Rotation

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Rotation
A polyhedron resembling a sphere rotating around an axis.

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.

Mathematics

Rotation of a planar figure around a point
Rotational Orbit v Spin
Relations between rotation axis, plane of orbit and axial tilt (for Earth).

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.

Astronomy

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.)

Rotation and 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.

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.

Physics

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.

Aviation

The principal axes of rotation in space

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.

Amusement rides

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.

Sports

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

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• rotation — [ rɔtasjɔ̃ ] n. f. • 1486, repris fin XVIIe; lat. rotatio 1 ♦ Mouvement d un corps qui se déplace autour d un axe (matériel ou non), au cours duquel chaque point du corps se meut avec la même vitesse angulaire. ⇒ giration. Rotation de la Terre.… …   Encyclopédie Universelle

• Rotation — (lat. rotatio: Drehung) bezeichnet: Allgemein: eine Drehung Rotation (Physik), die Drehbewegung eines Körpers Rotation (Medizin), in der Medizin eine Drehbewegung, beispielsweise des Kopfes in der Graphentheorie eine Anwendung am binären Suchbaum …   Deutsch Wikipedia

• Rotation [1] — Rotation, Rotationsachse und Rotationspaar. Unter Rotation versteht man jene Bewegung eines starren Körpers, bei der zwei und damit alle Punkte einer Geraden ruhen. Die ruhende Gerade heißt die Rotationsachse. Alle Punkte des Körpers beschreiben… …   Lexikon der gesamten Technik

• Rotation — Ro*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… …   The Collaborative International Dictionary of English

• Rotation — Ro*ta tion, a. Pertaining to, or resulting from, rotation; of the nature of, or characterized by, rotation; as, rotational velocity. [1913 Webster] …   The Collaborative International Dictionary of English

• rotation — index cycle, order (arrangement), sequence Burton s Legal Thesaurus. William C. Burton. 2006 …   Law dictionary

• rotation — [rō tā′shən] n. [L rotatio] 1. a rotating or being rotated 2. the spinning motion around the axis of a celestial body: cf. REVOLUTION (sense 1a) 3. regular and recurring succession of changes [a rotation of duties ] ☆ 4. Pool a game in which the… …   English World dictionary

• Rotation — (v. lat.), 1) Drehung, Drehungsbewegung, s.d.; die Rotationsfläche entsteht, wenn man irgend eine Fläche sich um eine feste gerade Linie bewegt denkt. Diese feste Gerade heißt die Rotationsachse (Drehungsachse); so beschreibt die Kante einer Thür …   Pierer's Universal-Lexikon

• Rotation — (lat.), Umdrehung. Drehung eines Körpers um eine Ache, wobei jeder Punkt des Körpers eine Kreislinie beschreibt, deren Mittelpunkt in der Achse liegt; in der Landwirtschaft soviel wie Fruchtfolge (s. d. und Landwirtschaftliche Betriebssysteme) …   Meyers Großes Konversations-Lexikon

• Rotation [2] — Rotation, spezifische, s. Molekularrotation …   Lexikon der gesamten Technik

• Rotation [3] — Rotation, im Meliorationswesen, die abwechselnde Bewässerung räumlich voneinander getrennter Flächen mittels gleicher Wasserbezugsquelle in der Weise, daß eine derselben 1 oder 2 Tage bewässert wird, dann 5–6 Tage trocken liegt und so eine… …   Lexikon der gesamten Technik