collision, Kfinal does not equal Kinitial.
There are a few characteristics that one can search for when identifying inelasticity. These indications include things such as:
*Objects stick together after the collision
*An object is in an excited state after the collision
*An object becomes deformed after the collision
*The objects become hotter after the collision
*There exists more vibration or rotation after the collision
[[File:inve.gif]]

*[[Maximally Inelastic Collision]]
Maximally inelastic collisions, also known as "sticking collisions", are the most extreme kinds of inelastic collisions. Just as its secondary name implies, a maximally inelastic collision is one in which the colliding objects stick together creating maximum dissipation. This does not automatically mean that the colliding objects stop dead because the law of conservation of momentum. In a maximally inelastic collision, the remaining kinetic energy is present only because total momentum can't change and must be conserved.
[[File:inel.gif]]

*[[Head-on Collision of Equal Masses]]
The easiest way to understand this phenomenon is to look at it through an example. In this case, we can analyze it through the common game of billiards. Taking the two, equally massed billiard balls as the system, we can neglect the small frictional force exerted on the balls by the billiard table. The Momentum Principle states that in this head-on collision of billiard balls the total final momentum in the x direction must equal the total initial momentum. However, this alone does not give us the knowledge to know how the momentum will be divided up between the two balls. Considering the law of conservation of energy, we can more accurately depict what will happen. This will also allow for one to identify what kind of collision occurs (elastic, inelastic, or maximally inelastic). It is important to know that head-on collisions of equal masses do not have a definite type of collision associated with it.
[[File:momentum-real-life-applications-2895.jpg]] [[File:8ball.gif]]

*[[Head-on Collision of Unequal Masses]]
Just as with head-on collisions of equal masses, it is easy to understand head-on collisions of unequal masses by viewing it through an example. Let's take for example two balls of unequal masses like a ping-pong ball and a bowling ball. For the purpose of this example (so as to allow for no friction and no other significant external forces), let's imagine these objects collide in outer space inside an orbiting spacecraft. If there were to be a collision between the two, what would one expect to happen? One could expect to see the ping-pong ball collide with the bowling ball and bounce straight back with a very small change of speed. What one might not expect as much is that the bowling ball also moves, just very slowly. Again, this can all be explained through the conservation of momentum and the conservation of energy.
[[File:mi3e.jpg]]

*[[Frame of Reference]]
In the world of Physics, a frame of reference is the perspective from which a system is observed. It can be stationary or sometimes it can even be moving at a constant velocity. In some rare cases, the frame of reference moves at an nonconstant velocity and is deemed "noninertial" meaning the basic laws of physics do not apply. Continuing with the trend of examples, pretend you are at a train station observing trains as they pass by. From your stationary frame of reference, you observe that the passenger on the train is moving at the same velocity as the train. However, from a moving frame of reference, say from the eyes of the train conductor, he would view the train passengers as "anchored" to the train.
[[File:train.png]]

*[[Scattering: Collisions in 2D and 3D]]
Experiments that involve scattering are often used to study the structure and behavior of atoms, nuclei, as well as of other small particles. In an experiment like such, a beam of particles collides with other particles. If it is an atomic or nuclear collision, we are unable to observe the curving trajectories inside the tiny region of interaction. Instead, we can only truly observe the trajectories before and after the collision. This is only possible because the particles are at a farther distance apart and have a very weak mutual interaction; this essentially means that the particles are moving almost in a straight line. A good example which demonstrates scattering is the collision between an alpha particle (the nucleus of a helium atom) and the nucleus of a gold atom. One will understand this phenomenon more in depth after first understanding the Rutherford Experiment which will get touched on later.

*[[Rutherford Experiment and Atomic Collisions]]
In England in 1911, a famous experiment was performed by a group of scientists led by Mr. Ernest Rutherford. This experiment, later known as "The Rutherford Experiment", was a tremendous breakthrough for its time because it led to the discovery of the nucleus inside the atom. Rutherford's experiment involved the scattering of a high-speed alpha particle (now known as a helium nuclei - 2 protons and 2 neutrons) as it was shot at a thin gold foil (consisting of a nuclei with 79 protons and 118 neutrons). In the experiment, Rutherford and his team discovered that the velocity of the alpha particles was not high enough to allow the particles to make actual contact with the gold nucleus. Although they never actually made contact, it is still deemed a collision because there exists a sizable force between the alpha particle and the gold nucleus over a very short period of time. In conclusion, we say the alpha particle is "scattered" by its interaction with the nucleus of a gold atom and experiments like such are called "scattering" experiments.
[[File:ruthef.jpg]]

*[[Coefficient of Restitution]]
The coefficient of restitution is a measure of the elasticity in a collision. It is the ratio of the differences in velocities before and after the collision. The coefficient is evaluated by taking the difference in the velocities of the colliding objects after the collision and dividing by the difference in the velocities of the colliding objects before the collision.

All of the following information was collected from the Matter and Interactions 4th Edition physics textbook. The book is cited as follows...

Chabay, Ruth W., and Bruce A. Sherwood. "Chapter 10: Collisions." Matter & Interactions. Fourth Edition ed. Wiley, 2015. 383-409. Print.

