Physics Book - User contributions [en]

Analytical Prediction

2015-12-03T18:42:10Z

Hmcleod6: /* Example 2 */

By Hayden McLeod (hmcleod6)

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===A Computational Model===

Below is a visualization of the analytical prediction of the average velocity. As you can see, it takes two points, (a, f(a)) and (b, f(b)), and finds the average between the two points. Also depicted in the image is the incapability to model non-linear curves by comparing the average slope (velocity) compared to the actual slope (velocity).

[[File: htmjpg2.jpg|300px]]

In addition, an example of using this method in GlowScript can be seen below.

[[File: Htmpng2.png|600px]]

Not only does this code show how to use the analytical prediction method using python/GlowScript, it also shows how you can use that average velocity to calculate the momentum and update the position. These are the typical calculations associated with prediction methods.

==Examples==
===Example 1===
A train is observed to be traveling at a speed of 24 m/s before it enters a city. While in the city, it is observed going 13 m/s. What is the average velocity of the train?

24 m/s + 13 m/s = 37 m/s

37/2 = 18.5

The average velocity of the train based on the analytical prediction method was 18.5 m/s.

===Example 2===
A car is traveling at a speed of (18, -2, 0) m/s. Later, the car is observed to be going (22, 6, 0) m/s. If the car started at the location (40, 170, 0) what is it's position after 30 seconds?

First, you have to find the average velocity:

(18, -2, 0) + (22, 6, 0) = (40, 4, 0)

(40, 4, 0) /2 = (20, 2, 0)

so the average velocity is (20, 2, 0) m/s

Second, calculate the change in position:

Change in position = average velocity x time

(20, 2, 0) * 30 = (600, 60, 0)

So the change in position is (600, 60, 0) m

Finally, update the position:

final position = initial position + change in position

(40, 170, 0) + (600, 60, 0) = (640, 230, 0)

The final position is (640, 230, 0) m

==Connectedness==
#How is this topic connected to something that you are interested in?
Since this topic is based on such a fundamental mathematical principle, my interest in it lies in how wide spread this principle can be used not only in physics but in many other applications, fields, and scenarios.

#How is it connected to your major?
As stated in the previous connection, this basic principle has ties in just about every major with any connection to math including business, sciences, and engineering. Specifically, methods like this are often used to try and model basic relationships of properties in material science.

#Is there an interesting industrial application?
In industry, methods like this, or methods very similar, are used every day to help process and analyze data in a very basic and quick way.

==History==

Historically, it is well known that basic algebra was discovered and implemented well before calculus, especially based on the fact that algebra was used as a basis to develop calculus. For this reason, it can be assumed that the analytical approach to physics problems related to velocity, or any other changing value, was used long before the iterative method. There is no information on who would have used this approach or when this approach was first used in a physics application.

== See also ==

Vectors,
Momentum Principle,
Iterative Prediction

===Further reading===

There are several easily accessible resources with more information on analytical prediction methods and arithmetic means

===External links===

==References==

http://www.platinumgmat.com/gmat_study_guide/statistics_mean (information)
http://ncalculators.com/statistics/group-arithmetic-mean.htm (image)
https://quizlet.com/24263897/mcat-physics-formulas-flash-cards/ (image)
http://mathinsight.org/approximating_nonlinear_function_by_linear (image)

[[Category:Momentum]]

Analytical Prediction

2015-12-03T18:41:43Z

Hmcleod6: /* Examples */

By Hayden McLeod (hmcleod6)

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===A Computational Model===

Below is a visualization of the analytical prediction of the average velocity. As you can see, it takes two points, (a, f(a)) and (b, f(b)), and finds the average between the two points. Also depicted in the image is the incapability to model non-linear curves by comparing the average slope (velocity) compared to the actual slope (velocity).

[[File: htmjpg2.jpg|300px]]

In addition, an example of using this method in GlowScript can be seen below.

[[File: Htmpng2.png|600px]]

Not only does this code show how to use the analytical prediction method using python/GlowScript, it also shows how you can use that average velocity to calculate the momentum and update the position. These are the typical calculations associated with prediction methods.

==Examples==
===Example 1===
A train is observed to be traveling at a speed of 24 m/s before it enters a city. While in the city, it is observed going 13 m/s. What is the average velocity of the train?

