# Axis of rotation

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An axis of rotation or rotation axis is a straight line that defines or describes a rotation or rotation . Both terms are preferred in mathematics , technology or the natural sciences . In physics , for example, the rotation of a body in space can be described qualitatively and quantitatively with the help of a rotation axis . Likewise, a certain figure can be described with the help of a rotation axis within mathematics. Accordingly, there are many other use cases, which are described in more detail below.

## Illustrations and use cases

The rotation of a rectangle forms a (full) cylinder , the longitudinal axis here the x-axis

As the axis of rotation is referred to in a rotational body that is precisely, this can rotate around the one without the view of the body that changed. In this case, the axis of rotation is also an axis of symmetry of the body. When rotating on circles, the individual points of the body move in planes perpendicular to the axis of rotation.

If the view is only the same in certain rotational positions, we speak of multiple or multiple symmetry or axes of rotation. A distinction is made between two (digyren), three (trigyren), four (tetragyren), five (pentagyren), six (hexagyren) and multiple symmetry or rotation axes.

An axis of rotation can also be illustrated using a wheel . The axis of rotation is perpendicular to the wheel disc and the circular wheel tire . From an abstract point of view, you can do without a disc and tire. All points of the wheel move on circular paths that span planes on which the axis of rotation is perpendicular.

The rotation can now have a direction, that is, it can point in one direction or in the opposite direction. When the circle rotates clockwise as seen by the observer, his gaze points in the same direction as the direction of the axis of rotation. This is an agreement (definition). See also direction of rotation .

If the internal mass distribution of a body rotating freely in space, e.g. B. of a celestial body changes, the axis of rotation of the body generally also changes. In general, however, the angular momentum is retained due to the conservation of angular momentum .

The combination of rotation and mirroring leads to the symmetry element of the rotating mirror axes, that of rotation and inversion to the rotation inversion axes ( gyroids ).

### Vehicle technology

Roll-Nick-Yaw angle ( Euler angle )
0 Rotation axes : Move:
↙ Longitudinal axis (roll / roll axis) : Roll , sway
transverse axis (pitch axis) : Nod, stamp
vertical axis (yaw axis) : Yaw (roll)

In automotive engineering, three important axes of rotation are used:

• Longitudinal axis : roll axis (engl. Roll axis ) or roll axis (in land vehicles): rotation about the longitudinally direction of the vehicle axis. The term banking is also used for the bank angle .${\ displaystyle x}$
• Transverse axis: pitch axis (engl. Pitch axis , rarely nick axis ) rotation about the axis of the vehicle.${\ displaystyle y}$
• High or vertical axis: yaw axis (engl. Yaw axis ) rotation about the axis of the reference system. The terms heading or azimuth are sometimes used for the direction angle .${\ displaystyle z}$

### chemistry

Rotation axes ( marked in blue ) in (from left to right) water, ammonia, xenon oxide tetrafluoride and hydrocyanic acid

The symmetry of a molecule can be described with symmetry elements. These indicate by which symmetry operations the molecule can be made to coincide with itself. Such a symmetry operation often corresponds to a rotation around an axis of rotation with a certain angle of rotation. The figure shows various examples of such rotary axes. They are marked with in the illustration . The index indicates the number of the axis of rotation. ${\ displaystyle C_ {n}}$${\ displaystyle n}$

### Crystallography

In crystallography the denticity of rotary axes also plays an important role. For example, when describing point groups or crystal classes with the help of the Hermann Mauguin symbolism, two-fold axes of rotation are designated directly with "2" and three-fold axes of rotation with "3". When naming room groups , combinations of rotation and translation are also required. The axes used are called screw axes.

## Individual evidence

1. Erwin Riedel and Christoph Janiak: Inorganische Chemie , 8th edition, 2011, Walter de Gruyter Verlag, p. 213, ISBN 978-3-11-022566-2 .