Physics Book - User contributions [en]

Moment of Inertia for a cylinder

2015-12-05T16:58:27Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

As can be seen here:
[[File:axis end rod.png|200px|center]]
==Examples==

Calculate the kinetic energy of a rod rotating about its end given that the rod has mass 200 kg, rotational velocity of 12 m/s, and length 15m, and radius 0.5m:

First, the equation that equals kinetic energy in rotational motion is <math> KE = \frac{1}{2}*I*ω^2 </math> where <math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

Thus, finding I: <math> I = \frac{1}{4}*200*0.5^2 + \frac{1}{3}*200*10^2 </math>

<math> I = 6679.166 kg*m^2 </math>

Thus <math> KE = \frac{1}{2}*6679.166 *kg*m^2*(12 \frac{m}{s})^2 </math>

<math> KE = 480900 J </math>

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

Moments of Inertia are very important in industrial processes, especially for engines. Think of a wind turbine. That is essentially the third equation above, and if an engineer wanted to figure out how much force would be needed to slow the blade, that is one of the components in that equation. But also, due to the torque applied to the blade, there would need to be a slow negative acceleration, so as to not break the wind turbine.

== See also ==

You can find more information in the text book about moments of inertia for different sized objects.

===External links===

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

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

[[Category:Angular Momentum]]

Moment of Inertia for a cylinder

2015-12-05T16:57:15Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

As can be seen here:
[[File:axis end rod.png|200px|center]]
==Examples==

Calculate the kinetic energy of a rod rotating about its end given that the rod has mass 200 kg, rotational velocity of 12 m/s, and length 15m, and radius 0.5m:

First, the equation that equals kinetic energy in rotational motion is <math> KE = \frac{1}{2}*I*ω^2 </math> where <math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

Thus, finding I: <math> I = \frac{1}{4}*200*0.5^2 + \frac{1}{3}*200*10^2 </math>

<math> I = 6679.166 kg*m^2 </math>

Thus <math> KE = \frac{1}{2}*6679.166 kg*m^2*(12 \frac{m}{s})^2 </math>

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

Moments of Inertia are very important in industrial processes, especially for engines. Think of a wind turbine. That is essentially the third equation above, and if an engineer wanted to figure out how much force would be needed to slow the blade, that is one of the components in that equation. But also, due to the torque applied to the blade, there would need to be a slow negative acceleration, so as to not break the wind turbine.

== See also ==

You can find more information in the text book about moments of inertia for different sized objects.

===External links===

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

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

[[Category:Angular Momentum]]

Moment of Inertia for a cylinder

2015-12-05T16:56:53Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

As can be seen here:
[[File:axis end rod.png|200px|center]]
==Examples==

Calculate the kinetic energy of a rod rotating about its end given that the rod has mass 200 kg, rotational velocity of 12 m/s, and length 15m, and radius 0.5m:

First, the equation that equals kinetic energy in rotational motion is <math> KE = \frac{1}{2}*I*ω^2 </math> where <math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

Thus, finding I: <math> I = \frac{1}{4}*200*0.5^2 + \frac{1}{3}*200*10^2 </math>

<math> I = 6679.166 kg*m^2 </math>

Thus <math> KE = \frac{1}{2}*6679.166 kg*m^2*12 \frac{m}{s}^2 </math>

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

Moments of Inertia are very important in industrial processes, especially for engines. Think of a wind turbine. That is essentially the third equation above, and if an engineer wanted to figure out how much force would be needed to slow the blade, that is one of the components in that equation. But also, due to the torque applied to the blade, there would need to be a slow negative acceleration, so as to not break the wind turbine.

== See also ==

You can find more information in the text book about moments of inertia for different sized objects.

===External links===

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

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

[[Category:Angular Momentum]]

Moment of Inertia for a cylinder

2015-12-05T16:52:51Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

As can be seen here:
[[File:axis end rod.png|200px|center]]
==Examples==

Calculate the kinetic energy of a rod rotating about its end given that the rod has mass 200 kg, rotational velocity of 12 m/s, and length 15m, and radius 0.5m:

First, the equation that equals kinetic energy in rotational motion is <math> KE = \frac{1}{2}*I*ω^2 </math>

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

Moments of Inertia are very important in industrial processes, especially for engines. Think of a wind turbine. That is essentially the third equation above, and if an engineer wanted to figure out how much force would be needed to slow the blade, that is one of the components in that equation. But also, due to the torque applied to the blade, there would need to be a slow negative acceleration, so as to not break the wind turbine.

