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Clockwise
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The clockwise direction
The counterclockwise or anticlockwise direction

Two-dimensional rotation can occur in two possible directions or senses of rotation. Clockwise motion (abbreviated CW) proceeds in the same direction as a clock's hands relative to the observer: from the top to the right, then down and then to the left, and back up to the top. The opposite sense of rotation or revolution is (in Commonwealth English) anticlockwise (ACW) or (in North American English) counterclockwise (CCW).[1] Three-dimensional rotation can have similarly defined senses when considering the corresponding angular velocity vector.

Terminology

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Viewed from the north, Earth rotates anticlockwise or counterclockwise

Before clocks were commonplace, the terms "sunwise" and the Scottish Gaelic-derived "deasil" (the latter ultimately from an Indo-European root for "right", shared with the Latin dexter) were used to describe clockwise motion, while "widdershins" (from Middle Low German weddersinnes, lit. "against direction") was used for counterclockwise motion.[2][3]

The terms clockwise and counterclockwise can only be applied to a rotational motion once a side of the rotational plane is specified, from which the rotation is observed. For example, the daily rotation of the Earth is clockwise when viewed from above the South Pole, and counterclockwise when viewed from above the North Pole (considering "above a point" to be defined as "farther away from the center of earth and on the same ray").

The shadow of a horizontal sundial in the Northern Hemisphere rotates clockwise

Clocks traditionally follow this sense of rotation because of the clock's predecessor: the sundial. Clocks with hands were first built in the Northern Hemisphere (see Clock), and they were made to work like horizontal sundials. In order for such a sundial to work north of the equator during spring and summer, and north of the Tropic of Cancer the whole year, the noon-mark of the dial must be placed northward of the pole casting the shadow. Then, when the Sun moves in the sky (from east to south to west), the shadow, which is cast on the sundial in the opposite direction, moves with the same sense of rotation (from west to north to east). This is why hours must be drawn in horizontal sundials in that manner, and why modern clocks have their numbers set in the same way, and their hands moving accordingly. For a vertical sundial (such as those placed on the walls of buildings, the dial being below the post), the movement of the sun is from right to top to left, and, accordingly, the shadow moves from left to down to right, i.e., counterclockwise. This effect is caused by the plane of the dial having been rotated through the plane of the motion of the sun and thus the shadow is observed from the other side of the dial's plane and is observed as moving in the opposite direction. Some clocks were constructed to mimic this. The best-known surviving example is the Münster astronomical clock, whose hands move counterclockwise.

Occasionally, clocks whose hands revolve counterclockwise are sold as a novelty. One historic Jewish clock was built that way in the Jewish Town Hall in Prague in the 18th century, using right-to-left reading in the Hebrew language. In 2014 under Bolivian president Evo Morales, the clock outside the Legislative Assembly in Plaza Murillo, La Paz, was shifted to counterclockwise motion to promote indigenous values.[4]

Usage

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Shop-work

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Typical nuts, screws, bolts, bottle caps, and jar lids are tightened (moved away from the observer) clockwise and loosened (moved towards the observer) counterclockwise in accordance with the right-hand rule.

Conventional direction of the axis of a rotating body

To apply the right-hand rule, place one's loosely clenched right hand above the object with the thumb pointing in the direction one wants the screw, nut, bolt, or cap ultimately to move, and the curl of the fingers, from the palm to the tips, will indicate in which way one needs to turn the screw, nut, bolt or cap to achieve the desired result. Almost all threaded objects obey this rule except for a few left-handed exceptions described below.

The reason for the clockwise standard for most screws and bolts is that supination of the arm, which is used by a right-handed person to tighten a screw clockwise, is generally stronger than pronation used to loosen.

Sometimes the opposite (left-handed, counterclockwise, reverse) sense of threading is used for a special reason. A thread might need to be left-handed to prevent operational stresses from loosening it. For example, some older cars and trucks had right-handed lug nuts on the right wheels and left-handed lug nuts on the left wheels, so that, as the vehicle moved forward, the lug nuts tended to tighten rather than loosen. For bicycle pedals, the one on the left must be reverse-threaded to prevent it unscrewing during use. Similarly, the flyer whorl of a spinning wheel uses a left-hand thread to keep it from loosening. A turnbuckle has right-handed threads on one end and left-handed threads on the other. Some gas fittings are left-handed to prevent disastrous misconnections: oxygen fittings are right-handed, but acetylene, propane, and other flammable gases are unmistakably distinguished by left-handed fittings.

Mathematics

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Further information: Signed angle

In trigonometry and mathematics in general, plane angles are conventionally measured counterclockwise, starting with 0° or 0 radians pointing directly to the right (or east), and 90° pointing straight up (or north). However, in navigation, compass headings increase clockwise around the compass face, starting with 0° at the top of the compass (the northerly direction), with 90° to the right (east).