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Fields===
<div class="mw-collapsible-content">
* [[Electric Field]] of a
** [[Point Charge]]
** [[Electric Dipole]]
** [[Capacitor]]
** [[Charged Rod]]
** [[Charged Ring]]
** [[Charged Disk]]
** [[Charged Spherical Shell]]
** [[integrating the spherical shell]]
** [[Charged Cylinder]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Charge Density]]
*[[Superposition Principle]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[Potential Difference at One Location]]
**[[Sign of Potential Difference]]
**[[Potential Difference in an Insulator]]
**[[Energy Density and Electric Field]]
** [[Systems of Charged Objects]]
*[[Electric Force]]
*[[Polarization]]
**[[Polarization of an Atom]]
**[[Charged Conductor and Charged Insulator]]
**[[Polarization and Drift Speed]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
**[[Electrostatic Discharge]]
*[[Magnetic Field]]
**[[Right-Hand Rule]]
**[[Direction of Magnetic Field]]
**[[Magnetic Field of a Long Straight Wire]]
**[[Magnetic Field of a Loop]]
**[[Magnetic Field of a Solenoid]]
**[[Bar Magnet]]
**[[Magnetic Dipole Moment]]
***[[Stern-Gerlach Experiment]]
**[[Magnetic Torque]]
**[[Magnetic Force]]
***[[Applying Magnetic Force to Currents]]
***[[Magnetic Force in a Moving Reference Frame]]
***[[The Hall Effect]]
**[[Earth's Magnetic Field]]
**[[Atomic Structure of Magnets]]
*[[Combining Electric and Magnetic Forces]]
**[[Hall Effect]]
**[[Lorentz Force]]
**[[Biot-Savart Law]]
**[[Biot-Savart Law for Currents]]
**[[Integration Techniques for Magnetic Field]]
**[[Sparks in Air]]
**[[Motional Emf]]
**[[Detecting a Magnetic Field]]
**[[Moving Point Charge]]
**[[Non-Coulomb Electric Field]]
**[[Electric Motors]]
**[[Solenoid Applications]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Simple Circuits===
<div class="mw-collapsible-content">
*[[Components]]
*[[Steady State]]
*[[Non Steady State]]
*[[Charging and Discharging a Capacitor]]
*[[Work and Power In A Circuit]]
*[[Thin and Thick Wires]]
*[[Node Rule]]
*[[Loop Rule]]
*[[Resistivity]]
*[[Power in a circuit]]
*[[Ammeters,Voltmeters,Ohmmeters]]
*[[Current]]
**[[AC]]
*[[Ohm's Law]]
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[RC]]
*[[Parallel Circuits vs. Series Circuits]]
*[[AC vs DC]]
**[[Rectification (Converting AC to DC)]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[Current in a RL Circuit]]
*[[Current in an LC Circuit]]
*[[RL Circuit]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
*[[Semiconductor Devices]]
*[[Insulators]]
*[[Volt]]
*[[Batteries]]
*[[Three Prong Circuits]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
***[[Examples of Flux Through Surfaces and Objects]]
**[[Magnetic Fields]]
**[[Proof of Gauss's Law]]
*[[Ampere's 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]]
**[[The Differential Form of Ampere's Law]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers (Physics)]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[Lenz's Rule]]
**[[Motional Emf using Faraday's Law]]
*[[Ampere-Maxwell Law]]
*[[Superconductors]]
**[[Meissner effect]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Radiation===
<div class="mw-collapsible-content">
*[[Producing a Radiative Electric Field]]
*[[Sinusoidal Electromagnetic Radiaton]]
*[[Lenses]]
*[[Energy and Momentum Analysis in Radiation]]
**[[Poynting Vector]]
*[[Electromagnetic Propagation]]
**[[Wavelength and Frequency]]
*[[Snell's Law]]
*[[Effects of Radiation on Matter]]
*[[Light Propagation Through a Medium]]
*[[Light Scaterring: Why is the Sky Blue]]
*[[Light Refraction: Bending of light]]
*[[Cherenkov Radiation]]
*[[Rayleigh Effect]]
*[[Image Formation]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Sound===
<div class="mw-collapsible-content">
*[[Doppler Effect]]
*[[Nature, Behavior, and Properties of Sound]]
*[[Speed of Sound]]
*[[Resonance]]
*[[Sound Barrier]]
*[[Sound Propagation in Water]]
*[[Chladni Plates]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Waves===
<div class="mw-collapsible-content">
*[[Bragg's Law]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Plasma waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Spectrum]]
*[[Color Light Wave]]
*[[X-Rays]]
*[[Rayleigh Wave]]
*[[Pendulum Motion]]
*[[Transverse and Longitudinal Waves]]
*[[Planck's Relation]]
*[[interference]]
*[[Polarization of Waves]]
*[[Angular Resolution]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Scanning Electron Microscopes]]
*[[Maglev Trains]]
*[[Spark Plugs]]
*[[Metal Detectors]]
*[[Speakers]]
*[[Radios]]
*[[Ampullae of Lorenzini]]
*[[Electrocytes]]
*[[Cyclotron]]
*[[Generator]]
*[[Using Capacitors to Measure Fluid Level]]
*[[Cyclotron]]
*[[Railgun]]
*[[Magnetic Resonance Imaging]]
*[[Electric Eels]]
*[[Windshield Wipers]]
*[[Galvanic Cells]]
*[[Electrolytic Cells]]
*[[Magnetoreception]]
*[[Memory Storage Devices]]
*[[Electric Pickups]]
*[[Inductive Sensors for Traffic Lights]]
*[[Multi-limbed Robotics]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

===Optics===
<div class="mw-collapsible-content">
*[[Mirrors]]
*[[Refraction]]
*[[Quantum Properties of Light]]
*[[Lasers]]
*[[Lenses]]
*[[Dispersion and Scattering]]
*[[Telescopes]]
*[[Resolving Power]]

</div>
</div>

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A page for review of [[Vectors]] and vector operations

</div>

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====Help with VPython====
<div class="mw-collapsible-content">
*[[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]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Interactions====
<div class="mw-collapsible-content">
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Velocity]]1
*[[Relative Velocity]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Momentum Principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
</div>
</div>
===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Analytical Prediction with a Constant Force====
<div class="mw-collapsible-content">
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
</div>
</div>
===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
</div>
</div>
===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Properties of Solids====
<div class="mw-collapsible-content">
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripital Force and Curving Motion]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[The Energy Principle]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of a Multiparticle System]]
*[[Potential Energy of Macroscopic Springs]]
*[[Gravitational Potential Energy]]
</div>
</div>
===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Forms of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
</div>
</div>
===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Real Systems]]
*[[Point Particle Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Models of Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
</div>
</div>
===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[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]]
</div>
</div>
===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Angular Momentum====
<div class="mw-collapsible-content">
*[[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]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
</div>
</div>
===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>
===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Quantized energy levels]]
</div>
</div>

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Insulators====
<div class="mw-collapsible-content">
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Conductors====
<div class="mw-collapsible-content">
*[[Conductivity]]
*[[Charge Transfer]]
*[[Resistivity]]
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Charging and discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
*[[Charged conductor and charged insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential DIfference Path Independence]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Curent]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Node rule====
<div class="mw-collapsible-content">
*[[Node Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Power in a circuit]]
*[[Non-Coulomb Electric Field]]
*[[Energy in a Circuit]]
*[[Work and Power In A Circuit]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity selector====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hall effect====
<div class="mw-collapsible-content">
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Motional EMF====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic force====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Rotation]]
*[[Angular Velocity]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Faraday's Law====
<div class="mw-collapsible-content">
*[[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]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Maxwell's equations====
<div class="mw-collapsible-content">
*[[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]]
*[[The Moments of Inertia]]
*[[Moment of Inertia for a cylinder]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Circuits revisited====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Quantized energy levels]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Inductors====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Quantized energy levels]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
</div>
</div>

Einstein's Theory of General Relativity

2015-12-04T19:22:40Z

Wxia33: /* Mathematical Framework */

(Created by William Xia)

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described. Multiple observations of the theory has been tested and experimentally verified, and new predictions have been observed through solving the equations in this theory.

