Rotation

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Rotation

A rotation is a movement of an object in a circular motion

Circular motion

In physics, circular motion is rotation along a circle: a circular path or a circular orbit. It can be uniform circular motion, that is, with constant angular rate of rotation, or non-uniform circular motion, that is, with a changing rate of rotation....
. A two-dimension

Dimension

In mathematics, the dimension of a space is roughly defined as the minimum number of coordinates needed to specify every point within it. For example: a point on the unit circle in the plane can be specified by two Cartesian coordinates but one can make do with a single coordinate , so the circle is 1-dimensional even though it exists in...
al object rotates around a center (or point
Point (geometry)

In geometry, topology and related branches of mathematics a spatial point describes a specific object within a given space that consists of neither volume, area, length, nor any other higher dimensional analogue....
) of rotation. A three-dimensional

Three-dimensional space

Three-dimensional space is a geometric model of the physical universe in which we live. The three dimensions are commonly called length, width, and depth , although any three mutually perpendicular directions can serve as the three dimensions....
object rotates around a line

Line

Line or lines may refer to:* Line , an infinitely-extending one-dimensional figure that has no curvature* Line , the fundamental unit of poetic composition...
called an axis. If the axis of rotation is within the body, the body is said to rotate upon itself, or spin
Spin

Spin may refer to:* Rotation or spin, a movement of an object in a circular motion* Spin or particle spin, a fundamental property of elementary particles...
—which implies relative speed

Speed

Speed is the rate of Motion , or equivalently the rate of change of distance.Speed is a Scalar quantity with dimensions length/time; the equivalent Vector quantity to speed is velocity....
and perhaps free-movement with angular momentum

Angular momentum

In physics, the angular momentum of a particle about an origin is a vector quantity related to rotation, equal to the mass of the particle multiplied by the cross product of the position vector of the particle with its velocity vector....
.

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Encyclopedia

A rotation is a movement of an object in a circular motion

Circular motion

Dimension

Three-dimensional space

Line

Speed

Angular momentum

Earth

Sun

The Sun , a G V star, is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 98.6% of the Solar System's mass....
, is called an orbit
ORBit

ORBit is a Common Object Request Broker Architecture 2.4 compliant Object Request Broker . It features mature C , C++ and Python bindings, and less developed bindings for Perl, Lisp , Pascal , Ruby , and Tcl....
or more properly an orbital revolution.

Mathematics

Mathematically

Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
, a rotation is a rigid body

Rigid body

In physics, a rigid body is an idealization of a solid Physical body of finite size in which deformation is neglected. In other words, the distance between any two given Point s of a rigid body remains constant in time regardless of external forces exerted on it....
movement which, unlike a translation

Translation (geometry)

In Euclidean geometry, a translation is moving every point a constant distance in a specified direction. It is one of the Euclidean groups . A translation can also be interpreted as the addition of a constant vector space to every point, or as shifting the Origin of the coordinate system....
, 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

Euler's rotation theorem

In kinematics, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a rotation about a fixed axis through that point....
.

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 lay within the axis of that motion. The axis is 90 degrees perpendicular to the plane of the motion.

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

Inverse element

In mathematics, the idea of inverse element generalises the concepts of additive inverse, in relation to addition, and Multiplicative inverse, in relation to multiplication....
) of a rotation is also a rotation. Thus, the rotations around a point/axis form a group

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set together with an Binary operation that combines any two of its element to form a third element....
. 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

Flight dynamics

Flight dynamics is the science of aircraft and spacecraft vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of mass, known as pitch, roll and yaw ....
, the principal rotations are known as pitch, roll and yaw (known as Tait-Bryan angles

Tait-Bryan angles

Yaw, pitch, and roll, also known as Tait?Bryan rotations, named after Peter Guthrie Tait and George Bryan, are a specific sequence of Euler angles very often used in aerospace applications to define the relative orientation of a vehicle....
). This terminology is also used in computer graphics

Computer graphics

Computer graphics are graphics created by computers and, more generally, the representation and manipulation of pictorial data by a computer....
.