== See also ==

You can find more information in the text book about moments of inertia for different sized objects.

===External links===

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

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

[[Category:Angular Momentum]]

Moment of Inertia for a cylinder

2015-12-05T16:51:56Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

As can be seen here:
[[File:axis end rod.png|200px|center]]
==Examples==

Calculate the kinetic energy of a rod rotating about its end given that the rod has mass 200 kg, rotational velocity of 12 m/s, and length 15m, and radius 0.5m:

First, the equation that equals kinetic energy in rotational motion is <math> KE = \frac{1}{2}*I*&#969 </math>

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

Moments of Inertia are very important in industrial processes, especially for engines. Think of a wind turbine. That is essentially the third equation above, and if an engineer wanted to figure out how much force would be needed to slow the blade, that is one of the components in that equation. But also, due to the torque applied to the blade, there would need to be a slow negative acceleration, so as to not break the wind turbine.

== See also ==

You can find more information in the text book about moments of inertia for different sized objects.

===External links===

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

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

[[Category:Angular Momentum]]

Moment of Inertia for a cylinder

2015-12-05T16:46:45Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

As can be seen here:
[[File:axis end rod.png|200px|center]]
==Examples==

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

Moments of Inertia are very important in industrial processes, especially for engines. Think of a wind turbine. That is essentially the third equation above, and if an engineer wanted to figure out how much force would be needed to slow the blade, that is one of the components in that equation. But also, due to the torque applied to the blade, there would need to be a slow negative acceleration, so as to not break the wind turbine.

== See also ==

You can find more information in the text book about moments of inertia for different sized objects.

===External links===

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

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

[[Category:Angular Momentum]]

Moment of Inertia for a cylinder

2015-12-05T16:44:41Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

As can be seen here:
[[File:axis end rod.png|200px|center]]
==Examples==

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

Moments of Inertia are very important in industrial processes, especially for engines. Think of a wind turbine. That is essentially the third equation above, and if an engineer wanted to figure out how much force would be needed to slow the blade, that is one of the components in that equation.

==History==

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

== See also ==

You can find more information in the text book about moments of inertia for different sized objects.

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

===External links===

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

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

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

Moment of Inertia for a cylinder

2015-12-05T16:40:21Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

As can be seen here:
[[File:axis end rod.png|200px|center]]
==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===

Internet resources on this topic

==References==

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

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

Main Page

2015-12-05T16:39:25Z

Jcorelli3:

__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]]
*[[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]]
*[[Electric Polarization]]
*[[Perpetual Freefall (Orbit)]]
*[[2-Dimensional Motion]]
*[[Center of Mass]]
*[[Reaction Time]]
*[[Time Dilation]]
</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 Multithreading]]
</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]]
</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]]
*[[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]]
*[[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]]
</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]]
*[[Non-Newtonian Fluids]]
*[[Ferrofluids]]
*[[Color]]
*[[Temperature]]
</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]]
* [[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]]
* [[Change in Momentum in Time for Curving Motion]]
* [[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 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]]

</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]]
**[[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]]
*[[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]]
</div>
</div>

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

===Collisions===
<div class="mw-collapsible-content">
*[[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.
*[[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.
*[[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.
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Frame of Reference]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
*[[testing123]]
</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]]
*[[Superposition Principle]]
*[[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 Torque]]
**[[Magnetic Force]]
**[[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]]
**[[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]]
*[[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]]
***[[Examples of Flux Through Surfaces and Objects]]
**[[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 (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]]
</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">
*[[Bragg's Law]]
*[[Multisource Interference: Diffraction]]
*[[Standing waves]]
*[[Gravitational waves]]
*[[Plasma waves]]
*[[Wave-Particle Duality]]
*[[Electromagnetic Spectrum]]
*[[Color Light Wave]]
*[[Mechanical Waves]]
*[[Pendulum Motion]]
*[[Transverse and Longitudinal Waves]]
*[[Planck's Relation]]
</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]]
*[[Speakers]]
*[[Radios]]
*[[Ampullae of Lorenzini]]
*[[Electrocytes]]
*[[Generator]]
*[[Measuring Water Level]]
</div>
</div>