==The Main Idea==

Gravity is the result of energy and matter distorting spacetime. The reason why one follows a curved trajectory when encountering an object in space is because the trajectory follows a least energy path through spacetime. In other words, if the smallest distance between two points in a plane is a straight line, then the smallest distance between two points in spacetime is described by how the object bends spacetime.

===Mathematical Framework===

Einstein developed a generalized coordinate system and summation notation to simplify his work and create a much more elegant system to describe his ideas. There are four important quantities to understand before tackling the Einstein Field Equations: metric tensor, christoffel symbols, geodesic equation, and the reimann tensor.

'''Metric Tensor'''

The metric tensor is a very important mathematical object in general relativity. Much of the information that describes a space is encoded in this object.

A tensor is a multidimensional quantity that describes direction and magnitude in a much more detailed way than a vector. For example, stress in an object is complex and contains many directions of forces at one single point, but by using a stress tensor one may compactly describe a point or even a collection of points. Writing equations in terms of tensors provides a very important quality: a tensor equation that equals zero in one frame of reference will equal zero in all frames of reference. This property provides a means for the study of physical phenomena in any system of coordinates imaginable.

The metric tensor is a subset of a tensor, in that the metric tensor is a generalization of the pythagorean theorem; a differential length is described by the metric tensor using generalized differential coordinates.

A basic example of the metric tensor is the Schwarzschild metric, which was one of the first metrics to be solved from Einstein's equations. The metric describes a simple sphere in spacetime, but despite the relative simplicity of the metric, it presents an interesting topic to study. By using the Schwarzschild metric, one may arrive at singularities, or mathematical points that explode to infinity. At these singularities, black holes are created, and these such points are still the subject of intense research.

[[File: Metric.png]]

'''Christoffel Symbols'''

Christoffel symbols can be loosely thought of as a residual when taking the derivative in a nonlinear coordinate system. If the coordinate system itself depends on a set of parameters, then taking the derivative of a function will not result in a simple derivative. Because of the product rule, there remains a correction term that must be required, and such term is the christoffel symbol. With respect to the metric tensor, the christoffel symbol has a concrete description of the tensor, and represents the correction quantity that must be used to describe geodesics, or shortest paths.

[[File:817b5f05dba23ecf09a37d4e4c06c3ea.png]]

'''Geodesic Equation'''

The geodesic equation describes the path a particle takes in a general coordinate system, and it is a generalization of acceleration equations. For flat space, or simple cartesian coordinates, if a particle moves then it must move in a straight line disregarding any external forces, and indeed the geodesic equation resembles newton's second law. However, for curved space, say for example a sphere, the shortest path between to points is actually curved. When massive objects distort spacetime, the geodesic equation is helpful in describing paths particles must take in the distorted coordinate frame. Within the mathematical framework, the geodesic equation employs the christoffel symbol to correct for distortions in spacetime.

[[File:Geodesic.png]]

'''Reimann Tensor'''

Although the geodesic equation can describe motion in curved spacetime, the equation itself is insufficient in describing space. For such a description, one must turn to the Reimann Curvature Tensor. This tensor is one of the most common objects used to describe curved manifolds, and it plays a very important role in the Einstein Field Equations. The Einstein tensor itself contains a derivation of the reimann tensor, the ricci curvature tensor, and is what results from energy and mass tensor quantities.

The tensor is constructed by taking covariant derivatives of the metric, but it can also be rewritten in terms of the christoffel symbol.

An important idea that can be taken from the Reimann Tensor is parallel transport. Imagine one is on a hill and facing one direction. Move a certain distance, then move in another path, but this time, remain perpendicular to the surface. Repeat the movement until one ends up in the same point one started at. If one is facing a different direction than when one initially started, then there exists curvature inherent in the manifold. Parallel transport provides an effective means through which to describe the curvature of spacetime.

[[File:ReimannCurv.png]]

==Experimental Verifications==

'''Orbit of Mercury'''

In a classical two-body system, one object orbits another in a predictable manner. However, the observation of Mercury's orbit demonstrated a precession, which can be visualized as the orbit itself rotating around the Sun. It was only until Einstein introduced his theory that the precession was accurately accounted for.

'''Gravitational Lensing'''

When light passes through an object, it follows the geodesic trajectory described by Einstein's equations, and as a result bends. The first confirmation of gravitational lensing of light resulted from the measurement of a star's location during a solar eclipse. On May 1919 Arthur Eddington and his team observed stars near the sun and concluded that Einstein's predictions were consistent with empirical results.

'''Gravitational Redshift'''

The effect was only accurately measured in 1959 with the Pound-Rebka Experiment.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

'''How is it connected to your major?'''

Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

'''Is there an interesting industrial application?'''

For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory, from 1907 to 1915. After he published his results on Special Relativity, Einstein wanted to incorporate gravity into his theory, but did not realize how to do so until he stumbled upon differential geometric methods.

When the theory was first introduced, the empirical evidence for the theory did not exist, and many scientists around the world were eager to test Einstein's theories. Because of the counter-intuitive nature of Einstein's works, many doubted the validity of the theory, but with the the verification of the precession of mercury and gravitational lensing phenomena, relativity was all but confirmed.

===Further reading===

https://en.wikipedia.org/wiki/General_relativity

==References==

Einstein, Albert. Relativity: The Special and General Theory. Methuen & Co Ltd, 1916. Print.

Pound, R. V.; Rebka, Jr. G. A. (November 1, 1959). "Gravitational Red-Shift in Nuclear Resonance". Physical Review Letters 3 (9): 439–441.

Rosenthal-Schneider, Ilse: Reality and Scientific Truth. Detroit: Wayne State University Press, 1980. p 74

[[Category:Which Category did you place this in?]]

Einstein's Theory of General Relativity

2015-12-04T19:19:55Z

Wxia33:

(Created by William Xia)

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described. Multiple observations of the theory has been tested and experimentally verified, and new predictions have been observed through solving the equations in this theory.

==The Main Idea==

Gravity is the result of energy and matter distorting spacetime. The reason why one follows a curved trajectory when encountering an object in space is because the trajectory follows a least energy path through spacetime. In other words, if the smallest distance between two points in a plane is a straight line, then the smallest distance between two points in spacetime is described by how the object bends spacetime.

===Mathematical Framework===

Einstein developed a generalized coordinate system and summation notation to simplify his work and create a much more elegant system to describe his ideas. There are four important quantities to understand before tackling the Einstein Field Equations: metric tensor, christoffel symbols, geodesic equation, and the reimann tensor.

