# Rotational energy

Rotating objects contain kinetic energy. An object's rotational energy or angular kinetic energy is part of its total kinetic energy. Looking at rotational energy separately in an object's centre of mass frame, one gets the following dependence on the object's moment of inertia:

[itex]E_{rotation} = \frac{1}{2} I \omega^2 [itex]

In SI units, rotational energy is measured in joules.

For example, Earth has a large amount of rotational energy: at its equator, it moves at the speed of ~450 m/s, hence 100 kJ/kg. On average, if the Earth were homogeneous, 40% of that, hence 40 kJ/kg. Since the density is larger in the centre, the average specific rotational energy is a little less: roughly 33 kJ/kg, i.e. Template:Sn J (Template:Sn Mt TNT). Compare with the kinetic energy of the orbital motion around the Sun: 450 MJ/kg.

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 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).

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