Rotational energy or angular kinetic energy is

kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acce ...

due to the

rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...

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

axis of rotation Rotation around a fixed axis is a special case of rotational motion. The fixed- axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's r ...

, the following dependence on the object's

moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular accele ...

is observed: :

E_\mathrm = \tfrac I \omega^2

where :

\omega \

is the

angular velocity In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object ...

I \

is the

around the axis of rotation :

E \

is the

The

mechanical work In physics, 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 Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...

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 balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...

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

E_\mathrm = \tfrac m v^2

In the rotating system, the

, ''I'', takes the role of the mass, ''m'', and the

\omega

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

rolling Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact ...

cylinder A cylinder (from ) has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an ...

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 harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's sur ...

. As the Earth has a

sidereal rotation period Sidereal time (as a unit also sidereal day or sidereal rotation period) (sidereal ) is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coor ...

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 Tidal power or tidal energy is harnessed by converting energy from tides into useful forms of power, mainly electricity using various methods. Although not yet widely used, tidal energy has the potential for future electricity generation. ...

. 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 In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed sy ...

, this process transfers angular momentum to the Moon's

orbit In celestial mechanics, an orbit 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 object or position in space such as ...

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

tidal locking Tidal locking between a pair of co- orbiting 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 a tidally locked b ...

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