'''Metric Tensor'''

The metric tensor is a very important mathematical object in general relativity. Much of the information that describes a space is encoded in this object.

A tensor is a multidimensional quantity that describes direction and magnitude in a much more detailed way than a vector. For example, stress in an object is complex and contains many directions of forces at one single point, but by using a stress tensor one may compactly describe a point or even a collection of points. Writing equations in terms of tensors provides a very important quality: a tensor equation that equals zero in one frame of reference will equal zero in all frames of reference. This property provides a means for the study of physical phenomena in any system of coordinates imaginable.

The metric tensor is a subset of a tensor, in that the metric tensor is a generalization of the pythagorean theorem; a differential length is described by the metric tensor using generalized differential coordinates.

A basic example of the metric tensor is the Schwarzschild metric, which was one of the first metrics to be solved from Einstein's equations. The metric describes a simple sphere in spacetime, but despite the relative simplicity of the metric, it presents an interesting topic to study. By using the Schwarzschild metric, one may arrive at singularities, or mathematical points that explode to infinity. At these singularities, black holes are created, and these such points are still the subject of intense research.
[[File: Metric.png]]

'''Christoffel Symbols'''

Christoffel symbols can be loosely thought of as a residual when taking the derivative in a nonlinear coordinate system. If the coordinate system itself depends on a set of parameters, then taking the derivative of a function will not result in a simple derivative. Because of the product rule, there remains a correction term that must be required, and such term is the christoffel symbol. With respect to the metric tensor, the christoffel symbol has a concrete description of the tensor, and represents the correction quantity that must be used to describe geodesics, or shortest paths.

[[File:817b5f05dba23ecf09a37d4e4c06c3ea.png]]

'''Geodesic Equation'''

The geodesic equation describes the path a particle takes in a general coordinate system, and it is a generalization of acceleration equations. For flat space, or simple cartesian coordinates, if a particle moves then it must move in a straight line disregarding any external forces, and indeed the geodesic equation resembles newton's second law. However, for curved space, say for example a sphere, the shortest path between to points is actually curved. When massive objects distort spacetime, the geodesic equation is helpful in describing paths particles must take in the distorted coordinate frame. Within the mathematical framework, the geodesic equation employs the christoffel symbol to correct for distortions in spacetime.

[[File:Geodesic.png]]

'''Reimann Tensor'''

Although the geodesic equation can describe motion in curved spacetime, the equation itself is insufficient in describing space. For such a description, one must turn to the Reimann Curvature Tensor. This tensor is one of the most common objects used to describe curved manifolds, and it plays a very important role in the Einstein Field Equations. The Einstein tensor itself contains a derivation of the reimann tensor, the ricci curvature tensor, and is what results from energy and mass tensor quantities.

The tensor is constructed by taking covariant derivatives of the metric, but it can also be rewritten in terms of the christoffel symbol.

An important idea that can be taken from the Reimann Tensor is parallel transport. Imagine one is on a hill and facing one direction. Move a certain distance, then move in another path, but this time, remain perpendicular to the surface. Repeat the movement until one ends up in the same point one started at. If one is facing a different direction than when one initially started, then there exists curvature inherent in the manifold. Parallel transport provides an effective means through which to describe the curvature of spacetime.

[[File:ReimannCurv.png]]

==Experimental Verifications==

'''Orbit of Mercury'''

In a classical two-body system, one object orbits another in a predictable manner. However, the observation of Mercury's orbit demonstrated a precession, which can be visualized as the orbit itself rotating around the Sun. It was only until Einstein introduced his theory that the precession was accurately accounted for.

'''Gravitational Lensing'''

When light passes through an object, it follows the geodesic trajectory described by Einstein's equations, and as a result bends. The first confirmation of gravitational lensing of light resulted from the measurement of a star's location during a solar eclipse. On May 1919 Arthur Eddington and his team observed stars near the sun and concluded that Einstein's predictions were consistent with empirical results.

'''Gravitational Redshift'''

The effect was only accurately measured in 1959 with the Pound-Rebka Experiment.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

'''How is it connected to your major?'''

Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

'''Is there an interesting industrial application?'''

For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory, from 1907 to 1915. After he published his results on Special Relativity, Einstein wanted to incorporate gravity into his theory, but did not realize how to do so until he stumbled upon differential geometric methods.

When the theory was first introduced, the empirical evidence for the theory did not exist, and many scientists around the world were eager to test Einstein's theories. Because of the counter-intuitive nature of Einstein's works, many doubted the validity of the theory, but with the the verification of the precession of mercury and gravitational lensing phenomena, relativity was all but confirmed.

===Further reading===

https://en.wikipedia.org/wiki/General_relativity

==References==

Einstein, Albert. Relativity: The Special and General Theory. Methuen & Co Ltd, 1916. Print.

Pound, R. V.; Rebka, Jr. G. A. (November 1, 1959). "Gravitational Red-Shift in Nuclear Resonance". Physical Review Letters 3 (9): 439–441.

Rosenthal-Schneider, Ilse: Reality and Scientific Truth. Detroit: Wayne State University Press, 1980. p 74

[[Category:Which Category did you place this in?]]

Einstein's Theory of General Relativity

2015-12-04T19:14:26Z

Wxia33: /* The Main Idea */

(Created by William Xia)

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described. Multiple observations of the theory has been tested and experimentally verified, and new predictions have been observed through solving the equations in this theory.

==The Main Idea==

Gravity is the result of energy and matter distorting spacetime. The reason why one follows a curved trajectory when encountering an object in space is because the trajectory follows a least energy path through spacetime. In other words, if the smallest distance between two points in a plane is a straight line, then the smallest distance between two points in spacetime is described by how the object bends spacetime.
[[File: Albert Einstein Head.jpg]]

===Mathematical Framework===

Einstein developed a generalized coordinate system and summation notation to simplify his work and create a much more elegant system to describe his ideas. There are four important quantities to understand before tackling the Einstein Field Equations: metric tensor, christoffel symbols, geodesic equation, and the reimann tensor.

'''Metric Tensor'''

The metric tensor is a very important mathematical object in general relativity. Much of the information that describes a space is encoded in this object.

A tensor is a multidimensional quantity that describes direction and magnitude in a much more detailed way than a vector. For example, stress in an object is complex and contains many directions of forces at one single point, but by using a stress tensor one may compactly describe a point or even a collection of points. Writing equations in terms of tensors provides a very important quality: a tensor equation that equals zero in one frame of reference will equal zero in all frames of reference. This property provides a means for the study of physical phenomena in any system of coordinates imaginable.