24 m/s + 13 m/s = 37 m/s

37/2 = 18.5

The average velocity of the train based on the analytical prediction method was 18.5 m/s.

===Example 2===
A car is traveling at a speed of (18, -2, 0) m/s. Later, the car is observed to be going (22, 6, 0) m/s. If the car started at the location (40, 170, 0) what is it's position after 30 seconds?

First, you have to find the average velocity:
(18, -2, 0) + (22, 6, 0) = (40, 4, 0)
(40, 4, 0) /2 = (20, 2, 0)
so the average velocity is (20, 2, 0) m/s

Second, calculate the change in position:
Change in position = average velocity x time
(20, 2, 0) * 30 = (600, 60, 0)
So the change in position is (600, 60, 0) m

Finally, update the position:
final position = initial position + change in position
(40, 170, 0) + (600, 60, 0) = (640, 230, 0)
The final position is (640, 230, 0) m

==Connectedness==
#How is this topic connected to something that you are interested in?
Since this topic is based on such a fundamental mathematical principle, my interest in it lies in how wide spread this principle can be used not only in physics but in many other applications, fields, and scenarios.

#How is it connected to your major?
As stated in the previous connection, this basic principle has ties in just about every major with any connection to math including business, sciences, and engineering. Specifically, methods like this are often used to try and model basic relationships of properties in material science.

#Is there an interesting industrial application?
In industry, methods like this, or methods very similar, are used every day to help process and analyze data in a very basic and quick way.

==History==

Historically, it is well known that basic algebra was discovered and implemented well before calculus, especially based on the fact that algebra was used as a basis to develop calculus. For this reason, it can be assumed that the analytical approach to physics problems related to velocity, or any other changing value, was used long before the iterative method. There is no information on who would have used this approach or when this approach was first used in a physics application.

== See also ==

Vectors,
Momentum Principle,
Iterative Prediction

===Further reading===

There are several easily accessible resources with more information on analytical prediction methods and arithmetic means

===External links===

==References==

http://www.platinumgmat.com/gmat_study_guide/statistics_mean (information)
http://ncalculators.com/statistics/group-arithmetic-mean.htm (image)
https://quizlet.com/24263897/mcat-physics-formulas-flash-cards/ (image)
http://mathinsight.org/approximating_nonlinear_function_by_linear (image)

[[Category:Momentum]]

Analytical Prediction

2015-12-03T18:41:08Z

Hmcleod6: /* Example 2 */

By Hayden McLeod (hmcleod6)

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===A Computational Model===

Below is a visualization of the analytical prediction of the average velocity. As you can see, it takes two points, (a, f(a)) and (b, f(b)), and finds the average between the two points. Also depicted in the image is the incapability to model non-linear curves by comparing the average slope (velocity) compared to the actual slope (velocity).

[[File: htmjpg2.jpg|300px]]

In addition, an example of using this method in GlowScript can be seen below.

[[File: Htmpng2.png|600px]]

Not only does this code show how to use the analytical prediction method using python/GlowScript, it also shows how you can use that average velocity to calculate the momentum and update the position. These are the typical calculations associated with prediction methods.

==Examples==
===Example 1===
A train is observed to be traveling at a speed of 24 m/s before it enters a city. While in the city, it is observed going 13 m/s. What is the average velocity of the train?

24 m/s + 13 m/s = 37 m/s
37/2 = 18.5

The average velocity of the train based on the analytical prediction method was 18.5 m/s.

===Example 2===
A car is traveling at a speed of (18, -2, 0) m/s. Later, the car is observed to be going (22, 6, 0) m/s. If the car started at the location (40, 170, 0) what is it's position after 30 seconds?

First, you have to find the average velocity:
(18, -2, 0) + (22, 6, 0) = (40, 4, 0)
(40, 4, 0) /2 = (20, 2, 0)
so the average velocity is (20, 2, 0) m/s

Second, calculate the change in position:
Change in position = average velocity x time
(20, 2, 0) * 30 = (600, 60, 0)
So the change in position is (600, 60, 0) m

Finally, update the position:
final position = initial position + change in position
(40, 170, 0) + (600, 60, 0) = (640, 230, 0)
The final position is (640, 230, 0) m

==Connectedness==
#How is this topic connected to something that you are interested in?
Since this topic is based on such a fundamental mathematical principle, my interest in it lies in how wide spread this principle can be used not only in physics but in many other applications, fields, and scenarios.

