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The rotational energy or angular kinetic energy is the kinetic energy due to the rotation of an object and is part of its 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:

E_{r o t a t i o n a l} = \frac{1}{2} I ω^{2}

where

ω

is the angular velocity

I

is the moment of inertia around the axis of rotation

E

is the kinetic energy

The mechanical work required for / applied during rotation is the torque times the rotation angle. The instantaneous 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:

E_{t r a n s l a t i o n a l} = \frac{1}{2} m v^{2}

In the rotating system, the moment of inertia, I, takes the role of the mass, m, and the angular velocity, $ω$ , takes the role of the linear velocity, v. The rotational energy of a rolling cylinder varies from one half of the translational energy (if it is massive) to the same as the translational energy (if it is hollow).

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 7.29×10⁻⁵ rad/s. The Earth has a moment of inertia, I = 8.04×10³⁷ kg·m².^[1] Therefore, it has a rotational kinetic energy of 2.138×10²⁹ J.

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 conservation of angular momentum, this process transfers angular momentum to the Moon's orbital motion, increasing its distance from Earth and its orbital period (see tidal locking for a more detailed explanation of this process).

References

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↑ Moment of inertia--Earth, Wolfram

[1] Moment of inertia--Earth, Wolfram

[1]

@@ Line 1: / Line 1: @@
-{{Infobox number
+{{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}}
-| number = 90
-| divisor = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
-| lang1 = [[Hebrew numerals|Hebrew]]
-| lang1 symbol = <span style="font-size:150%;">צ</span> (Tzadi)
-}}
-'''90''' ('''ninety''') is the [[natural number]] preceded by [[89 (number)|89]] and followed by [[91 (number)|91]].
-{{Wiktionary|ninety}}
+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]]:
-[[Image:I-90.svg|100px|thumb|[[Interstate 90]] is a freeway that runs from [[Washington (state)|Washington]] to [[Massachusetts]].]]
+:<math>E_\mathrm{rotational} = \frac{1}{2} I \omega^2 </math>
+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]].
-== In mathematics ==
+Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion:
-*Because 90 is the sum of its [[unitary divisor]]s (excluding itself), it is a [[unitary perfect number]], and because it is equal to the sum of a subset of its divisors, it is a [[semiperfect number]].  90 is a [[pronic number]].  But it is also a [[nontotient]].  It is a [[Perrin number]], preceded in the sequence by 39, 51, 68.
-*In normal space, the interior angles of a square measure 90 degrees each. Also, in a right triangle, the angle opposing the hypotenuse measures 90 degrees, with the other two angles adding up to 90 for a total of [[180 (number)|180]] degrees.<ref>[http://www.sparknotes.com/testprep/books/newsat/chapter20section4.rhtml http://www.sparknotes.com/testprep/books/newsat/chapter20section4.rhtml]</ref> Thus, an angle measuring 90 degrees is called a right angle.<ref>Friedman, Erich. [http://www.stetson.edu/~efriedma/numbers.html What's Special About This Number?]</ref>
-*90 is divisible by the sum of its base 10 digits, thus it is a [[Harshad number]].
-== In science ==
+:<math>E_\mathrm{translational} = \frac{1}{2} m v^2 </math>
-*Ninety is the atomic number of [[thorium]], an [[actinide]]. As an atomic weight, 90 identifies an [[isotope]] of [[strontium]], a by-product of nuclear reactions including fallout. It contaminates [[milk]].
+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).
-*The latitude of the [[North Pole]] and the [[South Pole]] are 90 degrees.
-==In sports==
+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.
-* [[Nike Total 90]] Apparel is a brand name of football apparel and football equipment from equipment bags to [[goalkeeper gloves]]
-* [[Major League baseball]] [[base (baseball)|base]]s are {{convert|90|ft}} away in distance
-* The car number most associated with former [[NASCAR]] team owner [[Junie Donlavey]]
-* The number of minutes in a [[football (soccer)]] match.
-* NFL: [[New York Jets]] [[Dennis Byrd]]'s #90 is retired
-{{Portal|Mathematics}}
+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).
+==See also==
+*[[Flywheel]]
+*[[List of energy storage projects]]
+*[[Rigid rotor]]
+*[[Rotational spectroscopy]]
 ==References==
-<references />
+{{reflist}}
-{{Integers|zero}}
+{{Footer energy}}
-[[Category:Integers]]
+{{DEFAULTSORT:Rotational Energy}}
+[[Category:Forms of energy]]
+[[Category:Rotation]]

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