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{{about|the rotation of an object around a single axis (a one-dimensional rotation)|the kinetic energy of an object that rotates in three dimensions|rigid rotor}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


The '''rotational energy''' or '''angular kinetic energy''' is the [[kinetic energy]] due to the rotation of an object and is part of its [[Kinetic energy#Rotation in systems|total kinetic energy]]. Looking at rotational energy separately around an object's [[axis of rotation]], one gets the following dependence on the object's [[moment of inertia]]:
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


:<math>E_\mathrm{rotational} = \frac{1}{2} I \omega^2 </math>
Registered users will be able to choose between the following three rendering modes:  
where
: <math> \omega \ </math> is the [[angular velocity]]
: <math> I \ </math> is the [[moment of inertia]] around the axis of rotation
: <math> E \ </math> is the [[kinetic energy]]
The [[mechanical work]] required for / applied during rotation is the torque times the rotation angle. The instantaneous [[power (physics)|power]] of an angularly accelerating body is the torque times the angular velocity. For free-floating (unattached) objects, the axis of rotation is commonly around its [[center of mass]].


Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion:
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


:<math>E_\mathrm{translational} = \frac{1}{2} m v^2 </math>
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


In the rotating system, the [[moment of inertia]], ''I'', takes the role of the mass, ''m'', and the [[angular velocity]], <math> \omega </math>, takes the role of the linear velocity, ''v''. The ''rotational energy'' of a [[wheel|rolling]] [[cylinder (geometry)|cylinder]] varies from one half of the translational energy (if it is massive) to the same as the translational energy (if it is hollow).
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


As an example, let us calculate the rotational kinetic energy of the Earth. As the Earth has a period of about 23.93 hours, it has an angular velocity of 7.29×10<sup>−5</sup> rad/s. The Earth has a moment of inertia, I = 8.04×10<sup>37</sup> kg·m<sup>2</sup>.<ref>[http://scienceworld.wolfram.com/physics/MomentofInertiaEarth.html Moment of inertia--Earth], Wolfram</ref> Therefore, it has a rotational kinetic energy of 2.138×10<sup>29</sup> J.
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


Part of it can be tapped using [[tidal power]]. Additional friction of the two global tidal waves creates energy in a physical manner, infinitesimally slowing down Earth's angular velocity ''ω''. Due to the [[Angular momentum#Conservation of angular momentum|conservation]] of [[angular momentum]], this process transfers angular momentum to the [[Moon]]'s [[orbit]]al motion, increasing its distance from Earth and its orbital period (see [[tidal locking]] for a more detailed explanation of this process).
==Demos==


==See also==
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


*[[Flywheel]]
*[[List of energy storage projects]]
*[[Rigid rotor]]
*[[Rotational spectroscopy]]


==References==
* accessibility:
{{reflist}}
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
{{Footer energy}}
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


{{DEFAULTSORT:Rotational Energy}}
==Test pages ==
[[Category:Forms of energy]]
 
[[Category:Rotation]]
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]
 
*[[Inputtypes|Inputtypes (private Wikis only)]]
*[[Url2Image|Url2Image (private Wikis only)]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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