#How is it connected to your major?
As stated in the previous connection, this basic principle has ties in just about every major with any connection to math including business, sciences, and engineering. Specifically, methods like this are often used to try and model basic relationships of properties in material science.

#Is there an interesting industrial application?
In industry, methods like this, or methods very similar, are used every day to help process and analyze data in a very basic and quick way.

==History==

Historically, it is well known that basic algebra was discovered and implemented well before calculus, especially based on the fact that algebra was used as a basis to develop calculus. For this reason, it can be assumed that the analytical approach to physics problems related to velocity, or any other changing value, was used long before the iterative method. There is no information on who would have used this approach or when this approach was first used in a physics application.

== See also ==

Vectors,
Momentum Principle,
Iterative Prediction

===Further reading===

There are several easily accessible resources with more information on analytical prediction methods and arithmetic means

===External links===

==References==

http://www.platinumgmat.com/gmat_study_guide/statistics_mean (information)
http://ncalculators.com/statistics/group-arithmetic-mean.htm (image)
https://quizlet.com/24263897/mcat-physics-formulas-flash-cards/ (image)
http://mathinsight.org/approximating_nonlinear_function_by_linear (image)

[[Category:Momentum]]

Analytical Prediction

2015-12-03T18:40:20Z

Hmcleod6: /* Examples */

By Hayden McLeod (hmcleod6)

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===A Computational Model===

Below is a visualization of the analytical prediction of the average velocity. As you can see, it takes two points, (a, f(a)) and (b, f(b)), and finds the average between the two points. Also depicted in the image is the incapability to model non-linear curves by comparing the average slope (velocity) compared to the actual slope (velocity).

[[File: htmjpg2.jpg|300px]]

In addition, an example of using this method in GlowScript can be seen below.

[[File: Htmpng2.png|600px]]

Not only does this code show how to use the analytical prediction method using python/GlowScript, it also shows how you can use that average velocity to calculate the momentum and update the position. These are the typical calculations associated with prediction methods.

==Examples==
===Example 1===
A train is observed to be traveling at a speed of 24 m/s before it enters a city. While in the city, it is observed going 13 m/s. What is the average velocity of the train?

24 m/s + 13 m/s = 37 m/s
37/2 = 18.5

The average velocity of the train based on the analytical prediction method was 18.5 m/s.

===Example 2===
A car is traveling at a speed of (18, -2, 0) m/s. Later, the car is observed to be going (22, 6, 0) m/s. If the car started at the location (40, 170, 0) what is it's position after 30 seconds?

First, you have to find the average velocity:
(18, -2, 0) + (22, 6, 0) = (40, 4, 0)
(40, 4, 0) /2 = (20, 2, 0)
so the average velocity is (20, 2, 0) m/s

Second, calculate the change in position:
Change in position = average velocity x time
(20, 2, 0) * 30 = (600, 60, 0)
So the change in position is (600, 60, 0) m

Finally, update the position:
final position = initial position + change in position
(40, 170, 0) + (600, 60, 0) = (640, 230, 0)
The final position is (640, 230, 0) m

==Connectedness==
#How is this topic connected to something that you are interested in?
Since this topic is based on such a fundamental mathematical principle, my interest in it lies in how wide spread this principle can be used not only in physics but in many other applications, fields, and scenarios.

#How is it connected to your major?
As stated in the previous connection, this basic principle has ties in just about every major with any connection to math including business, sciences, and engineering. Specifically, methods like this are often used to try and model basic relationships of properties in material science.

#Is there an interesting industrial application?
In industry, methods like this, or methods very similar, are used every day to help process and analyze data in a very basic and quick way.

==History==

Historically, it is well known that basic algebra was discovered and implemented well before calculus, especially based on the fact that algebra was used as a basis to develop calculus. For this reason, it can be assumed that the analytical approach to physics problems related to velocity, or any other changing value, was used long before the iterative method. There is no information on who would have used this approach or when this approach was first used in a physics application.

