Editing Rotation (section)

=== Circular motion ===
{{See also|Circular motion|Rotation around a fixed axis}}[[File:Circular_motion_vs_rotation.svg|thumb|The motion on the left, an example of curvilinear translation, cannot be treated as rotation since there is no change in orientation, whereas the right can be treated as rotation. |264x264px]]
It is possible for [[Rigid body|objects]] to have periodic [[Circular motion|circular trajectories]] without changing their [[Orientation (geometry)|orientation]]. These types of motion are treated under [[circular motion]] instead of rotation, more specifically as a curvilinear translation. Since translation involves [[Displacement (geometry)|displacement]] of [[Rigid body|rigid bodies]] while preserving the [[Orientation (geometry)|orientation]] of the body, in the case of curvilinear translation, all the points have the same instantaneous velocity whereas relative motion can only be observed in motions involving rotation.<ref name=":0">{{Cite book |last1=Harrison |first1=H. |url=https://books.google.com/books?id=IBkD6pSdjl0C |title=Advanced Engineering Dynamics |last2=Nettleton |first2=T. |date=1997-08-01 |publisher=Butterworth-Heinemann |isbn=978-0-08-052335-4 |pages=55 |language=en |chapter=Rigid body motion in three dimensions |chapter-url=https://books.google.com/books?id=IBkD6pSdjl0C&pg=PA55}}</ref>

In rotation, the [[Orientation (geometry)|orientation]] of the object changes and the change in [[Orientation (geometry)|orientation]] is independent of the observers whose [[Frame of reference|frames of reference]] have constant relative orientation over time. By [[Euler's rotation theorem|Euler's theorem]], any change in orientation can be described by rotation about an axis through a chosen reference point.<ref name=":0" /> Hence, the distinction between rotation and circular motion can be made by requiring an instantaneous axis for rotation, a line passing through [[Instant centre of rotation|instantaneous center of circle]] and perpendicular to the [[Plane of rotation|plane of motion]]. In the example depicting curvilinear translation, the center of circles for the motion lie on a straight line but it is parallel to the plane of motion and hence does not resolve to an axis of rotation. In contrast, a rotating body will always have its instantaneous axis of zero velocity, perpendicular to the plane of motion.<ref>{{Cite book |last=Hibbeler |first=R. C. |url=https://books.google.com/books?id=PxjGxmLhSBwC |title=Engineering Mechanics: Statics & dynamics |date=2007 |publisher=Prentice-Hall |isbn=978-0-13-221509-1 |language=en |chapter=Planar kinematics of a rigid body: Instantaneous center of zero velocity |chapter-url=https://books.google.com/books?id=PxjGxmLhSBwC&pg=PA680}}</ref>

More generally, due to [[Chasles' theorem (kinematics)|Chasles' theorem]], any motion of [[Rigid body|rigid bodies]] can be treated as a composition of '''rotation''' and [[Translation (geometry)|translation]], called general plane motion.<ref name=":0" /> A simple example of pure rotation is considered in [[rotation around a fixed axis]].