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

===Optics===
<div class="mw-collapsible-content">
*[[Mirrors]]
*[[Refraction]]
*[[Quantum Properties of Light]]
</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

File:Axis end rod.png

2015-12-01T00:18:35Z

Jcorelli3:

Moment of Inertia for a cylinder

2015-12-01T00:18:21Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>
As can be seen here:
[[File:axis end rod.png|200px|center]]
==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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-12-01T00:10:20Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

If the axis of rotation has the same direction as the second equation, that is perpendicular to the length, but is at the end of the rod, just touching one of the circular caps, then the equation would be:
<math> I = \frac{1}{4}*M*R^2 + \frac{1}{3}*M*L^2 </math>

==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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-12-01T00:07:22Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A Brief Overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

==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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-12-01T00:07:05Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==A brief overview==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===Governing Equations===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

==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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-12-01T00:06:10Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==The Main Idea==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===A Mathematical Model===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|200px|center]]

==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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-12-01T00:05:12Z

Jcorelli3:

File:Rod perp axis.png

2015-12-01T00:04:05Z

Jcorelli3:

Moment of Inertia for a cylinder

2015-12-01T00:03:44Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==The Main Idea==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===A Mathematical Model===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

As can be seen here:

[[File:rod perp axis.png|300px|center]]

==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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-11-30T23:58:59Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a cylinder or rod.

Written by Jack Corelli

==The Main Idea==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===A Mathematical Model===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here:

[[File:cylinder axis.png|300px|center]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

==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===

Internet resources on this topic

==References==

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

Moment of Inertia for a ring

2015-11-30T23:57:42Z

Jcorelli3: Jcorelli3 moved page Moment of Inertia for a ring to Moment of Inertia for a cylinder

#REDIRECT [[Moment of Inertia for a cylinder]]

Moment of Inertia for a cylinder

2015-11-30T23:57:42Z

Jcorelli3: Jcorelli3 moved page Moment of Inertia for a ring to Moment of Inertia for a cylinder

This page discusses the moment of inertia specifically in the case of a ring

Written by Jack Corelli

==The Main Idea==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===A Mathematical Model===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.

As can be seen here: [[File:cylinder axis.png]]

If the axis of rotation is no longer the center of the cylinder or rod, the equations for moment of inertia change distinctly.
At the center of a rod, with the axis of rotation perpendicular to the length:

<math> I = \frac{1}{4}*M*R^2 + \frac{1}{12}*M*L^2 </math>

===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===

Internet resources on this topic

==References==

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

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

Main Page

2015-11-30T23:56:47Z

Jcorelli3:

Main Page

2015-11-30T23:56:07Z

Jcorelli3:

Moment of Inertia for a cylinder

2015-11-30T23:53:48Z

Jcorelli3:

Moment of Inertia for a cylinder

2015-11-30T23:39:07Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a ring

Written by Jack Corelli

==The Main Idea==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===A Mathematical Model===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis.
As can be seen here ->[[File:cylinder axis.png]]

===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===

Internet resources on this topic

==References==

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

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

File:Cylinder axis.png

2015-11-30T23:38:30Z

Jcorelli3:

Moment of Inertia for a cylinder

2015-11-30T23:37:30Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a ring

Written by Jack Corelli

==The Main Idea==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===A Mathematical Model===

In its simplest form, the moment of inertia can be found for a simple, constant density and shape rod by the equation:

<math> I = \frac{1}{2}*M*R^2 </math>
Where I is the moment of inertia, M is the mass of the object being rotated and R is the radius of the rod.
This describes the moment of inertia calculated when a rod is spun about its center axis. As can be seen here ->[[File:cylinder axis.png]]

===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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-11-30T23:19:57Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a ring

Written by Jack Corelli

==The Main Idea==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===A Mathematical Model===
<math> I = \frac{1}{2}*M*R </math>

===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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-11-30T23:04:57Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a ring

Written by Jack Corelli

==The Main Idea==
See [[The Moments of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===A Mathematical Model===

===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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-11-30T23:04:03Z

Jcorelli3:

This page discusses the moment of inertia specifically in the case of a ring

Written by Jack Corelli

==The Main Idea==
See [[Moment of Inertia]] for a more general explanation of moments of inertia.

