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1.the act of rotating as if on an axis"the rotation of the dancer kept time with the music"

2.a planned recurrent sequence (of crops or personnel etc.)"crop rotation makes a balanced demand on the fertility of the soil" "the manager had only four starting pitchers in his rotation"

3.a single complete turn (axial or orbital)"the plane made three rotations before it crashed" "the revolution of the earth about the sun takes one year"

4.(mathematics) a transformation in which the coordinate axes are rotated by a fixed angle about the origin

1.(MeSH)Motion of an object in which either one or more points on a line are fixed. It is also the motion of a particle about a fixed point. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)

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RotationRo*ta"tion (?), n. [L. rotatio: cf. F. rotation.]

1. The act of turning, as a wheel or a solid body on its axis, as distinguished from the progressive motion of a revolving round another body or a distant point; thus, the daily turning of the earth on its axis is a rotation; its annual motion round the sun is a revolution.

2. Any return or succesion in a series.

Moment of rotation. See Moment of inertia, under Moment. -- Rotation in office, the practice of changing public officers at frequent intervals by discharges and substitutions. -- Rotation of crops, the practices of cultivating an orderly succession of different crops on the same land.

RotationRo*ta"tion (?), a. Pertaining to, or resulting from, rotation; of the nature of, or characterized by, rotation; as, rotational velocity.

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definition of Wikipedia

cycle, frequency, gyration, revolution, rotary motion, rotate, spin, spinning, turning, whirlpool

Optical Rotation • Rotation failure of of caecum and colon • Rotation incomplete of caecum and colon • Rotation insufficient of caecum and colon • Rotation of tooth or teeth • axial rotation • axis of rotation • clockwise rotation • counterclockwise rotation • crop rotation • in rotation • optical rotation • orbital rotation • specific rotation • speed of rotation

Absolute rotation • Ad rotation • Anticyclonic rotation • Atlanta Braves 1990s pitching rotation • Axis of rotation • Backup rotation scheme • Bartels' Rotation Number • Bit rotation • Bitwise rotation • Bond rotation barrier • Carrington rotation • Common Rotation • Continuous sub-grain rotation type dynamic recrystallization • Crop rotation • Cullars Rotation • Cyclonic rotation • Differential rotation • Dipole rotation • Earth's rotation • Euler's rotation theorem • Extended rotation forest • External rotation • Faraday Rotation • Food rotation system • Galaxy rotation curve • Givens rotation • Heavy Rotation • Heavy Rotation (Deceptikonz album) • Heavy Rotation Tour • Improper rotation • Instant centre of rotation • Internal rotation • International Earth Rotation and Reference Systems Service • Irrational rotation • Job rotation • Laboratory rotation • Left rotation • Magneto-optical rotation • Magnetooptical rotation • Mental rotation • Music rotation • Old Rotation • Optical rotation • Optimal rotation age • Pingu episodes removed from rotation • Plane of rotation • Pokémon episodes removed from rotation • Proper rotation • Quaternions and spatial rotation • Recurrent rotation • Reverse rotation effect • Robson Rotation • Rotation (album) • Rotation (disambiguation) • Rotation (film) • Rotation (mathematics) • Rotation (music) • Rotation (pool) • Rotation Babelsberg • Rotation around a fixed axis • Rotation estimation • Rotation flap • Rotation group • Rotation in office • Rotation method • Rotation number • Rotation of ammunition • Rotation operator • Rotation period • Rotation symmetry • Rotation system • Rotation-reflection axis • Sector rotation • Short rotation coppice • Short rotation forestry • Solar rotation • Soul Rotation • Specific rotation • Squad rotation system • Stellar rotation • Stock rotation • Synchronous rotation • Tabor Rotation • Terrell rotation • Three-field crop rotation • Tire rotation • Tree rotation • Varimax rotation • Wick rotation

mouvement d'un corps autour d'un axe (fr)[ClasseParExt.]

action de (ou fait d'être) (fr)[Classe...]

rotation (fr)[Thème]

tourner autour d'un axe (fr)[Thème]

factotum[Domaine]

BodyMotion[Domaine]

move - rotary motion, rotation - gyration, revolution, rotation, turning - circumvolution - revolutionary, rotary, rotatory[Dérivé]

circumvolve, rotate[Domaine]

go around, revolve, rotate[Cause]

motility, motion, move, movement[Hyper.]

go around, revolve, rotate - circumvolve[Dérivé]

rotation (n.)↕

replacement[Classe]

succession de choses (fr)[Classe]

cycle[Classe]

temporal arrangement, temporal order - string, train - grow - serve - alternate[Hyper.]