Astronomy

In astronomy

Astronomy

Astronomy is the science of Astronomical object and Phenomenon that originate outside the Earth's atmosphere . It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the physical cosmology....
, rotation is a commonly observed phenomenon. Star

Star

A star is a massive, luminous ball of Plasma that is held together by its own gravity. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth....
s, planet

Planet

A planet , as 2006 definition of planet by the International Astronomical Union , is a celestial body orbiting a star or Stellar evolution#Stellar remnants that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared the neighbourhood of planetesimals....
s 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

Stellar rotation

Stellar rotation is the angular motion of a star about its axis. The rate of rotation can be measured from the spectrum of the star, or by timing the movements of active features on the surface....
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

Equator

The equator is the intersection of the Earth's surface with the Plane perpendicular to the Earth's rotation and containing the Earth's center of mass....
. 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

Precession

Precession refers to a change in the direction of the axis of a rotation object. In physics, there are two types of precession, torque-free and torque-induced, the latter being discussed here in more detail....
. Like a gyroscope

Gyroscope

A gyroscope is a device for measuring or maintaining orientation , based on the principles of angular momentum. The device is a spinning wheel or disk whose axle is free to take any orientation....
, the overall effect is a slight "wobble" in the movement of the axis of a planet. Currently the tilt of the Earth

Earth

Earth is the third planet from the Sun. Earth is the largest of the terrestrial planets in the Solar System in diameter, mass and density. It is also referred to as the World and Wiktionary:Terra.Note that by International Astronomical Union convention, the term "Terra" is used for naming extensive land masses, rather...
'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

Precession of the equinoxes

In astronomy, precession refers to a gravitationally-induced slow but continuous change in an astronomical body's rotational axis or orbital path....
and Pole star

Pole star

A pole star is a visible star, especially a prominent one, that is approximately aligned with the Earth's axis of rotation; that is, a star whose apparent position is close to one of the celestial poles, and which lies directly overhead when viewed from the Earth's North Pole or South Pole....
.)

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

Galaxy

A galaxy is a massive, gravitation system that consists of stars and stellar remnants, an interstellar medium of gas and cosmic dust, and an important but poorly-understood component tentatively dubbed dark matter....
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

Tidal locking

Tidal locking occurs when the gravitational gradient makes one side of an Astronomical object always face another; for example, one side of the Earth's Moon always faces the Earth....
) so that the same side of the Moon always faces the Earth (the other side is called the far side of the Moon

Far side of the Moon

The far side of the Moon is the Moon hemisphere that is permanently turned away from the Earth. The far hemisphere was first photographed by the Soviet Luna 3 probe in 1959, and was first directly observed by human eyes when the Apollo 8 mission orbited the Moon in 1968....
).

Retrograde rotation

Most planet

Planet

Solar System

The Solar System consists of the Sun and those Astronomical object bound to it by gravity: the eight planets and five dwarf planets, their 173 known Natural satellite, and billions of Small Solar System body....
, including Earth

Earth

Sun

Venus

Venus is the second-closest planet to the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus , the Roman mythology goddess of love....
and Uranus

Uranus

Uranus is the seventh planet from the Sun and the third-largest and fourth most massive planet in the Solar System. It is named after the ancient Greek deity of the sky Uranus the father of Kronos and grandfather of Zeus ....
. 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

Dwarf planet

A dwarf planet, as defined by the International Astronomical Union , is a celestial body orbiting the Sun that is massive enough to be rounded by its own gravity but has not Clearing the neighbourhood of planetesimals and is not a natural satellite....
Pluto

Pluto

Pluto , Minor planet names Pluto, is the second-largest known dwarf planet in the Solar System and the tenth-largest body observed directly orbiting the Sun....
(formerly considered a planet) is anomalous in this and other ways.

Physics

The speed of rotation is given by the angular frequency

Angular frequency

In physics , angular frequency ? is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity....
(rad/s) or frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
(turns

Turn (geometry)

A turn is a unit of plane angle, equal to 360? or 2p radians. As an angular unit it is mainly useful for large angles, such as in connection with coils and rotation objects....
/s, turns/min), or period

Periodicity

Periodicity is the quality of occurring at regular intervals or periods and can occur in different contexts:In timing devices:* A clock marks time at periodic intervals....
(seconds, days, etc.). The time-rate of change of angular frequency is angular acceleration (rad/s²), This change is caused by torque

Torque

Torque is the tendency of a force to rotate an object about an axis . Just as a force is a push or a pull, a torque can be thought of as a twist....
. The ratio of the two (how heavy is it to start, stop, or otherwise change rotation) is given by the moment of inertia

Moment of inertia

Moment of inertia, also called mass moment of inertia or the angular mass, is a measure of an object's resistance to changes in its rotation rate....
.

