# Direction of rotation

The terms of rotation and direction of rotation , even of circulation or circulation direction called, indicate the direction in which, from a certain point of view, points to a circular move being made between the two alternatives

• clockwise , clockwise or in the geodetically positive direction of rotation or rotation (in the mathematically negative sense)

such as

• counterclockwise , counterclockwise or in the mathematically positive direction of rotation or rotation (in the geodetically negative sense)

differs.

## Definitions

"
Clockwise" or "clockwise"
"Counterclockwise" or
"counterclockwise"
Analog wrist watch

### Clockwise

Let there be a circular area that rotates about an axis running perpendicularly through its center point and is viewed in the direction of the axis of rotation. If points on the surface that are above the center point describe a movement running to the right , the direction of rotation is “right”, “clockwise”, or “in the mathematically negative direction”.

### Left turning

Let there be a circular area that rotates about an axis running perpendicularly through its center point and is viewed in the direction of the axis of rotation. If points on the surface that are above the center point describe a movement to the left during rotation , the direction of rotation is “left”, “counterclockwise”, or “in the mathematically positive direction of rotation”.

Left: left-handed coordinate system ; right: right-handed coordinate system

### Mathematical definitions relating to coordinate systems

The above information "in the mathematically positive direction of rotation" or "in the mathematically negative direction of rotation" presuppose the so-called right - handed coordinate system (right-hand in the figure) that is commonly used .

In mathematics, there is also the so - called left - handed coordinate system (left in the figure) with reversed directions of rotation. Here “in the mathematically positive direction of rotation” is identical with “clockwise”.

In the two-dimensional xy system, regardless of whether it is right-handed or left-handed, the following applies: The positive direction of rotation is the one through which the positive x-axis is transferred to the positive y-axis in the shortest possible way .

In the three-dimensional xyz system, the following applies analogously, regardless of whether you are right-handed or left-handed: In both cases, the definition applies that the positive direction of rotation (around the z-axis) is the one through which the positive x-axis takes the shortest path to the positive y- Axis is transferred. When rotating around the x-axis, the positive direction of rotation is that which in turn transfers the positive y-axis to the positive z-axis by the shortest possible route . When rotating around the y-axis, it is “positive”, which converts the positive z-axis to the positive x-axis by the shortest possible route.

### Memory aid

for the relationship between right / left turning and right / left-handed coordinate system:

If you look from below, that is, in the direction of the positive z-axis , on the xy-plane , this rotates
• with a right-handed coordinate system to the right , i.e. clockwise ,
• with a left-handed coordinate system to the left , i.e. counterclockwise .

### Direction of rotation and axial vector

When depicting rotations and rotational quantities such as angles, angular velocities, angular accelerations, torques, pulses, etc. with the help of axial vectors , their orientation corresponds - clearly: the direction of their arrowhead - with the direction of rotation: they can be found with the help of the left, depending on the coordinate system selected - or right-fist rule .

## Examples for the application of the direction of rotation

### Clock hands

Because the hands of most clocks are clockwise, clockwise rotation is usually simply referred to as clockwise ( UZS ). Left-rotating clocks are rare. In Münster there is a left-turning astronomical clock from the 16th century, when clockwise rotation of astronomical and all other clocks had not yet established itself. The presumed reason that clock hands turned clockwise is the fact that the rod shadow of horizontal sundials in the northern hemisphere also rotates in this direction (sundials whose time is displayed with the shadow of a rod on a vertical wall turn to the left). Practically the entire development of timing devices took place in the northern hemisphere . In the formation of the word “clockwise”, sense has retained the original meaning of “direction”. In 2007 it was decided in Bolivia to turn the clock on the congress building to the left to demonstrate independence from the states of the northern hemisphere.

Angle of rotation of cars and other land vehicles
Angle of rotation of ships and other watercraft

In geodesy , a positive sense of rotation is synonymous with a clockwise rotation (cf. Cartesian coordinate system (geodesy) ), with angles of rotation usually being measured from the north direction.

In navigation, on the other hand, depending on the vehicle type and the right-handed reference system used, both clockwise and counterclockwise rotations are considered positive : For land vehicles that use the ENU (East-North-Up) system as the reference system, a positive rotation one counter-clockwise , whereas in spacecraft, aircraft and watercraft including submarines, which continue to use the NED system (North-East-Down) as a reference for reasons of compatibility with the traditional compass direction , one positive rotation is one clockwise .

How this apparent contradiction can be explained is shown in the adjacent figures: ENU and NED systems are similar in that the xy plane of both runs parallel to the earth's surface, while the z-axis perpendicular to it points away from the center of the earth in the case of land vehicles , in contrast to spacecraft, aircraft and watercraft towards the center of the earth (see also roll-pitch-yaw angle: details ).

### meteorology

In meteorology (and thus also in the navigation in aircraft, ships) is a right-handed designated wind as right-handed , a left-handed wind than back rotation .

A screw is provided with a right-hand thread (also called a right-hand thread ) if it moves away from the viewer when it is turned clockwise into the nut (further away from the viewer) .

Left-hand thread screws are only used for special purposes, e.g. B. in turnbuckles , on gas bottles for flammable gases, for parts of bicycles ( pedals and inner bearing shells ), as well as operating screws of thermostats .

### Motor shafts

The majority of all internal combustion engines have clockwise rotating crankshafts (cars and trucks; by definition, looking from the front (fan wheel) to the rear (flywheel)). The direction of rotation of prime movers (e.g. electric motors) is specified as that which can be seen when looking at the front of the output side (cannot be used with output on both sides). According to this, a drill rotates counterclockwise. The direction of motor rotation is often marked with the help of an arrow (for example on grinding machines ) or with the international abbreviations CCW ( Counterclockwise , counterclockwise) and CW ( ClockWise , like the clock).

### propeller

For the designation of the direction of rotation of propellers of watercraft, the forward drive is decisive: if they turn to the right when moving forward, they are called clockwise, if they turn to the left when moving forward, they are called counterclockwise. The wheel effect that occurs when reversing moves the stern of the ship to the left when the propeller is rotating to the right and to the right when the propeller is rotating to the left.

In ships with propellers arranged in pairs, these are operated in opposite directions. As a result, the torques on the boat hull cancel each other out.

### Rotation of the plane of polarization of light

In chemistry, clockwise or counter-clockwise rotation is an optically active substance , i.e. a substance that rotates the plane of polarization of polarized light in that same direction. The reference direction is the viewing direction opposite to the direction of movement of the light. Direct application is e.g. B. the circular polarizing layer on a 3D television . A well-known example from food chemistry are the mutually enantiomeric (mirror-image) compounds L - (+) - lactic acid and D - (-) - lactic acid in clockwise or counterclockwise rotating yoghurt cultures.

### Galaxies

In astronomy , spiral galaxies are characterized, among other things, by their direction of rotation under which they appear when viewed from Earth. The direction of rotation can be recognized by the shape and arrangement of its spiral arms. A distinction is made between “S-shaped” galaxies that turn left and “Z-shaped” galaxies that turn right.

### Walkways

The Kaaba is circled counterclockwise .

Since the majority of Europeans are right-handed , walking paths ( supermarket , short-distance running , speed skating and cycling races in sports stadiums ) are usually laid out in an anti-clockwise direction. Right-handers tend to take larger steps with their right leg and therefore prefer left turns.

#### Walking around sanctuaries

Catholic and Orthodox clergymen up to Pope and Patriarch circle the altar counterclockwise during the service , as do Muslims the Kaaba and Bonpos their shrines, Buddhists and Hindus however clockwise .