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Rotation

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	Topics Rotation Topic Home A rotation is a movement of an object in a circular motion. A two-dimensionDimension In common usage, a dimension is a parameter or measurement required to define the characteristics of an object—i.e.... al object rotates around a center (or pointPoint (geometry) A spatial point is an entity with a location in space but no extent.... ) 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 speedSpeed Speed is the rate of motion, or equivalently the rate of change of position, many times expressed as distance d moved p... and perhaps free-movement with angular momentumAngular momentum In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the... . A circular motion about an external point, e.g. the EarthEarth Earth is the third planet in the solar system in terms of distance from the Sun, and the fifth largest.... about the SunSun \|+ The Sun \|+\|-\| colspan="2" align="center" \| \|-... , is called an orbitORBit ORBit is a CORBA compliant Object Request Broker.... or more properly an orbital revolutionOrbital revolution Summary Orbital revolution is the cyclical path taken by one object around another object ... . Mathematics MathematicallyMathematics Mathematics is the discipline that deals with concepts such as quantity, structure, space and change.... , a rotation is, unlike a translationTranslation (geometry) In Euclidean geometry, a translation is moving every point a constant distance in a specified direction.... , a rigid bodyRigid body In physics, a rigid body is an idealization of a solid body of finite size in which deformation is neglected.... 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 theoremFacts About Euler's rotation theorem Euler's rotation theorem states that, in 3D space, for any two coordinate systems with a common origin, there is a single ei... . 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 of a rotation is also a rotation. Thus, the rotations around a point/axis form a groupGroup (mathematics) In mathematics, a group is a set together with a binary operation satisfying certain axioms, detailed below.... . 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 dynamicsFlight dynamics Flight dynamics is the study of orientation of air and space vehicles and how to control the critical flight parameters, typ... , the principal rotations are known as pitch, roll and yaw (known as Tait-Bryan anglesTait-Bryan angles In geometry, Tait-Bryan angles are three angles used to describe a general rotation in three-dimensional Euclidean space by ... ). This terminology is also used in computer graphicsComputer graphics Computer graphics is the field of visual computing, where one utilizes computers both to generate visual synthetically and... . Astronomy In astronomyAstronomy Astronomy is the science of celestial objects and phenomena that originate outside the Earth's atmosphere .... , rotation is a commonly observed phenomenon. StarStar A star is a massive, compact body of plasma in outer space that is held together by its own gravity and, unlike a planet, is... s, planetPlanet The International Astronomical Union , the official scientific body for astronomical nomenclature, currently defines "plane... 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 rotationStellar rotation Stellar rotation is the angular motion of a star about its axis.... 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 equatorEquator The equator is an imaginary circle drawn around a planet at a distance halfway between the poles.... . 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 precessionPrecession Precession refers to a change in the direction of the axis of a rotating object.... . Like a gyroscopeGyroscope Overview A gyroscope is a device for measuring or maintaining orientation, based on the principle of conservation of angular momentum... , the overall effect is a slight "wobble" in the movement of the axis of a planet. Currently the tilt of the EarthEarth Earth is the third planet in the solar system in terms of distance from the Sun, and the fifth largest.... 's axis to its orbital plane is 23.45 degrees, but this angle changes slowly (over thousands of years). (See also Precession of the equinoxesPrecession of the equinoxes The precession of the equinoxes refers to the precession of Earth's axis of rotation with respect to inertial space.... and Pole starPole star A pole star is a visible star that is approximately aligned with the Earth's axis of rotation; that is, a star that lies in ... .) 