A circle defined parametrically in a positive Cartesian plane by the equations x = cos t and y = sin t is traced counterclockwise as the angle t increases in value, from the right-most point at t = 0. An alternative formulation with sin and cos swapped gives a clockwise trace from the upper-most point, where t can be considered akin to a compass heading.

Games and activities

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In general, most card games, board games, parlor games, and multiple team sports play in a clockwise turn rotation in Western Countries and Latin America and there is typically resistance to playing counterclockwise. Traditionally, and for the most part today, turns pass counterclockwise in many Asian countries. In Western countries, when speaking and discussion activities take place in a circle, the position of the speaker tends to move clockwise, even though there is no requirement that it do so. Unlike with games, there is usually no objection if turns begin to move counterclockwise.[citation needed]

Notably, the game of baseball is played counterclockwise.

Alternative, normal right/left rotation

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As an alternative to using a clock to describe the rotation of a body, it is possible to use the right/left hand rule to determine the rotation. The thumb shall point in the normal direction of the surface in question and the four remaining fingers in the direction of the rotation of the surface. The resulting direction of the rotation is thereby[citation needed]

  • Normal right rotation = counterclockwise
  • Normal left rotation = clockwise

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Clockwise

View on Grokipedia
from Grokipedia
Clockwise, often abbreviated , denotes the direction of rotational motion that corresponds to the apparent movement of the hands on a traditional analog , proceeding from the 12 o'clock position toward the 3 o'clock position when viewed from the front. This convention originated from the behavior of s in the , where the shadow cast by the traces a clockwise path as the Sun moves across the sky from east to west due to . When mechanical clocks were developed in medieval , their mechanisms were designed to replicate this sundial motion, establishing clockwise as the standard for timepieces worldwide despite variations in the . In physics and , clockwise rotation is precisely defined using the right-hand grip rule: if the fingers of the right hand curl in the direction of rotation, the thumb points along the axis of rotation in the positive direction when viewed from the side where the rotation appears clockwise. This standardized convention facilitates consistent descriptions in fields such as , , and , where directionality relative to an observer is critical. The opposite direction, counterclockwise (CCW), follows a left-hand rule and is prevalent in certain natural phenomena or alternative conventions, but clockwise predominates in human-engineered systems like screw threads and vehicle wheels due to historical precedents.

Definition and Terminology

Directional Description

Clockwise refers to the direction of rotational motion matching the progression of an analog clock's hands as viewed from the front, proceeding from the top (12 o'clock position) to the right (3 o'clock), bottom (6 o'clock), left (9 o'clock), and back to the top. This path describes a circular trajectory turning to the right relative to the observer facing the clock face or rotating object. The definition depends on the observer's perspective; rotation appears clockwise when facing the side from which the clock hands advance in that manner, but reverses to counterclockwise when viewed from the opposite side. In technical descriptions, such as physics or engineering, clockwise is often specified with respect to a defined viewpoint to avoid ambiguity, typically the front or top view of the mechanism. Counterclockwise, also termed anticlockwise in British English, denotes the opposite direction, moving leftward from the top position. This convention originates from clock mechanisms but applies broadly to any rotational direction, with clockwise equated to a right-handed turn in the observer's plane.

Etymology and Pre-Clock Terms

The term "clockwise" originated in English during the as a of "clock," referring to timepieces with rotating hands, and the suffix "-wise," indicating manner or direction of motion. Its earliest documented use appears in 1874, in an article in describing rotational movement in alignment with the hands of analog clocks. This nomenclature formalized a convention already embedded in clock design since the late , when mechanical clocks in adopted the directional path of shadows in the , moving from left to right across the dial face. Prior to the invention and proliferation of mechanical clocks around 1300 CE, rotational directions lacked standardized mechanical references and were instead described relative to natural phenomena, particularly the sun's apparent daily arc or anatomical . In English and Scots usage, "sunwise" denoted motion following the sun's path across the sky as observed from the , with the term itself emerging in written records by 1775, though the concept predates it in and . Similarly, "deasil" (also spelled deiseil or deosil), borrowed into English around 1771 from deiseil meaning "southward" or "sunward," specifically indicated rightward or clockwise turning, often in ritual circumambulation to invoke good fortune, deriving ultimately from an Indo-European root shared with Latin dexter ("right"). The antonymous term "" (or withershins), entering Scots English circa 1513 from weddersinnes ("against the way" or "opposite direction"), described counterclockwise motion contrary to the sun's course, frequently connoting misfortune or reversal in traditional beliefs. These pre-clock descriptors, rooted in and cultural practices rather than mechanical analogy, persisted in and into the , even as "clockwise" gained prevalence with industrialized timekeeping. Their endurance highlights how directional conventions arose from empirical tracking of in agrarian societies, independent of horological technology.

