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Encyclopedia > Rotation
A sphere rotating around its axis.

## Contents

Rotation of a planar figure around a point

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. In the three-dimensional space, the possible moves of a rigid body are rotations and translations. ... Image File history File links Download high resolution version (936x989, 18 KB) Summary Made by myself with matlab. ... Image File history File links Download high resolution version (936x989, 18 KB) Summary Made by myself with matlab. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... In Euclidean geometry, translation is a transformation of Euclidean space which moves every point by a fixed distance in the same direction. ... In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. ... In mathematics, Eulers rotation theorem states that any rotation has an axis. ...

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. In mathematics, the inverse of an element x, with respect to an operation *, is an element x such that their compose gives a neutral element. ... This picture illustrates how the hours on a clock form a group under modular addition. ...

The principal axes of rotation in space

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. Image File history File links Size of this preview: 800 Ã— 600 pixelsFull resolution (2048 Ã— 1536 pixel, file size: 836 KB, MIME type: image/png) This image is supposed to replace the jpg-compressed version, Image:Flight dynamics. ... Image File history File links Size of this preview: 800 Ã— 600 pixelsFull resolution (2048 Ã— 1536 pixel, file size: 836 KB, MIME type: image/png) This image is supposed to replace the jpg-compressed version, Image:Flight dynamics. ...

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. Flight dynamics is the science of air and space vehicle orientation and control in three dimensions. ... In geometry, Tait-Bryan angles are three angles used to describe a general rotation in three-dimensional Euclidean space by three successive rotations, once about the x-axis, once about the y-axis, and once about the z-axis. ... This article is about the scientific discipline of computer graphics. ...

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

For other uses, see Curl (disambiguation). ... A cyclic permutation is a permutation that shifts all elements of given ordered set by a fixed offset, with the elements shifted off the end inserted back at the beginning in the same order, i. ... Euler angles are a means of representing the spatial orientation of an object. ... In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected. ... The simplest three-dimensional case of rotation is rotation of a body about a fixed axis of rotation: each point of the body moves in a plane perpendicular to the axis, carrying out a circular motion, with the circle centered at the intersection of the plane and the axis. ... In mechanics and geometry, the rotation group is the set of all rotations about the origin of 3-dimensional Euclidean space, R3. ... A rotation matrix is a matrix which when multiplied by a vector has the effect of changing the direction of the vector but not its magnitude. ... The axis angle representation of a rotation parameterizes a rotation by two values: an axis, or a line, and an angle describing the magnitude of the rotation about the axis. ... In mathematics, the quaternions are a non-commutative extension of the complex numbers. ... In mathematics, an isometry, isometric isomorphism or congruence mapping is a distance-preserving isomorphism between metric spaces. ...

## Astronomy

This rotation induces a centrifugal acceleration 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. Centrifugal force (from Latin centrum center and fugere to flee) is a term which may refer to two different forces which are related to rotation. ... World map showing the equator in red In tourist areas, the equator is often marked on the sides of roads The equator marked as it crosses IlhÃ©u das Rolas, in SÃ£o TomÃ© and PrÃ­ncipe. ... Oblate also refers to a member of the Roman Catholic religious order of the Missionary Oblates of Mary Immaculate, or in some cases to a lay or religious person who has officially associated himself (or herself) with a monastic community such as the Benedictines for reasons of personal enrichment without...

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.) Precession redirects here. ... A gyroscope For other uses, see Gyroscope (disambiguation). ... This article is about Earth as a planet. ... The Obliquity of the ecliptic is the angle between the plane of the Earths equator and the ecliptic plane in which the Earth rotates around the Sun. ... Precession of the equinoxes refers to the precession of the Earths axis of rotation. ... For other uses of the words Pole star and Polestar see Polestar (disambiguation). ...

### Rotation and revolution

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 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. Orbital revolution is the cyclical path taken by one object around another object (or point, line, etc. ... NGC 4414, a typical spiral galaxy in the constellation Coma Berenices, is about 56,000 light years in diameter and approximately 60 million light years distant. ... For other uses, see Galaxy (disambiguation). ...

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). Tidal locking makes one side of an astronomical body always face another, like the Moon facing the Earth. ... Far side of the Moon. ...

## Physics

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. This gyroscope remains upright while spinning due to its angular momentum. ... It has been suggested that this article or section be merged into Angular velocity. ... For other uses, see Frequency (disambiguation). ... ... Periodicity is the quality of occurring at regular intervals (e. ... For other senses of this word, see torque (disambiguation). ... Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, (SI units kg mÂ², Former British units slug ft2), is the rotational analog of mass. ...

The angular velocity vector also describes the direction of the axis of rotation. Similarly the torque is a vector. Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ...

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. The left-handed orientation is shown on the left, and the right-handed on the right. ... Screws come in a variety of shapes and sizes for different purposes. ...

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

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. ... Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ... Centrifugal force (from Latin centrum centre and fugere to flee) is a term which may refer to two different forces which are related to rotation. ... The centripetal force is the external force required to make a body follow a circular path at constant speed. ... In physics, circular motion is rotation along a circle: a circular path or a circular orbit. ... In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. ... In the inertial frame of reference (upper part of the picture), the black object moves in a straight line. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... Rotational spectroscopy or microwave spectroscopy studies the absorption and emission of electromagnetic radiation (typically in the microwave region of the electromagnetic spectrum) by molecules associated with a corresponding change in the rotational quantum number of the molecule. ... In physics, rigid body dynamics is the study of the motion of a rigid object. ...

## 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. Flight dynamics is the science of air and space vehicle orientation and control in three dimensions. ...

## 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. For other uses, see Tennis (disambiguation). ... This article is about the various cue sports. ... Curveball Pitch Curveball Pitch The curveball is a type of pitch in baseball thrown with a grip and hand motion that imparts forward spin to the ball. ... Spin bowling, sometimes known as slow bowling, is a technique used for bowling in the sport of cricket. ... â€œPing Pongâ€ redirects here. ...

Results from FactBites:

 Rotation - Wikipedia, the free encyclopedia (994 words) Rotation is the movement of an object in a circular motion. This is a consequence of Euler's rotation theorem. In astronomy, rotation is a commonly observed phenomenon.
 Galaxy rotation curve - Wikipedia, the free encyclopedia (1108 words) Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). The rotation curve of a galaxy is a graph that plots the orbital velocity of the stars or gas in the galaxy on the y-axis against the distance from the center of the galaxy on the x-axis. The galaxy rotation problem is this discrepancy between the observed rotation speeds of matter in the disk portions of spiral galaxies and the predictions of Newtonian dynamics considering the visible mass.
More results at FactBites »

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