Rotation

A sphere rotating about an axis

A rotation is a circular movement of an object around a center (or point) of rotation. A three-dimensional object can always be rotated around an infinite number of imaginary lines called rotation axes (z/ AK-seez). If the axis passes through the body's 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. The axis is called a pole.

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 an “orbit” and or "spin". The key distinction is simply where the axis of the rotation lies, either within or outside of 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.

Other Languages
العربية: دوران
asturianu: Rotación
भोजपुरी: घूर्णन
български: Въртене
བོད་ཡིག: འཁོར་འགྲོས།
bosanski: Rotacija
català: Rotació
čeština: Otáčení
chiShona: Dendera
dansk: Rotation
Ελληνικά: Περιστροφή
Esperanto: Rotacio
euskara: Errotazio
فارسی: چرخش
galego: Rotación
한국어: 회전
हिन्दी: घूर्णन
hrvatski: Vrtnja
Ido: Rotaco
Bahasa Indonesia: Rotasi
italiano: Rotazione
Basa Jawa: Rotasi
ಕನ್ನಡ: ಪರಿಭ್ರಮಣ
қазақша: Айналу
Latina: Rotatio
македонски: Вртење
मराठी: अक्ष
Bahasa Melayu: Putaran
日本語: 回転
norsk nynorsk: Rotasjon
ਪੰਜਾਬੀ: ਗੇੜਾ
Plattdüütsch: Rotatschoon (Physik)
polski: Obrót
română: Rotație
русский: Вращение
Scots: Rotation
sicilianu: Rutazzioni
Simple English: Rotation
slovenščina: Vrtenje
Soomaaliga: Wareega Meere
српски / srpski: Rotaciono kretanje čvrstog tela
srpskohrvatski / српскохрватски: Rotacija
Basa Sunda: Puteran
தமிழ்: சுழற்சி
తెలుగు: భ్రమణం
Türkçe: Dönüş
українська: Обертання
Tiếng Việt: Quay
中文: 转动