Rotational energy
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rotational energy
(rō′tā·shən·əl ′en·ər·jē)
(mechanics) The kinetic energy of a rigid body due to rotation.
(physical chemistry) For a diatomic molecule, the difference between the energy of the actual molecule and that of an idealized molecule which is obtained by the hypothetical process of gradually stopping the relative rotation of the nuclei without placing any new constraint on their vibration, or on motions of electrons.
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rotational energy
Energy stored in a spinning system. Rotational energy depends on both the moment of inertia and angular velocity, and is given by: rotational energy = 1/2Iw2, where I = the moment of inertia of the object about an axis through the centre of gravity of the system, and w = the angular velocity of the system about an axis through the centre of gravity of the system.
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Rotational energy
This article is about the rotation of an object around a single axis (a one-dimensional rotation). See rigid rotor for the kinetic energy of an object that rotates in three dimensions.
The rotational energy or angular kinetic energy is the kinetic energy 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, one gets the following dependence on the object's moment of inertia:
where
is the Angular velocity
is the moment of inertia around the axis of rotation.
is the kinetic energy.
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 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 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. The Earth has a moment of inertia, I = 8.04×1037 kg·m2.[1] Therefore, it has a rotational kinetic energy of 2.138×1029 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 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).
See also
References
- ^ Moment of inertia--Earth, Wolfram
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McGraw-Hill Science & Technology Dictionary
McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved.
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Oxford Dictionary of Sports Science & Medicine
The Oxford Dictionary of Sports Science & Medicine. Copyright © Michael Kent 1998, 2006, 2007. All rights reserved.
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