sequence - sequence - come after, follow, succeed - consecutive, sequent, sequential, serial, successive - rotation[Dérivé]

chronological sequence, chronological succession, sequence, succession, successiveness[Hyper.]

rotate - tourner (fr) - faire à tour de rôle (fr)[Dérivé]

rotation (n.)↕

ligne courbe (fr)[Classe]

ligne (géométrie) (fr)[Classe]

cycle[Classe]

fait et circonstance (fr)[Classe...]

intervalle borné de temps, caractérisé par un phénomène (fr)[Classe...]

mouvement tournant (fr)[Classe]

turn; rotate; revolve; spin; spin around; whirl; reel; gyrate[ClasseHyper.]

qui concerne la rotation (fr)[Classe]

qui tourne (fr)[Classe]

ligne courbe (fr)[Thème]

tourner autour d'un axe (fr)[Thème]

(alien; extraterrestrial; extraterrestrial being), (star)[Thème]

(celestial body; heavenly body)[Thème]

mouvement dans l'espace sidéral (fr)[Thème]

(comet)[Thème]

motion, movement - circle, circulate, ring - turn - go around, revolve, rotate[Hyper.]

change by reversal, reverse, turn - turn - fork, move around, turn - turn - artificial satellite, orbiter, satellite - gyration, revolution, rotation, turning - celestial orbit, orbit - electron orbit, orbit - rotary motion, rotation - eddying, gyration, swirling, twirling, whirling - spin, twirl, twist, twisting, whirl - spinner - whirler - whirler, whirling dervish - convolution, swirl, vortex, whirl[Dérivé]

rotation (fr)[QuiCAuse]

circumvolve, rotate[Domaine]

ligne courbe (géométrie) (fr)[Classe]

cycle[Classe]

intervalle borné de temps, caractérisé par un phénomène (fr)[Classe...]

mouvement d'un corps autour d'un axe (fr)[Classe]

(alien; extraterrestrial; extraterrestrial being), (star)[termes liés]

(celestial body; heavenly body)[termes liés]

mouvement dans l'espace sidéral (fr)[termes liés]

comète (fr)[DomainDescrip.]

factotum[Domaine]

DirectionChange[Domaine]

turn, turning[Hyper.]

orb, orbit, place in orbit, revolve - go around, rotate - gyrate, reel, spin, spin around, turn, whirl - revolutionary, rotary, rotatory[Dérivé]

rotation (n.)↕

mathematical sciences[Classe]

(abstract)[termes liés]

mathematics[Domaine]

FieldOfStudy[Domaine]

function, map, mapping, mathematical function, single-valued function[Hyper.]

transform - mathematician - mathematical - mathematic, mathematical[Dérivé]

math, mathematics, maths - science, scientific discipline[Domaine]

transformation[Hyper.]

math, mathematics, maths[Domaine]

rotation (n.)↕

This article is about movement of a physical body. For other uses, see Rotation (disambiguation).

This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2008) |

A **rotation** is a circular movement of an object around a *center* (or *point*) *of rotation*. A three-dimensional object rotates always around an imaginary line called a *rotation axis*. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or *spin*. A **rotation** about an external point, e.g. the Earth about the Sun, is called a revolution or *orbital revolution*, typically when it is produced by gravity.

## Contents |

Main article: Rotation (mathematics)

Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed. This definition applies to rotations within both two and three dimensions (in a plane and in space, respectively.)

All rigid body movements are rotations, translations, or combinations of the two.

A rotation is simply a progressive radial orientation to a common point. That common point lies within the axis of that motion. The axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lies external of the body in question then the body is said to orbit. There is no fundamental difference between a “rotation” and a “orbit” and or "spin". The key distinction is simply where the axis of the rotation lies, either within or without a body in question. This distinction can be demonstrated for both “rigid” and “non rigid” bodies.

If a rotation around a point or axis is followed by a second rotation around the same point/axis, a third rotation results. The reverse (inverse) of a rotation is also a rotation. Thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a different point/axis may result in something other than a rotation, e.g. a translation.

Rotations around the *x*, *y* and *z* axes are called *principal rotations*. Rotation around any axis can be performed by taking a rotation around the *x* axis, followed by a rotation around the *y* axis, and followed by a rotation around the *z* axis. That is to say, any spatial rotation can be decomposed into a combination of principal rotations.

In flight dynamics, the principal rotations are known as *yaw*, *pitch*, and *roll* (known as Tait-Bryan angles). This terminology is also used in computer graphics.