Historical Origins

Sundials in the Northern Hemisphere

In the Northern Hemisphere, the shadow cast by a sundial's gnomon traces a clockwise path across the dial face due to the Sun's apparent daily motion from east to west across the southern sky. For a horizontal sundial with a vertical gnomon aligned perpendicular to the dial, the shadow originates near the western edge in the morning, progresses southward to the noon position, and continues eastward in the afternoon, creating a clockwise sweep when the dial is oriented facing south. This directional pattern stems from the Earth's rotation on its axis tilted at approximately 23.44 degrees relative to the orbital plane, positioning the Sun's path to the south of observers at latitudes greater than 0 degrees north. The , typically a straight rod or blade, must be oriented parallel to the Earth's rotational axis, inclined at an angle equal to the local and pointing toward to accurately project the shadow onto hyperbolic or circular hour lines arranged in a clockwise sequence from the 6 a.m. to 6 p.m. positions. Vertical sundials facing exhibit a similar clockwise shadow progression, with the tip of the shadow descending from upper hour lines to lower ones as the day advances. This geometry ensures mean approximation, though adjustments for are required for precision, as the Earth's elliptical orbit causes variations up to 16 minutes from uniform clock time. Sundials employing this clockwise convention date to ancient civilizations, with Egyptian shadow clocks—simple gnomons on marked surfaces—evident from around 1500 BCE, used to divide daylight into 12 temporal hours. Greek advancements around 300 BCE refined dial designs, incorporating latitude-specific inclinations to maintain the clockwise hour progression, influencing Roman and medieval European timekeeping. This established solar motion directly informed the hand rotation of early mechanical clocks in 14th-century Europe, which mimicked the familiar shadow direction to align with users' expectations in the . In contrast, at the , shadows on days trace a straight west-to-east line without clockwise curvature, highlighting the latitude-dependent nature of the convention.

Transition to Mechanical Clocks

The first mechanical clocks emerged in during the late , primarily as large, weight-driven tower installations in monasteries, cathedrals, and civic structures, replacing less reliable predecessors like water clocks and complementing sundials for public time signaling. These early devices, often equipped with striking mechanisms to chime hours via bells, lacked the precision of modern clocks but introduced automated, continuous motion through mechanisms that regulated falling weights. By the early , such clocks proliferated across , with documented examples including the 1324 installation in and the 1335 clock in , marking a technological leap driven by monastic needs for precise timings and urban demands for coordinated daily activities. A key aspect of this transition involved replicating the directional conventions of sundials prevalent in the , where the gnomon's shadow traces a path from left to right—east to west—mirroring the sun's apparent daily arc and defining what later became termed "clockwise" . Clockmakers calibrated the hands of these mechanical dials to follow this same trajectory, ensuring intuitive readability for observers familiar with solar shadows that progressed rightward from the noon marker, rather than adopting an arbitrary or reversed direction that would have required retraining. This imitation stemmed from practical continuity: sundials, used since antiquity in , had standardized hour markings with arranged for shadow movement in the clockwise sense, and mechanical faces inherited this layout to minimize user confusion in time interpretation. The adoption solidified by the mid-14th century as clock production scaled, with and pinions engineered for unidirectional transmission that aligned with the sundial-derived progression, embedding clockwise motion as the normative standard for Western timepieces and influencing global conventions thereafter. Unlike water clocks, which lacked visual directional cues, or early verge-and-foliot escapements that prioritized regularity over symbolism, this solar emulation reflected a causal link to astronomical , prioritizing empirical alignment with diurnal cycles over novel inventions.

Applications in Technology and Mechanics

Timekeeping Mechanisms

In mechanical clocks, the transmits power from the or falling weight to the , regulating the release of to maintain consistent motion. The motion works, a specialized portion of the , drives the hour, minute, and seconds hands via concentric pinions and wheels, configured to rotate clockwise when viewed from the dial side. This arrangement ensures the minute hand completes one revolution per hour and the hour hand one per 12 hours, with gear ratios typically yielding a 12:1 reduction between minute and hour wheels. The direction of rotation in the is determined by the meshing of , where each successive pair reverses direction; clock designs incorporate an even or odd number of reversals as needed to achieve clockwise hand motion from the front, aligning with established conventions. Escapements such as the or verge release impulses that propagate through the , preserving the clockwise sweep despite the alternating tendencies of individual . In modern quartz analog timepieces, a quartz crystal vibrates at 32,768 Hz under electrical oscillation, dividing down to drive a stepper motor that advances the gear train in discrete steps, replicating the clockwise progression of mechanical hands. The motor shaft connects to the seconds wheel, turning it 6 degrees per minute (or 1.5 degrees per second in smooth variants), with subsequent gears maintaining the traditional direction.

