Rotational energy or angular kinetic energy is

kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

due to the

rotation Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersect ...

of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's

axis of rotation Rotation or rotational/rotary motion is the circular movement of an object around a central line, known as an ''axis of rotation''. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersect ...

, the following dependence on the object's moment of inertia is observed:

E_\text = \tfrac I \omega^2

where The

mechanical work In science, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...

required for or 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 In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weight function, weighted relative position (vector), position of the d ...

. Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion:

E_\text = \tfrac m v^2

In the rotating system, the moment of inertia, ''I'', takes the role of the mass, ''m'', and the

angular velocity In physics, angular velocity (symbol or \vec, the lowercase Greek letter omega), also known as the angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i ...

\omega

, takes the role of the linear velocity, ''v''. The rotational energy of a

rolling Rolling is a Motion (physics)#Types of motion, type of motion that combines rotation (commonly, of an Axial symmetry, axially symmetric object) and Translation (geometry), translation of that object with respect to a surface (either one or the ot ...

cylinder varies from one half of the translational energy (if it is massive) to the same as the translational energy (if it is hollow). An example is the calculation of the rotational kinetic energy of the

Earth Earth is the third planet from the Sun and the only astronomical object known to Planetary habitability, harbor life. This is enabled by Earth being an ocean world, the only one in the Solar System sustaining liquid surface water. Almost all ...

. As the Earth has a sidereal rotation period of 23.93 hours, it has an angular velocity of . The Earth has a moment of inertia, ''I'' = .Moment of inertia--Earth
Wolfram Therefore, it has a rotational kinetic energy of . Part of the Earth's rotational energy can also 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 Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of Momentum, linear momentum. It is an important physical quantity because it is a Conservation law, conserved quantity – the total ang ...

, this process transfers angular momentum to the Moon's

orbit In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an ...

al motion, increasing its distance from Earth and its orbital period (see

tidal locking Tidal locking between a pair of co-orbiting astronomical body, astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where ...

for a more detailed explanation of this process).

Notes

References

* Resnick, R. and Halliday, D. (1966) ''PHYSICS'', Section 12-5, John Wiley & Sons Inc. {{DEFAULTSORT:Rotational Energy Forms of energy Rotation

See also

Notes

References