The metric tensor is a subset of a tensor, in that the metric tensor is a generalization of the pythagorean theorem; a differential length is described by the metric tensor using generalized differential coordinates.

A basic example of the metric tensor is the Schwarzschild metric, which was one of the first metrics to be solved from Einstein's equations. The metric describes a simple sphere in spacetime, but despite the relative simplicity of the metric, it presents an interesting topic to study. By using the Schwarzschild metric, one may arrive at singularities, or mathematical points that explode to infinity. At these singularities, black holes are created, and these such points are still the subject of intense research.
[[File: Metric.png]]

'''Christoffel Symbols'''

Christoffel symbols can be loosely thought of as a residual when taking the derivative in a nonlinear coordinate system. If the coordinate system itself depends on a set of parameters, then taking the derivative of a function will not result in a simple derivative. Because of the product rule, there remains a correction term that must be required, and such term is the christoffel symbol. With respect to the metric tensor, the christoffel symbol has a concrete description of the tensor, and represents the correction quantity that must be used to describe geodesics, or shortest paths.

[[File:817b5f05dba23ecf09a37d4e4c06c3ea.png]]

'''Geodesic Equation'''

The geodesic equation describes the path a particle takes in a general coordinate system, and it is a generalization of acceleration equations. For flat space, or simple cartesian coordinates, if a particle moves then it must move in a straight line disregarding any external forces, and indeed the geodesic equation resembles newton's second law. However, for curved space, say for example a sphere, the shortest path between to points is actually curved. When massive objects distort spacetime, the geodesic equation is helpful in describing paths particles must take in the distorted coordinate frame. Within the mathematical framework, the geodesic equation employs the christoffel symbol to correct for distortions in spacetime.

[[File:Geodesic.png]]

'''Reimann Tensor'''

Although the geodesic equation can describe motion in curved spacetime, the equation itself is insufficient in describing space. For such a description, one must turn to the Reimann Curvature Tensor. This tensor is one of the most common objects used to describe curved manifolds, and it plays a very important role in the Einstein Field Equations. The Einstein tensor itself contains a derivation of the reimann tensor, the ricci curvature tensor, and is what results from energy and mass tensor quantities.

The tensor is constructed by taking covariant derivatives of the metric, but it can also be rewritten in terms of the christoffel symbol.

An important idea that can be taken from the Reimann Tensor is parallel transport. Imagine one is on a hill and facing one direction. Move a certain distance, then move in another path, but this time, remain perpendicular to the surface. Repeat the movement until one ends up in the same point one started at. If one is facing a different direction than when one initially started, then there exists curvature inherent in the manifold. Parallel transport provides an effective means through which to describe the curvature of spacetime.

[[File:ReimannCurv.png]]

==Experimental Verifications==

'''Orbit of Mercury'''

In a classical two-body system, one object orbits another in a predictable manner. However, the observation of Mercury's orbit demonstrated a precession, which can be visualized as the orbit itself rotating around the Sun. It was only until Einstein introduced his theory that the precession was accurately accounted for.

'''Gravitational Lensing'''

When light passes through an object, it follows the geodesic trajectory described by Einstein's equations, and as a result bends. The first confirmation of gravitational lensing of light resulted from the measurement of a star's location during a solar eclipse. On May 1919 Arthur Eddington and his team observed stars near the sun and concluded that Einstein's predictions were consistent with empirical results.

'''Gravitational Redshift'''

The effect was only accurately measured in 1959 with the Pound-Rebka Experiment.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

'''How is it connected to your major?'''

Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

'''Is there an interesting industrial application?'''

For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory, from 1907 to 1915. When the theory was first introduced, the empirical evidence for the theory did not exist, and many scientists around the world were eager to test Einstein's theories. Because of the counter-intuitive nature of Einstein's works, many doubted the validity of the theory.

== See also ==

===Further reading===

https://en.wikipedia.org/wiki/General_relativity

===External links===

==References==

Einstein, Albert. Relativity: The Special and General Theory. Methuen & Co Ltd, 1916. Print.

Pound, R. V.; Rebka, Jr. G. A. (November 1, 1959). "Gravitational Red-Shift in Nuclear Resonance". Physical Review Letters 3 (9): 439–441.

Rosenthal-Schneider, Ilse: Reality and Scientific Truth. Detroit: Wayne State University Press, 1980. p 74

[[Category:Which Category did you place this in?]]

File:ReimannCurv.png

2015-12-04T19:14:13Z

Wxia33:

File:Metric.png

2015-12-04T19:13:27Z

Wxia33:

File:Geodesic.png

2015-12-04T19:11:11Z

Wxia33:

File:Albert Einstein Head.jpg

2015-12-04T19:10:18Z

Wxia33:

Einstein's Theory of General Relativity

2015-12-04T19:07:43Z

Wxia33: /* Mathematical Framework */

(Created by William Xia)

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described. Multiple observations of the theory has been tested and experimentally verified, and new predictions have been observed through solving the equations in this theory.

==The Main Idea==

Gravity is the result of energy and matter distorting spacetime. The reason why one follows a curved trajectory when encountering an object in space is because the trajectory follows a least energy path through spacetime. In other words, if the smallest distance between two points in a plane is a straight line, then the smallest distance between two points in spacetime is described by how the object bends spacetime.

===Mathematical Framework===

Einstein developed a generalized coordinate system and summation notation to simplify his work and create a much more elegant system to describe his ideas. There are four important quantities to understand before tackling the Einstein Field Equations: metric tensor, christoffel symbols, geodesic equation, and the reimann tensor.

'''Metric Tensor'''

The metric tensor is a very important mathematical object in general relativity. Much of the information that describes a space is encoded in this object.

A tensor is a multidimensional quantity that describes direction and magnitude in a much more detailed way than a vector. For example, stress in an object is complex and contains many directions of forces at one single point, but by using a stress tensor one may compactly describe a point or even a collection of points. Writing equations in terms of tensors provides a very important quality: a tensor equation that equals zero in one frame of reference will equal zero in all frames of reference. This property provides a means for the study of physical phenomena in any system of coordinates imaginable.

The metric tensor is a subset of a tensor, in that the metric tensor is a generalization of the pythagorean theorem; a differential length is described by the metric tensor using generalized differential coordinates.

A basic example of the metric tensor is the Schwarzschild metric, which was one of the first metrics to be solved from Einstein's equations. The metric describes a simple sphere in spacetime, but despite the relative simplicity of the metric, it presents an interesting topic to study. By using the Schwarzschild metric, one may arrive at singularities, or mathematical points that explode to infinity. At these singularities, black holes are created, and these such points are still the subject of intense research.