Threaded Fasteners and Tools

Threaded fasteners, including , bolts, and nuts, overwhelmingly utilize right-hand threads, where —as observed from the tool end—drives the fastener forward into the receiving material, effecting a secure connection. This directional convention adheres to the : extending the right parallel to the axis of in the advancement direction positions the curled fingers to trace the path required for tightening. The ergonomic basis for this standardization traces to human physiology, favoring the majority right-handed population by aligning with intuitive application using the dominant hand. International standards, such as ISO 261 for metric screw threads established in 1973 and revised in 1998, codify thread profiles and dimensions but presuppose the right-hand orientation as the default for general-purpose fasteners, ensuring interoperability across manufacturing. Historical precedents date to early 19th-century efforts, including Joseph Whitworth's 1841 proposal for uniform British threads at 55-degree angles, which implicitly adopted the right-hand form prevalent in contemporary and screws. Left-hand threads, tightened counterclockwise, remain exceptional, deployed in scenarios where ambient rotation might otherwise loosen standard fasteners, such as left-side pedals or certain components, comprising less than 1% of commercial production. Tools for engaging these fasteners, including manual screwdrivers, torque wrenches, and powered drills with compatible bits, incorporate mechanisms optimized for clockwise tightening to maximize and minimize slippage. For instance, wrenches allow unidirectional clockwise drive, reversing only for loosening, which enhances in assembly tasks. Precision applications, like or automotive assembly, often mandate calibrated in the clockwise direction to achieve specified clamping forces, typically ranging from 5 Nm for small screws to over 500 Nm for large structural bolts, preventing failures from under- or over-tightening. This clockwise permeates global engineering practice, with deviations requiring explicit designation to avoid mismatch errors.

Everyday Objects and Devices

Many household containers, including jars and bottles, feature lids with right-handed threads that tighten when rotated clockwise, securing contents against leakage and during storage and transport. This design, rooted in the for , predominates in consumer packaging standards to minimize accidental loosening from vibrations or handling. Plumbing components such as faucets and shutoff valves follow a similar convention, closing or reducing flow via clockwise turns, which intuitively mirrors the tightening action for right-handed users. Gate valves in lines, for instance, require clockwise to fully seal and halt movement, a mechanism ensuring reliable control in residential systems. Ceiling fans incorporate reversible set to clockwise rotation (viewed from below) in winter, generating an that circulates trapped warm air downward for better room heating and energy savings at low speeds. Analog knobs on audio devices, like volume controls on radios, also adhere to clockwise advancement to raise output levels, standardizing operation across for user familiarity.

Usage in Mathematics and Physics

Geometric Rotations and Angles

In , clockwise describes the motion of a point or figure around a central axis in the same direction as the hands of an analog clock, progressing from the 12 o'clock position toward 3, 6, 9, and back to 12. This direction is opposite to counterclockwise and is fundamental in defining . The standard mathematical convention for measuring angles in the Cartesian plane places the vertex at the origin with the initial side along the positive x-axis. Positive angles are generated by rotating the terminal side counterclockwise from the initial side, while clockwise rotations produce negative angles of equal magnitude. For instance, a -90° angle corresponds to a 90° clockwise rotation, equivalent to a 270° counterclockwise rotation in terms of terminal position. Specific transformation rules apply to clockwise rotations of common angles around the origin. A 90° clockwise maps a point (x, y) to (y, -x); 180° to (-x, -y); 270° to (-y, x); and 360° returns to (x, y). These rules preserve distances and angles, classifying clockwise rotations as rigid transformations or isometries in . In , clockwise rotations align with negative arguments in standard functions, ensuring computational consistency; for example, sin(-θ) = -sin(θ) reflects the odd symmetry derived from the counterclockwise-positive convention. This framework originated from historical astronomical observations but was formalized in Cartesian coordinates to facilitate vector analysis and representations, where multiplication by e^{-iθ} denotes .

Right-Hand Rule and Vector Conventions

In mathematics and physics, the right-hand rule establishes the convention for assigning directions to rotational quantities, such as angular velocity vectors and torque. The rule dictates that the vector points along the axis of rotation with its direction determined by orienting the right hand such that the thumb aligns with the vector while the curled fingers indicate the sense of positive rotation. This convention designates counterclockwise rotation as positive when viewed along the direction opposite to the vector (i.e., looking towards the thumb's tip from the vector's base). Consequently, clockwise rotation, when observed from the same perspective, corresponds to a negative scalar value for the angular quantity or a reversal of the vector direction. This vector convention ensures consistency across vector operations, including the , where the determines the resultant direction perpendicular to the plane of the input vectors. In standard right-handed Cartesian coordinates, a positive rotation about the z-axis (counterclockwise in the xy-plane when viewed from the positive z-direction) yields an angular velocity vector ω⃗=ωk^\vec{\omega} = \omega \hat{k}
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