- Rotational energy
The

**rotational energy**or**angular kinetic energy**is thekinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately in an object'scentre of mass frame, one gets the following dependence on the object'smoment of inertia ::$E\_\{rotation\}\; =\; frac\{1\}\{2\}\; I\; omega^2$where: $omega$ is the

angular velocity : $I$ is themoment of inertia .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 frequency.Note the close relationship between the results for linear (or translational) and rotational motion; the formula for the :$E\_\{translational\}\; =\; frac\{1\}\{2\}\; m\; v^2$

In the rotating system, the

moment of inertia , "I", takes the role of the mass, "m", and theangular velocity , $omega$, 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^{-1}. Assuming that the Earth is perfectly spherical and uniform in mass density, it has a moment of inertia, I = 9.72×10^{37}kg·m^{2}. Therefore, it has a rotational kinetic energy of 2.58×10^{29}J.Part of it can be tapped using

tidal power . This creates additional friction of the two global tidal waves, infinitesimally slowing down Earth's angular velocity "ω". Due to conservation ofangular momentum this process transfers angular momentum to theMoon 'sorbit al motion, increasing its distance from Earth and its orbital period (seetidal locking for a more detailed explanation of this process).**ee also***

Flywheel

*Rigid rotor

*Rotational spectroscopy

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