See also: curl (mathematics), cyclic permutation, Euler angles, rigid body, rotation around a fixed axis, rotation group SO(3), rotation matrix, axis angle, quaternion, and isometry

In astronomy, rotation is a commonly observed phenomenon. Stars, planets and similar bodies all spin around on their axis. The rotation rate of planets in the solar system was first measured by tracking visual features. Stellar rotation is measured through Doppler shift or by tracking active surface features.

This rotation induces a centrifugal acceleration in the reference frame of the Earth which slightly counteracts the effect of gravity the closer one is to the equator. One effect is that an object weighs slightly less at the equator. Another is that the Earth is slightly deformed into an oblate spheroid.

Another consequence of the rotation of a planet is the phenomenon of precession. Like a gyroscope, the overall effect is a slight "wobble" in the movement of the axis of a planet. Currently the tilt of the Earth's axis to its orbital plane (obliquity of the ecliptic) is 23.44 degrees, but this angle changes slowly (over thousands of years). (See also Precession of the equinoxes and Pole star.)

Main article: Orbital revolution

While revolution is often used as a synonym for rotation, in many fields, particularly astronomy and related fields, revolution, often referred to as orbital revolution for clarity, is used when one body moves around another while rotation is used to mean the movement around an axis. Moons revolve around their planet, planets revolve about their star (such as the Earth around the Sun); and stars slowly revolve about their galaxial center. The motion of the components of galaxies is complex, but it usually includes a rotation component.

Main article: Retrograde motion

Most planets in our solar system, including Earth, spin in the same direction as they orbit the Sun. The exceptions are Venus and Uranus. Uranus rotates nearly on its side relative to its orbit. Current speculation is that Uranus started off with a typical prograde orientation and was knocked on its side by a large impact early in its history. Venus may be thought of as rotating slowly backwards (or being "upside down"). The dwarf planet Pluto (formerly considered a planet) is anomalous in this and other ways.

Main article: Angular momentum

The speed of rotation is given by the angular frequency (rad/s) or frequency (turns/s, turns/min), or period (seconds, days, etc.). The time-rate of change of angular frequency is angular acceleration (rad/s²), This change is caused by torque. The ratio of the two (how heavy is it to start, stop, or otherwise change rotation) is given by the moment of inertia.

The angular velocity *vector* also describes the direction of the axis of rotation. Similarly the torque is a vector.

According to the right-hand rule, the direction away from the observer is associated with clockwise rotation and the direction towards the observer with counterclockwise rotation, like a screw.

See also: rotational energy, angular velocity, Centrifugal force (fictitious), centripetal force, circular motion, circular orbit, Coriolis effect, spin (physics), rotational spectroscopy, and Rigid body dynamics#Rigid body angular momentum

In flight dynamics, the principal rotations are known as *pitch*, *roll* and *yaw*. The term rotation is also used in aviation to refer to the upward pitch (nose moves up) of an aircraft, particularly when starting the climb after takeoff.

Many amusement rides provide rotation. A Ferris wheel has a horizontal central axis, and parallel axes for each gondola, where the rotation is opposite, by gravity or mechanically. As a result at any time the orientation of the gondola is upright (not rotated), just translated. The tip of the translation vector describes a circle. A carousel provides rotation about a vertical axis. Many rides provide a combination of rotations about several axes. In Chair-O-Planes the rotation about the vertical axis is provided mechanically, while the rotation about the horizontal axis is due to the centripetal force. In roller coaster inversions the rotation about the horizontal axis is one or more full cycles, where inertia keeps people in their seats.

Rotation, usually called *spin*, plays a role in many sports. *Topspin* and *backspin* in tennis. *English*, *follow* and *draw* in billiards and pool. Curve balls in baseball and spin bowling in cricket. Table tennis paddles are specialized to allow players to spin the ball as they hit.

- Absolute rotation
- Balancing machine
- Mach's principle
- Rotating locomotion in living systems
- Rotation formalisms in three dimensions

- Product of Rotations at cut-the-knot. cut-the-knot.org
- When a Triangle is Equilateral at cut-the-knot. cut-the-knot.org
- Rotate Points Using Polar Coordinates, howtoproperly.com
- Rotation in Two Dimensions by Sergio Hannibal Mejia after work by Roger Germundsson and Understanding 3D Rotation by Roger Germundsson, Wolfram Demonstrations Project. demonstrations.wolfram.com
- Rotation and Geometry, circumsolatious.blogspot.com

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