The angular velocity

Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed, and axis about which an object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc....
vector also describes the direction of the axis of rotation. Similarly the torque is a vector.

According to the right-hand rule

Right-hand rule

In mathematics and physics, the right-hand rule is a common mnemonic for understanding notation conventions for vector in 3 dimensions. It was invented for use in electromagnetism by British physicist Zachariah William Cole in the late 1800s....
, the direction away from the observer is associated with clockwise rotation and the direction towards the observer with counterclockwise rotation, like a screw

Screw

A screw is a shaft with a helix groove or screw thread formed on its surface and provision at one end to turn the screw. Its main uses are as a threaded fastener used to hold objects together, and as a simple machine used to translate torque into linear force....
.

2. A Rotation is simply a progressive radial orientation to a common point. That common point is within the axis of that motion. The axis is 90 degrees perpendicular to the plane of the motion.

Aviation

In flight dynamics

Flight dynamics

Amusement rides

Many amusement ride

Amusement ride

An amusement ride is any number of devices found at Traveling Carnivals, funfair, or amusement parks meant to appeal to various senses of the rider....
s provide rotation. A Ferris wheel

Ferris wheel

A Ferris wheel is a nonbuilding structure, consisting of an upright wheel with passenger gondolas attached to the rim.The original Ferris wheel was designed by George Washington Gale Ferris, Jr., as a landmark for the 1893 World's Columbian Exposition in Chicago....
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

Carousel

A carousel , or merry-go-round, is an amusement ride consisting of a rotation platform with seats for passengers. The "seats" are traditionally in the form of wooden horses or animals, which are often moved mechanically up and down to simulate Horse gait#Gallop, to the accompaniment of Music loop circus music....
provides rotation about a vertical axis. Many rides provide a combination of rotations about several axes. In Chair-O-Planes

Chair-O-Planes

The Chair-O-Planes, sometimes called a swing carousel or wave swinger, is a fairground ride that is a variation on the carousel in which the chairs are suspended on chains from the rotation top of the carousel....
the rotation about the vertical axis is provided mechanically, while the rotation about the horizontal axis is due to the centripetal force

Centripetal force

The centripetal force is the external force required to make a body follow a curved path. Hence centripetal force is a kinematic force requirement, not a particular kind of force like gravity or electromagnetism....
. 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

Tennis

Tennis is a sport played between two players or between two teams of two players each . Each player uses a strung racquet to strike a hollow rubber Tennis ball covered with felt over a net into the opponent's tennis court....
. English, follow and draw in billiards and pool

Billiards

Cue sports are a wide variety of Game of skill generally played with a cue stick which is used to strike billiard balls, moving them around a Baize-covered billiards table bounded by rubber ....
. Curve balls in baseball and spin bowling

Spin bowling

Spin bowling, sometimes known as slow bowling, is a technique used for bowling in the sport of cricket. Practitioners are known as spinners or spin bowler s....
in cricket. Table tennis

Table tennis

Table tennis, also known as ping pong, is a sport in which two or four players hit a lightweight, hollow ball back and forth with rackets ....
paddles are specialized to allow players to spin the ball as they hit it. rotation is the axis

External links

at cut-the-knot
Cut-the-knot

Cut-the-knot is an educational website maintained by Alexander Bogomolny and devoted to popular exposition of a great variety of topics in mathematics....
at cut-the-knot
Cut-the-knot

Cut-the-knot is an educational website maintained by Alexander Bogomolny and devoted to popular exposition of a great variety of topics in mathematics....
by Sergio Hannibal Mejia after work by Roger Germundsson and by Roger Germundsson, Wolfram Demonstrations Project
Wolfram Demonstrations Project

The Wolfram Demonstrations Project is a website developed by Wolfram Research, whose stated goal is to bring computational exploration to the widest possible audience....
.