The moment of inertia of an object relates the mass of the object, the distance between the center of mass and the shape of rotation. In a ring, or uniform loop, the center of mass is exactly at the center of the ring, and the moment of inertia can be found by approximating the exterior ring as a single line, akin to a circle.

===A Mathematical Model===

===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===

Internet resources on this topic

==References==

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

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

Moment of Inertia for a cylinder

2015-11-30T22:59:20Z

Jcorelli3: Created page with "This page discusses the moment of inertia specifically in the case of a ring Written by Jack Corelli ==The Main Idea== See Moment of Inertia for a more general explanation o..."

This page discusses the moment of inertia specifically in the case of a ring

Written by Jack Corelli

==The Main Idea==
See Moment of Inertia for a more general explanation of moments of inertia.

===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===

Internet resources on this topic

==References==

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

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

Main Page

2015-11-30T22:57:51Z

Jcorelli3:

The Moments of Inertia

2015-11-30T22:27:24Z

Jcorelli3:

This page discusses the idea of inertia as it relates to angular motion.

Written by Jack Corelli

(claimed by sans47)

==The Main Idea==

Inertia of a solid mass is a simple concept. As described by Newton's laws, objects tend to keep doing what they are currently doing, ie. they resist change. Inertia is a 'measure' of this. A larger, more massive object is said to have more inertia, as it would resist change more than a smaller, less massive object. This is a simple concept to apply in 1d motion. For a constant force, increasing mass lowers acceleration, and vice versa. However, the same equation can still apply in 2d motion, it is however split into its component x and y in order to simplify calculations.

In 2d rotational motion, a new description is needed to describe an objects inertia, and this is aptly named a 'moment of inertia'. Simply put, moments of inertia refer to an objects resistance to change in 2d rotational motion. In other words, when talking about moving in a straight line, the governing equation F = m*A is adequate to describe the relationship between mass and acceleration. In rotational motion, the mass of an object is not adequate in describing how the shape, distribution of mass, and total mass impact the acceleration of an object. Thus, a moment of inertia is needed to fully describe this relationship. In rotational motion, the moment of inertia of an object relates three things:
1. The mass of the object
2. The distance between the center of mass and the axis of rotation
3. The shape of the object being rotated

===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===

Internet resources on this topic

==References==

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

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

The Moments of Inertia

2015-11-30T22:21:17Z

Jcorelli3:

This page discusses the idea of inertia as it relates to angular motion
Written by Jack Corelli
(claimed by sans47)
==The Main Idea==

Inertia of a solid mass is a simple concept. As described by Newton's laws, objects tend to keep doing what they are currently doing, ie. they resist change. Inertia is a 'measure' of this. A larger, more massive object is said to have more inertia, as it would resist change more than a smaller, less massive object. This is a simple concept to apply in 1d motion. For a constant force, increasing mass lowers acceleration, and vice versa. However, the same equation can still apply in 2d motion, it is however split into its component x and y in order to simplify calculations.

In 2d rotational motion, a new description is needed to describe an objects inertia, and this is aptly named a 'moment of inertia'. Simply put, moments of inertia refer to an objects resistance to change in 2d rotational motion. In other words, when talking about moving in a straight line, the governing equation F = m*A is adequate to describe the relationship between mass and acceleration. In rotational motion, the mass of an object is not adequate in describing how the shape, distribution of mass, and total mass impact the acceleration of an object. Thus, a moment of inertia is needed to fully describe this relationship. In rotational motion, the moment of inertia of an object relates three things:
1. The mass of the object
2. The distance between the center of mass and the axis of rotation
3. The shape of the object being rotated

===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===

Internet resources on this topic

==References==

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

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