== See also ==

Vectors,
Momentum Principle,
Iterative Prediction

===Further reading===

There are several easily accessible resources with more information on analytical prediction methods and arithmetic means

===External links===

==References==

http://www.platinumgmat.com/gmat_study_guide/statistics_mean (information)
http://ncalculators.com/statistics/group-arithmetic-mean.htm (image)
https://quizlet.com/24263897/mcat-physics-formulas-flash-cards/ (image)
http://mathinsight.org/approximating_nonlinear_function_by_linear (image)

[[Category:Momentum]]

Analytical Prediction

2015-12-03T18:24:17Z

Hmcleod6: /* Connectedness */

By Hayden McLeod (hmcleod6)

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===A Computational Model===

Below is a visualization of the analytical prediction of the average velocity. As you can see, it takes two points, (a, f(a)) and (b, f(b)), and finds the average between the two points. Also depicted in the image is the incapability to model non-linear curves by comparing the average slope (velocity) compared to the actual slope (velocity).

[[File: htmjpg2.jpg|300px]]

In addition, an example of using this method in GlowScript can be seen below.

[[File: Htmpng2.png|600px]]

Not only does this code show how to use the analytical prediction method using python/GlowScript, it also shows how you can use that average velocity to calculate the momentum and update the position. These are the typical calculations associated with prediction methods.

==Examples==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
Since this topic is based on such a fundamental mathematical principle, my interest in it lies in how wide spread this principle can be used not only in physics but in many other applications, fields, and scenarios.

#How is it connected to your major?
As stated in the previous connection, this basic principle has ties in just about every major with any connection to math including business, sciences, and engineering. Specifically, methods like this are often used to try and model basic relationships of properties in material science.

#Is there an interesting industrial application?
In industry, methods like this, or methods very similar, are used every day to help process and analyze data in a very basic and quick way.

==History==

Historically, it is well known that basic algebra was discovered and implemented well before calculus, especially based on the fact that algebra was used as a basis to develop calculus. For this reason, it can be assumed that the analytical approach to physics problems related to velocity, or any other changing value, was used long before the iterative method. There is no information on who would have used this approach or when this approach was first used in a physics application.

== See also ==

Vectors,
Momentum Principle,
Iterative Prediction

===Further reading===

There are several easily accessible resources with more information on analytical prediction methods and arithmetic means

===External links===

==References==

http://www.platinumgmat.com/gmat_study_guide/statistics_mean (information)
http://ncalculators.com/statistics/group-arithmetic-mean.htm (image)
https://quizlet.com/24263897/mcat-physics-formulas-flash-cards/ (image)
http://mathinsight.org/approximating_nonlinear_function_by_linear (image)

[[Category:Momentum]]

Analytical Prediction

2015-12-03T18:20:12Z

Hmcleod6: /* References */

Analytical Prediction

2015-12-03T18:14:47Z

Hmcleod6: /* See also */

Analytical Prediction

2015-12-03T18:14:20Z

Hmcleod6: /* See also */

Analytical Prediction

2015-12-03T18:10:27Z

Hmcleod6: /* A Computational Model */

Analytical Prediction

2015-12-03T18:08:32Z

Hmcleod6: /* A Computational Model */

Analytical Prediction

2015-12-03T18:08:14Z

Hmcleod6: /* A Mathematical Model */

Analytical Prediction

2015-12-03T18:07:52Z

Hmcleod6: /* A Computational Model */

Analytical Prediction

2015-12-03T18:07:37Z

Hmcleod6: /* A Computational Model */

Analytical Prediction

2015-12-03T18:07:21Z

Hmcleod6: /* A Computational Model */

Analytical Prediction

2015-12-03T18:05:32Z

Hmcleod6: /* A Computational Model */

File:Htmpng2.png

2015-12-03T18:05:14Z

Hmcleod6:

Analytical Prediction

2015-12-03T17:50:54Z

Hmcleod6:

Analytical Prediction

2015-12-03T17:48:02Z

Hmcleod6: /* History */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===A Computational Model===

Below is a visualization of the analytical prediction of the average velocity. As you can see, it takes two points, (a, f(a)) and (b, f(b)), and finds the average between the two points. Also depicted in the image is the incapability to model non-linear curves by comparing the average slope (velocity) compared to the actual slope (velocity).

[[File: htmjpg2.jpg|300px]]

==Examples==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Historically, it is well known that basic algebra was discovered and implemented well before calculus, especially based on the fact that algebra was used as a basis to develop calculus. For this reason, it can be assumed that the analytical approach to physics problems related to velocity, or any other changing value, was used long before the iterative method. There is no information on who would have used this approach or when this approach was first used in a physics application.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:43:25Z

Hmcleod6: /* A Computational Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===A Computational Model===

Below is a visualization of the analytical prediction of the average velocity. As you can see, it takes two points, (a, f(a)) and (b, f(b)), and finds the average between the two points. Also depicted in the image is the incapability to model non-linear curves by comparing the average slope (velocity) compared to the actual slope (velocity).