'''Christoffel Symbols'''

Christoffel symbols can be loosely thought of as a residual when taking the derivative in a nonlinear coordinate system. If the coordinate system itself depends on a set of parameters, then taking the derivative of a function will not result in a simple derivative. Because of the product rule, there remains a correction term that must be required, and such term is the christoffel symbol. With respect to the metric tensor, the christoffel symbol has a concrete description of the tensor, and represents the correction quantity that must be used to describe geodesics, or shortest paths.

[[File:817b5f05dba23ecf09a37d4e4c06c3ea.png]]

'''Geodesic Equation'''

The geodesic equation describes the path a particle takes in a general coordinate system, and it is a generalization of acceleration equations. For flat space, or simple cartesian coordinates, if a particle moves then it must move in a straight line disregarding any external forces, and indeed the geodesic equation resembles newton's second law. However, for curved space, say for example a sphere, the shortest path between to points is actually curved. When massive objects distort spacetime, the geodesic equation is helpful in describing paths particles must take in the distorted coordinate frame. Within the mathematical framework, the geodesic equation employs the christoffel symbol to correct for distortions in spacetime.

'''Reimann Tensor'''

Although the geodesic equation can describe motion in curved spacetime, the equation itself is insufficient in describing space. For such a description, one must turn to the Reimann Curvature Tensor. This tensor is one of the most common objects used to describe curved manifolds, and it plays a very important role in the Einstein Field Equations. The Einstein tensor itself contains a derivation of the reimann tensor, the ricci curvature tensor, and is what results from energy and mass tensor quantities.

The tensor is constructed by taking covariant derivatives of the metric, but it can also be rewritten in terms of the christoffel symbol.

An important idea that can be taken from the Reimann Tensor is parallel transport. Imagine one is on a hill and facing one direction. Move a certain distance, then move in another path, but this time, remain perpendicular to the surface. Repeat the movement until one ends up in the same point one started at. If one is facing a different direction than when one initially started, then there exists curvature inherent in the manifold. Parallel transport provides an effective means through which to describe the curvature of spacetime.

==Experimental Verifications==

'''Orbit of Mercury'''

In a classical two-body system, one object orbits another in a predictable manner. However, the observation of Mercury's orbit demonstrated a precession, which can be visualized as the orbit itself rotating around the Sun. It was only until Einstein introduced his theory that the precession was accurately accounted for.

'''Gravitational Lensing'''

When light passes through an object, it follows the geodesic trajectory described by Einstein's equations, and as a result bends. The first confirmation of gravitational lensing of light resulted from the measurement of a star's location during a solar eclipse. On May 1919 Arthur Eddington and his team observed stars near the sun and concluded that Einstein's predictions were consistent with empirical results.

'''Gravitational Redshift'''

The effect was only accurately measured in 1959 with the Pound-Rebka Experiment.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

'''How is it connected to your major?'''

Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

'''Is there an interesting industrial application?'''

For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory, from 1907 to 1915. When the theory was first introduced, the empirical evidence for the theory did not exist, and many scientists around the world were eager to test Einstein's theories. Because of the counter-intuitive nature of Einstein's works, many doubted the validity of the theory.

== See also ==

===Further reading===

https://en.wikipedia.org/wiki/General_relativity

===External links===

==References==

Einstein, Albert. Relativity: The Special and General Theory. Methuen & Co Ltd, 1916. Print.

Pound, R. V.; Rebka, Jr. G. A. (November 1, 1959). "Gravitational Red-Shift in Nuclear Resonance". Physical Review Letters 3 (9): 439–441.

Rosenthal-Schneider, Ilse: Reality and Scientific Truth. Detroit: Wayne State University Press, 1980. p 74

[[Category:Which Category did you place this in?]]

File:817b5f05dba23ecf09a37d4e4c06c3ea.png

2015-12-04T19:06:53Z

Wxia33: Christoffel Symbol

Christoffel Symbol

Einstein's Theory of General Relativity

2015-12-04T19:05:10Z

Wxia33:

(Created by William Xia)

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described. Multiple observations of the theory has been tested and experimentally verified, and new predictions have been observed through solving the equations in this theory.

==The Main Idea==

Gravity is the result of energy and matter distorting spacetime. The reason why one follows a curved trajectory when encountering an object in space is because the trajectory follows a least energy path through spacetime. In other words, if the smallest distance between two points in a plane is a straight line, then the smallest distance between two points in spacetime is described by how the object bends spacetime.

===Mathematical Framework===

Einstein developed a generalized coordinate system and summation notation to simplify his work and create a much more elegant system to describe his ideas. There are four important quantities to understand before tackling the Einstein Field Equations: metric tensor, christoffel symbols, geodesic equation, and the reimann tensor.

'''Metric Tensor'''

The metric tensor is a very important mathematical object in general relativity. Much of the information that describes a space is encoded in this object.

A tensor is a multidimensional quantity that describes direction and magnitude in a much more detailed way than a vector. For example, stress in an object is complex and contains many directions of forces at one single point, but by using a stress tensor one may compactly describe a point or even a collection of points. Writing equations in terms of tensors provides a very important quality: a tensor equation that equals zero in one frame of reference will equal zero in all frames of reference. This property provides a means for the study of physical phenomena in any system of coordinates imaginable.

The metric tensor is a subset of a tensor, in that the metric tensor is a generalization of the pythagorean theorem; a differential length is described by the metric tensor using generalized differential coordinates.

A basic example of the metric tensor is the Schwarzschild metric, which was one of the first metrics to be solved from Einstein's equations. The metric describes a simple sphere in spacetime, but despite the relative simplicity of the metric, it presents an interesting topic to study. By using the Schwarzschild metric, one may arrive at singularities, or mathematical points that explode to infinity. At these singularities, black holes are created, and these such points are still the subject of intense research.

'''Christoffel Symbols'''

Christoffel symbols can be loosely thought of as a residual when taking the derivative in a nonlinear coordinate system. If the coordinate system itself depends on a set of parameters, then taking the derivative of a function will not result in a simple derivative. Because of the product rule, there remains a correction term that must be required, and such term is the christoffel symbol. With respect to the metric tensor, the christoffel symbol has a concrete description of the tensor, and represents the correction quantity that must be used to describe geodesics, or shortest paths.