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 galaxiesGalaxy Overview A galaxy is a huge gravitationally bound system of stars, interstellar gas and dust, plasma, and unseen 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 lockingTidal locking Tidal locking makes one side of an astronomical body always face another, like the Moon facing the Earth.... ) so that the same side of the Moon always faces the Earth (the other side is called the far side of the MoonFar side of the Moon The far side of the Moon is the lunar hemisphere that is permanently turned away from the Earth.... ). Retrograde rotation Most planetPlanet The International Astronomical Union , the official scientific body for astronomical nomenclature, currently defines "plane... s in our solar systemSolar System The Solar System or solar system is the stellar system comprising the Sun and the retinue of celestial objects gravita... , including EarthEarth Earth is the third planet in the solar system in terms of distance from the Sun, and the fifth largest.... , spin in the same direction as they orbit the SunSun \|+ The Sun \|+\|-\| colspan="2" align="center" \| \|-... . The exceptions are VenusVenus Venus is the second-closest planet to the Sun, orbiting it every 224.7 Earth days.... and UranusUranus Uranus is the seventh planet from the Sun.... . 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 planetDwarf planet Summary A dwarf planet is a category of celestial bodies in the solar system as introduced in a resolution by the International Astr... PlutoPluto Pluto is the second-largest known dwarf planet in the solar system.... (formerly considered a planet) is anomalous in this and other ways. Physics The speed of rotation is given by the angular frequencyAngular frequency Overview RadianPulsation ... (rad/s) or frequencyFrequency Frequency is the measurement of the number of times that a repeated event occurs per unit of time.... \|turns]]/s, turns/min), or periodPeriodicity Summary Periodicity is the quality of occurring at regular intervals and can occur in different contexts:... (seconds, days, etc.). The time-rate of change of angular frequency is angular acceleration (rad/s²), This change is caused by torqueTorque In physics, torque can informally be thought of as "rotational force".... . The ratio of the two (how heavy is it to start, stop, or otherwise change rotation) is given by the moment of inertiaMoment of inertia Moment of inertia, also called mass moment of inertia and, sometimes, the angular mass, quantifies the rotationa... . The angular velocityAngular velocity In physics angular velocity is the speed at which something rotates together with the direction it rotates in.... vector also describes the direction of the axis of rotation. Similarly the torque is a vector. According to the right-hand ruleRight-hand rule In mathematics and physics, the right-hand rule is a convention for determining relative directions of certain vectors.... , the direction away from the observer is associated with clockwise rotation and the direction towards the observer with counterclockwise rotation, like a screwScrew A screw is a shaft with a helical groove or thread formed on its surface and provision at one end to turn the screw.... . Aviation In flight dynamicsFlight dynamics Flight dynamics is the study of orientation of air and space vehicles and how to control the critical flight parameters, typ... , 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 rideAmusement ride An amusement ride is any number of devices found in funfairs and amusement parks meant to appeal to various senses of the ri... s provide rotation. A Ferris wheelFacts About Ferris wheel A Ferris wheel is a nonbuilding structure consisting of an upright wheel with passenger gondolas suspended from the rim.... 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 carouselCarousel A carousel is an amusement ride consisting of a rotating platform with seats for passengers.... provides rotation about a vertical axis. Many rides provide a combination of rotations about several axes. In Chair-O-PlanesChair-O-Planes The Chair-O-Planes, sometimes called a swing carousel or wave swinger, is a fairground ride that is a variation ... the rotation about the vertical axis is provided mechanically, while the rotation about the horizontal axis is due to the centripetal forceCentripetal force The centripetal force is the force needed to move an object in a circle at constant speed.... . 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 tennisTennis Tennis is a game played between either two players or two teams of two players .... . English, follow and draw in billiards and poolBilliards Billiards is a family of games played on a table with a stick, known as a cue stick, which is used to strike balls, moving t... . Curve balls in baseball and spin bowlingSpin bowling Spin bowling, sometimes known as slow bowling, is a technique used for bowling in the sport of cricket.... in cricket. Table tennisTable tennis Table tennis is one of the most popular sports in the world in terms of player numbers, as well as being one of the newest o... paddles are specialized to allow players to spin the ball as they hit it. External links at cut-the-knotCut-the-knot cut-the-knot is an educational website maintained by Alexander Bogomolny and devoted to popular exposition of a great variet... at cut-the-knotCut-the-knot cut-the-knot is an educational website maintained by Alexander Bogomolny and devoted to popular exposition of a great variet... by Sergio Hannibal Mejia after work by Roger Germundsson and by Roger Germundsson, The Wolfram Demonstrations Project.