[[File: htmjpg2.jpg|300px]]

==Examples==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:43:07Z

Hmcleod6: /* A Computational Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===A Computational Model===

Below is a visualization of the analytical prediction of the average velocity. As you can see, it takes two points, (a, f(a)) and (b, f(b)), and finds the average between the two points. Also depicted in the image is the incapability to model non-linear curves by comparing the average slope (velocity) compared to the actual slope (velocity).

[[File: htmjpg2.jpg|300px]]

==Examples==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:42:54Z

Hmcleod6: /* A Computational Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===A Computational Model===

Below is a visualization of the analytical prediction of the average velocity. As you can see, it takes two points, (a, f(a)) and (b, f(b)), and finds the average between the two points. Also depicted in the image is the incapability to model non-linear curves by comparing the average slope (velocity) compared to the actual slope (velocity).

[[File: htmjpg2.jpg|150px]]

==Examples==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

File:Htmjpg2.jpg

2015-12-03T17:42:38Z

Hmcleod6:

Analytical Prediction

2015-12-03T17:33:53Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Here, X bar is the arithmetic mean, sigma f x is the sum of all the values, and sigma f is the total number of terms. Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:31:17Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: htmpng1.png|150px]]

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

File:Htmpng1.png

2015-12-03T17:30:50Z

Hmcleod6:

Analytical Prediction

2015-12-03T17:29:31Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: 1.png|150px]]

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:28:22Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

[[File: 1.jpg|150px]]

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:26:11Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:25:55Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px|middle]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:25:03Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|150px]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:24:53Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|250px]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:24:40Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|400px]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:24:13Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|300px|thumb|middle| Where x bar is the average, sigma f x is the sum of all the of the numbers, and sigma f is the total number of terms]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:22:57Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|300px|thumb|left| Where x bar is the average, sigma f x is the sum of all the of the numbers, and sigma f is the total number of terms]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:21:33Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpg|200px|thumb|left|stuff]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:20:41Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpeg|200px|thumb|left|stuff]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T17:19:15Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

[[File: 1.jpeg|200px|thumb|right|you can write]]

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

File:1.jpg

2015-12-03T17:17:55Z

Hmcleod6:

Analytical Prediction

2015-12-03T16:57:16Z

Hmcleod6: /* A Mathematical Model */

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution. However, due to the method of derivation of the velocity, the analytical method is only accurate to a high degree when the force applied to the system is constant. Due to this limitation, the iterative prediction method is much more generally applicable.

===A Mathematical Model===

Unlike the iterative prediction method which is derived directly from the momentum principle, the formula for analytical prediction is based of the formula for the arithmetic mean.

Insert formula here

Since we only need two values of velocity to calculate the average velocity, the formula, for this purpose, can be simplified.

Insert formula here

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T16:48:55Z

Hmcleod6:

Analytical Prediction

2015-12-03T16:43:20Z

Hmcleod6:

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

Analytical prediction uses a mathematical function that can describe the position of or velocity of a system at any given time. In contrast to iterative prediction, this means that there is no need to make multiple calculations at small steps in order to find a solution.

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T16:35:11Z

Hmcleod6:

By Hayden McLeod (hmcleod6)

Short Description of Topic

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Analytical Prediction

2015-12-03T16:33:23Z

Hmcleod6: Created page with "By Hayden McLeod Short Description of Topic ==The Main Idea== State, in your own words, the main idea for this topic Electric Field of Capacitor ===A Mathematical Model===..."