'''Geodesic Equation'''

The geodesic equation describes the path a particle takes in a general coordinate system, and it is a generalization of acceleration equations. For flat space, or simple cartesian coordinates, if a particle moves then it must move in a straight line disregarding any external forces, and indeed the geodesic equation resembles newton's second law. However, for curved space, say for example a sphere, the shortest path between to points is actually curved. When massive objects distort spacetime, the geodesic equation is helpful in describing paths particles must take in the distorted coordinate frame. Within the mathematical framework, the geodesic equation employs the christoffel symbol to correct for distortions in spacetime.

'''Reimann Tensor'''

Although the geodesic equation can describe motion in curved spacetime, the equation itself is insufficient in describing space. For such a description, one must turn to the Reimann Curvature Tensor. This tensor is one of the most common objects used to describe curved manifolds, and it plays a very important role in the Einstein Field Equations. The Einstein tensor itself contains a derivation of the reimann tensor, the ricci curvature tensor, and is what results from energy and mass tensor quantities.

The tensor is constructed by taking covariant derivatives of the metric, but it can also be rewritten in terms of the christoffel symbol.

An important idea that can be taken from the Reimann Tensor is parallel transport. Imagine one is on a hill and facing one direction. Move a certain distance, then move in another path, but this time, remain perpendicular to the surface. Repeat the movement until one ends up in the same point one started at. If one is facing a different direction than when one initially started, then there exists curvature inherent in the manifold. Parallel transport provides an effective means through which to describe the curvature of spacetime.

==Experimental Verifications==

'''Orbit of Mercury'''

In a classical two-body system, one object orbits another in a predictable manner. However, the observation of Mercury's orbit demonstrated a precession, which can be visualized as the orbit itself rotating around the Sun. It was only until Einstein introduced his theory that the precession was accurately accounted for.

'''Gravitational Lensing'''

When light passes through an object, it follows the geodesic trajectory described by Einstein's equations, and as a result bends. The first confirmation of gravitational lensing of light resulted from the measurement of a star's location during a solar eclipse. On May 1919 Arthur Eddington and his team observed stars near the sun and concluded that Einstein's predictions were consistent with empirical results.

'''Gravitational Redshift'''

The effect was only accurately measured in 1959 with the Pound-Rebka Experiment.

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

'''How is it connected to your major?'''

Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

'''Is there an interesting industrial application?'''

For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory, from 1907 to 1915. When the theory was first introduced, the empirical evidence for the theory did not exist, and many scientists around the world were eager to test Einstein's theories. Because of the counter-intuitive nature of Einstein's works, many doubted the validity of the theory.

== See also ==

===Further reading===

https://en.wikipedia.org/wiki/General_relativity

===External links===

==References==

Einstein, Albert. Relativity: The Special and General Theory. Methuen & Co Ltd, 1916. Print.

Pound, R. V.; Rebka, Jr. G. A. (November 1, 1959). "Gravitational Red-Shift in Nuclear Resonance". Physical Review Letters 3 (9): 439–441.

Rosenthal-Schneider, Ilse: Reality and Scientific Truth. Detroit: Wayne State University Press, 1980. p 74

[[Category:Which Category did you place this in?]]

Einstein's Theory of General Relativity

2015-12-04T18:45:15Z

Wxia33:

(Created by William Xia)

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described. Multiple observations of the theory has been tested and experimentally verified, and new predictions have been observed through solving the equations in this theory.

==The Main Idea==

Gravity is the result of energy and matter distorting spacetime. The reason why one follows a curved trajectory when encountering an object in space is because the trajectory follows a least energy path through spacetime. In other words, if the smallest distance between two points in a plane is a straight line, then the smallest distance between two points in spacetime is described by how the object bends spacetime.

===Mathematical Framework===

Einstein developed a generalized coordinate system and summation notation to simplify his work and create a much more elegant system to describe his ideas. There are four important quantities to understand before tackling the Einstein Field Equations: metric tensor, christoffel symbols, geodesic equation, and the reimann tensor.

'''Metric Tensor'''

The metric tensor is a very important mathematical object in general relativity. Much of the information that describes a space is encoded in this object.

A tensor is a multidimensional quantity that describes direction and magnitude in a much more detailed way than a vector. For example, stress in an object is complex and contains many directions of forces at one single point, but by using a stress tensor one may compactly describe a point or even a collection of points. Writing equations in terms of tensors provides a very important quality: a tensor equation that equals zero in one frame of reference will equal zero in all frames of reference. This property provides a means for the study of physical phenomena in any system of coordinates imaginable.

The metric tensor is a subset of a tensor, in that the metric tensor is a generalization of the pythagorean theorem; a differential length is described by the metric tensor using generalized differential coordinates.

A basic example of the metric tensor is the Schwarzschild metric, which was one of the first metrics to be solved from Einstein's equations. The metric describes a simple sphere in spacetime, but despite the relative simplicity of the metric, it presents an interesting topic to study. By using the Schwarzschild metric, one may arrive at singularities, or mathematical points that explode to infinity. At these singularities, black holes are created, and these such points are still the subject of intense research.

'''Christoffel Symbols'''

Christoffel symbols can be loosely thought of as a residual when taking the derivative in a nonlinear coordinate system. If the coordinate system itself depends on a set of parameters, then taking the derivative of a function will not result in a simple derivative. Because of the product rule, there remains a correction term that must be required, and such term is the christoffel symbol. With respect to the metric tensor, the christoffel symbol has a concrete description of the tensor, and represents the correction quantity that must be used to describe geodesics, or shortest paths.

'''Geodesic Equation'''

The geodesic equation describes the path a particle takes in a general coordinate system, and it is a generalization of acceleration equations. For flat space, or simple cartesian coordinates, if a particle moves then it must move in a straight line disregarding any external forces, and indeed the geodesic equation resembles newton's second law. However, for curved space, say for example a sphere, the shortest path between to points is actually curved. When massive objects distort spacetime, the geodesic equation is helpful in describing paths particles must take in the distorted coordinate frame. Within the mathematical framework, the geodesic equation employs the christoffel symbol to correct for distortions in spacetime.

'''Reimann Tensor'''

Although the geodesic equation can describe motion in curved spacetime, the equation itself is insufficient in describing space. For such a description, one must turn to the Reimann Curvature Tensor. This tensor is one of the most common objects used to describe curved manifolds, and it plays a very important role in the Einstein Field Equations. The Einstein tensor itself contains a derivation of the reimann tensor, the ricci curvature tensor, and is what results from energy and mass tensor quantities.

The tensor is constructed by taking covariant derivatives of the metric, but it can also be rewritten in terms of the christoffel symbol.

===A Computational Model===

==Examples==

===Simple===
===Middling===
===Difficult===

==Connectedness==
'''How is this topic connected to something that you are interested in?'''

