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 acc ...
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, the following dependence on the object's
moment of inertia is observed:
:
where
:
is the
angular velocity
:
is the
moment of inertia around the axis of rotation
:
is the
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 acc ...
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.
Note the close relationship between the result for rotational energy and the energy held by linear (or translational) motion:
:
In the rotating system, the
moment of inertia, ''I'', takes the role of the mass, ''m'', and the
angular velocity,
, 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 infin ...
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 surfa ...
. 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. Ti ...
. 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 syste ...
, 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 ...
for a more detailed explanation of this process).
See also
*Flywheel
A flywheel is a mechanical device which uses the conservation of angular momentum to store rotational energy; a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed. In particular, as ...
*List of energy storage projects
This is a list of energy storage power plants worldwide, other than pumped hydro storage.
Many individual energy storage plants augment electrical grids by capturing excess electrical energy during periods of low demand and storing it in o ...
*Rigid rotor
In rotordynamics, the rigid rotor is a mechanical model of Rotation, rotating systems. An arbitrary rigid rotor is a 3-dimensional Rigid body, rigid object, such as a top. To orient such an object in space requires three angles, known as Euler an ...
*Rotational spectroscopy
Rotational spectroscopy is concerned with the measurement of the energies of transitions between quantized rotational states of molecules in the gas phase. The spectra of polar molecules can be measured in absorption or emission by microwave ...
Notes
References
* Resnick, R. and Halliday, D. (1966) ''PHYSICS'', Section 12-5, John Wiley & Sons Inc.
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Forms of energy
Rotation