By Hayden McLeod

Short Description of Topic

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===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==

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

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

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

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

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

Main Page

2015-12-03T16:31:32Z

Hmcleod6: /* Momentum */

__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 catagories.

<div class="toccolours mw-collapsible mw-collapsed">
===Interactions===
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
**[[Ball and Spring Model of Matter]]
*[[Detecting Interactions]]
*[[Fundamental Interactions]]
*[[Determinism]]
*[[System & Surroundings]]
*[[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]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
</div>
</div>

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

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

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

===Notable Scientists===
<div class="mw-collapsible-content">
*[[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]]
*[[Erwin Schrödinger]]
*[[Enrico Fermi]]
*[[Robert J. Van de Graaff]]
*[[Charles de Coulomb]]
*[[Hans Christian Ørsted]]
*[[Philo Farnsworth]]
*[[Niels Bohr]]
*[[Georg Ohm]]
*[[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]]
*[[Benjamin Franklin]]
*[[James Chadwick]]
*[[Henry Cavendish]]
*[[Thomas Young]]
*[[James Prescott Joule]]
*[[John Bardeen]]
*[[Leo Baekeland]]
*[[Alhazen]]
*[[Willebrod Snell]]
*[[Johannes Kepler]]
*[[Johann Wilhelm Ritter]]

</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]]
*[[Conductivity]]
*[[Malleability]]
*[[Weight]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Inertia]]
</div>
</div>

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

===Contact Interactions===
<div class="mw-collapsible-content">
* [[Young's Modulus]]
* [[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 a Solid]]
* [[Iterative Prediction of Spring-Mass System]]
</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]]
* [[Momentum Principle]]
* [[Impulse Momentum]]
* [[Curving 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]]
* [[Change in Momentum in Time for Curving Motion]]
</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 ring]]
* [[Rotation]]
* [[Torque]]
* [[Systems with Zero Torque]]
* [[Systems with Nonzero Torque]]
* [[Right Hand Rule]]
* [[Angular Velocity]]
* [[Predicting the Position of a Rotating System]]
* [[Translational Angular Momentum]]
* [[The Angular Momentum Principle]]
* [[Rotational Angular Momentum]]
* [[Total Angular Momentum]]
* [[Gyroscopes]]
* [[Angular Momentum Compared to Linear Momentum]]

</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]]
*[[Work]]
*[[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]]
*[[Air Resistance]]
*[[Electronic Energy Levels]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Specific Heat Capacity]]
*[[Electronic Energy Levels and Photons]]
*[[Energy Density]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Path Independence of Electric Potential]]
</div>
</div>

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

===Collisions===
<div class="mw-collapsible-content">
*[[Collisions]]
*[[Maximally Inelastic Collision]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Frame of Reference]]
*[[Rutherford Experiment and Atomic Collisions]]
</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]]
** [[Charged Cylinder]]
** [[Charge Density]]
**[[A Solid Sphere Charged Throughout Its Volume]]
*[[Electric Potential]]
**[[Potential Difference Path Independence]]
**[[Potential Difference in a Uniform Field]]
**[[Potential Difference of point charge in a non-Uniform Field]]
**[[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]]
*[[Charge Motion in Metals]]
*[[Charge Transfer]]
*[[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 Force]]
*[[Combining Electric and Magnetic Forces]]
**[[Magnetic Torque]]
**[[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]]
**[[Motors and Generators]]
**[[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]]
*[[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]]
*[[AC vs DC]]
*[[Charge in a RC Circuit]]
*[[Current in a RC circuit]]
*[[Circular Loop of Wire]]
*[[Current in a RL Circuit]]
*[[RL Circuit]]
*[[LC Circuit]]
*[[Surface Charge Distributions]]
*[[Feedback]]
*[[Transformers (Circuits)]]
*[[Resistors and Conductivity]]
*[[Semiconductor Devices]]
</div>
</div>

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

===Maxwell's Equations===
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
**[[Electric Fields]]
**[[Magnetic Fields]]
*[[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]]
*[[Faraday's Law]]
**[[Curly Electric Fields]]
**[[Inductance]]
***[[Transformers from a physics standpoint]]
***[[Energy Density]]
**[[Lenz's Law]]
***[[Lenz Effect and the Jumping Ring]]
**[[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]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

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

===Waves===
<div class="mw-collapsible-content">
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Waves]]
*[[Electromagnetic Spectrum]]
*[[Color Light Wave]]
*[[Mechanical Waves]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

===Real Life Applications of Electromagnetic Principles===
<div class="mw-collapsible-content">
*[[Electromagnetic Junkyard Cranes]]
*[[Maglev Trains]]
*[[Spark Plugs]]
*[[Metal Detectors]]
*[[The Microwave]]
*[[Speakers]]
</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]]
* An overview of [[VPython]], [http://www.physicsbook.gatech.edu/VPython_basics beginner guide to VPython]