I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

'''How is it connected to your major?'''

Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

'''Is there an interesting industrial application?'''

For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory, from 1907 to 1915.

== See also ==

===Further reading===

===External links===

==References==

Einstein, Albert. Relativity: The Special and General Theory. Methuen & Co Ltd, 1916. Print.

[[Category:Which Category did you place this in?]]

Einstein's Theory of General Relativity

2015-12-04T18:39:57Z

Wxia33: /* Mathematical Framework */

(Created by William Xia)

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described. Multiple observations of the theory has been tested and experimentally verified, and new predictions have been observed through solving the equations in this theory.

==The Main Idea==

Gravity is the result of energy and matter distorting spacetime. The reason why one follows a curved trajectory when encountering an object in space is because the trajectory follows a least energy path through spacetime. In other words, if the smallest distance between two points in a plane is a straight line, then the smallest distance between two points in spacetime is described by how the object bends spacetime.

===Mathematical Framework===

Einstein developed a generalized coordinate system and summation notation to simplify his work and create a much more elegant system to describe his ideas. There are four important quantities to understand before tackling the Einstein Field Equations: metric tensor, christoffel symbols, geodesic equation, and the reimann tensor.

'''Metric Tensor'''

The metric tensor is a very important mathematical object in general relativity. Much of the information that describes a space is encoded in this object.

A tensor is a multidimensional quantity that describes direction and magnitude in a much more detailed way than a vector. For example, stress in an object is complex and contains many directions of forces at one single point, but by using a stress tensor one may compactly describe a point or even a collection of points. Writing equations in terms of tensors provides a very important quality: a tensor equation that equals zero in one frame of reference will equal zero in all frames of reference. This property provides a means for the study of physical phenomena in any system of coordinates imaginable.

The metric tensor is a subset of a tensor, in that the metric tensor is a generalization of the pythagorean theorem; a differential length is described by the metric tensor using generalized differential coordinates.

A basic example of the metric tensor is the Schwarzschild metric, which was one of the first metrics to be solved from Einstein's equations. The metric describes a simple sphere in spacetime, but despite the relative simplicity of the metric, it presents an interesting topic to study. By using the Schwarzschild metric, one may arrive at singularities, or mathematical points that explode to infinity. At these singularities, black holes are created, and these such points are still the subject of intense research.

'''Christoffel Symbols'''

Christoffel symbols can be loosely thought of as a residual when taking the derivative in a nonlinear coordinate system. If the coordinate system itself depends on a set of parameters, then taking the derivative of a function will not result in a simple derivative. Because of the product rule, there remains a correction term that must be required, and such term is the christoffel symbol. With respect to the metric tensor, the christoffel symbol has a concrete description of the tensor, and represents the correction quantity that must be used to describe geodesics, or shortest paths.

'''Geodesic Equation'''

The geodesic equation describes the path a particle takes in a general coordinate system, and it is a generalization of acceleration equations. For flat space, or simple cartesian coordinates, if a particle moves then it must move in a straight line disregarding any external forces, and indeed the geodesic equation resembles newton's second law. However, for curved space, say for example a sphere, the shortest path between to points is actually curved. When massive objects distort spacetime, the geodesic equation is helpful in describing paths particles must take in the distorted coordinate frame. Within the mathematical framework, the geodesic equation employs the christoffel symbol to correct for distortions in spacetime.

'''Reimann Tensor'''

Although the geodesic equation can describe motion in curved spacetime, the equation itself is insufficient in describing space. For such a description, one must turn to the Reimann Curvature Tensor. This tensor is one of the most common objects used to describe curved manifolds, and it plays a very important role in the Einstein Field Equations. The Einstein tensor itself contains a derivation of the reimann tensor, the ricci curvature tensor, and is what results from energy and mass tensor quantities.

The tensor is constructed by taking covariant derivatives of the metric, but it can also be rewritten in terms of the christoffel symbol.

===A Computational Model===

==Examples==

===Simple===
===Middling===
===Difficult===

==Connectedness==
How is this topic connected to something that you are interested in?

I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

How is it connected to your major?

Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

Is there an interesting industrial application?

For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory before he published his work. 1907,1912

== See also ==

===Further reading===

===External links===

==References==

Einstein, Albert. Relativity: The Special and General Theory. Methuen & Co Ltd, 1916. Print.

[[Category:Which Category did you place this in?]]

Einstein's Theory of General Relativity

2015-12-04T18:23:13Z

Wxia33:

Einstein's Theory of General Relativity

2015-12-04T06:37:15Z

Wxia33:

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described.

==The Main Idea==

Gravity is the result of energy and matter distorting space and time.

===A Mathematical Model===

Geodesics are an important idea in this theory.

\mathbf{G}=\frac{8\pi G}{c^4}\mathbf{T}

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
===Middling===
===Difficult===

==Connectedness==
How is this topic connected to something that you are interested in?

I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

How is it connected to your major?

Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

Is there an interesting industrial application?

For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory before he published his work.

== See also ==

===Further reading===

===External links===

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Einstein's Theory of General Relativity

2015-12-04T06:27:04Z

Wxia33: /* Connectedness */

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described.

==The Main Idea==

Gravity is the result of energy and matter distorting space and time.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
===Middling===
===Difficult===

==Connectedness==
How is this topic connected to something that you are interested in?
I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

How is it connected to your major?
Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

Is there an interesting industrial application?
For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory before he published his work.

== See also ==

===Further reading===

===External links===

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Einstein's Theory of General Relativity

2015-12-04T06:26:31Z

Wxia33: Created page with "Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described. ==The Main Idea== Gravity is the result of en..."

Einstein's Theory of General Relativity described gravity in the most detailed and accurate way that has ever been described.

==The Main Idea==

Gravity is the result of energy and matter distorting space and time.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
I have always been fascinated by how gravity can be described in a rigorous mathematical sense, and the revolutionary nature of Einstein's work.

#How is it connected to your major?
Electrical Engineers, when designing satellites, have to take into account the effects of GR in order to produce accurate time measurements. Recent experiments have also sought to measure minuscule changes in length and time due to gravitational waves and high velocities.

#Is there an interesting industrial application?
For now, GR is restricted to mostly space applications. Away from the Earth's gravity, residents or machines orbiting the earth or traveling through space experience different effects on time and space due to fluctuating gravitational fields.

==History==

Einstein spent nearly 10 years refining his theory before he published his work.

== See also ==

===Further reading===

===External links===

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Main Page

2015-12-04T06:18:09Z

Wxia33: /* Theory */