# Dictionary Definition

rotation

### Noun

1 the act of rotating as if on an axis; "the
rotation of the dancer kept time with the music" [syn: rotary
motion]

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

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" [syn: revolution, gyration]

4 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"

# User Contributed Dictionary

## English

### Etymology

- From rotationem (accusative of rotatio).

### Noun

- the act of turning around a centre or an axis
- a single complete cycle of such a turning
- a transformation of a coordinate system by rotating the axes around the origin
- a regular variation in a sequence, such as crop rotation

#### Translations

turning around a centreregular variation in a sequence

- Finnish: kierto

## French

### Noun

fr-noun f## Swedish

### Noun

- act of turning a physical object or a coordinate system around a center or an axis

#### Conjugation

# Extensive Definition

A rotation is a movement of an object in a
circular motion. A two-dimensional object rotates
around a center (or point)
of rotation. A three-dimensional object rotates around a line
called an axis. If the axis of rotation is within the body, the
body is said to rotate upon itself, or spin—which implies relative
speed and perhaps
free-movement with angular
momentum. A circular motion about an external point, e.g. the
Earth about
the Sun, is
called an orbit or more
properly an orbital
revolution.

## Mathematics

Mathematically, a rotation is, unlike a translation, a rigid body movement which keeps a point fixed. This definition applies to rotations within both two and three dimensions (in a plane and in space, respectively.) A rotation in three-dimensional space keeps an entire line fixed, i.e. a rotation in three-dimensional space is a rotation around an axis. This follows from Euler's rotation theorem.All rigid body movements are rotations,
translations, or combinations of the two.

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 pitch, roll and
yaw (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 axes (the plural of 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 23.45 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 about 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.The Moon makes one complete rotation during one
complete orbital revolution around the Earth (an effect called
tidal
locking) so that the same side of the Moon always faces the
Earth (the other side is called the far
side of the Moon).

### Retrograde rotation

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

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 and observation wheel have 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 it.## External links

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

rotation in Arabic: دوران

rotation in Czech: Rotace

rotation in Danish: Rotation

rotation in German: Rotation (Physik)

rotation in Spanish: Rotación

rotation in Esperanto: Rotacio

rotation in French: Rotation vectorielle

rotation in Galician: Rotación

rotation in Indonesian: Rotasi

rotation in Italian: Rotazione

rotation in Hungarian: Forgómozgás

rotation in Marathi: अक्ष

rotation in Japanese: 回転

rotation in Norwegian Nynorsk: Rotasjon

rotation in Polish: Obrót

rotation in Russian: Вращение

rotation in Slovenian: Vrtenje

rotation in Finnish: Pyörimisliike

rotation in Swedish: Rotation

rotation in Tamil: சுழற்சி

rotation in Thai: การหมุน

rotation in Ukrainian: Обертання

rotation in Chinese: 自转

# Synonyms, Antonyms and Related Words

Indian file, array, arsis, articulation, bank, beat, booster rocket, bout, buzz, catapult, catena, catenation, chain, chain reaction, chaining, circle, circuit, circulation, circumvolution, coming
after, concatenation, connection, consecution, consecutiveness,
continuation,
continuity, continuum, course, cycle, descent, diastole, downbeat, drone, endless belt, endless
round, extension,
file, filiation, following, gamut, gradation, ground loop,
gyration, gyre, hopoff, hum, line, lineage, logical sequence,
monotone, nexus, order, order of succession,
pendulum, periodicity, plenum, posteriority, postposition, powder train,
procession, progression, prolongation, pulse, queue, range, rank, recurrence, reticulation, revolution, round, routine, row, run, scale, sequence, series, single file, spectrum, spell, string, subjunction, succession, successiveness, suffixation, swath, systole, takeoff, thesis, thread, tier, train, turn, upbeat, wheel, whirl, windrow