1.
International standard
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International standards are standards developed by international standards organizations. International standards are available for consideration and use worldwide, the most prominent organization is the International Organization for Standardization. International standards may be used either by application or by a process of modifying an international standard to suit local conditions. Technical barriers arise when different groups together, each with a large user base. Establishing international standards is one way of preventing or overcoming this problem, the implementation of standards in industry and commerce became highly important with the onset of the Industrial Revolution and the need for high-precision machine tools and interchangeable parts. Henry Maudslay developed the first industrially practical screw-cutting lathe in 1800, maudslays work, as well as the contributions of other engineers, accomplished a modest amount of industry standardization, some companies in-house standards spread a bit within their industries. Joseph Whitworths screw thread measurements were adopted as the first national standard by companies around the country in 1841 and it came to be known as the British Standard Whitworth, and was widely adopted in other countries. By the end of the 19th century differences in standards between companies were making trade increasingly difficult and strained, the Engineering Standards Committee was established in London in 1901 as the worlds first national standards body. After the First World War, similar national bodies were established in other countries, by the mid to late 19th century, efforts were being made to standardize electrical measurement. An important figure was R. E. B, Crompton, who became concerned by the large range of different standards and systems used by electrical engineering companies and scientists in the early 20th century. Many companies had entered the market in the 1890s and all chose their own settings for voltage, frequency, current, adjacent buildings would have totally incompatible electrical systems simply because they had been fitted out by different companies. Crompton could see the lack of efficiency in this system and began to consider proposals for a standard for electric engineering. In 1904, Crompton represented Britain at the Louisiana Purchase Exposition in Saint Louis as part of a delegation by the Institute of Electrical Engineers. He presented a paper on standardisation, which was so well received that he was asked to look into the formation of a commission to oversee the process. By 1906 his work was complete and he drew up a permanent constitution for the first international standards organization, the body held its first meeting that year in London, with representatives from 14 countries. In honour of his contribution to electrical standardisation, Lord Kelvin was elected as the bodys first President, the International Federation of the National Standardizing Associations was founded in 1926 with a broader remit to enhance international cooperation for all technical standards and specifications. The body was suspended in 1942 during World War II, after the war, ISA was approached by the recently formed United Nations Standards Coordinating Committee with a proposal to form a new global standards body. List of international common standards List of technical standard organisations Global Frameworks and standards organized along function lines, accessed 2014 ^ Cordova
2.
Units of measurement
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A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same quantity. Any other value of quantity can be expressed as a simple multiple of the unit of measurement. For example, length is a physical quantity, the metre is a unit of length that represents a definite predetermined length. When we say 10 metres, we actually mean 10 times the definite predetermined length called metre, the definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common, now there is a global standard, the International System of Units, the modern form of the metric system. In trade, weights and measures is often a subject of regulation, to ensure fairness. The International Bureau of Weights and Measures is tasked with ensuring worldwide uniformity of measurements, metrology is the science for developing nationally and internationally accepted units of weights and measures. In physics and metrology, units are standards for measurement of quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method, a standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights, science, medicine, and engineering often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measurement can aid researchers in problem solving, in the social sciences, there are no standard units of measurement and the theory and practice of measurement is studied in psychometrics and the theory of conjoint measurement. A unit of measurement is a quantity of a physical property. Units of measurement were among the earliest tools invented by humans, primitive societies needed rudimentary measures for many tasks, constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. Weights and measures are mentioned in the Bible and it is a commandment to be honest and have fair measures. As of the 21st Century, multiple unit systems are used all over the world such as the United States Customary System, the British Customary System, however, the United States is the only industrialized country that has not yet completely converted to the Metric System. The systematic effort to develop an acceptable system of units dates back to 1790 when the French National Assembly charged the French Academy of Sciences to come up such a unit system. After this treaty was signed, a General Conference of Weights, the CGPM produced the current SI system which was adopted in 1954 at the 10th conference of weights and measures. Currently, the United States is a society which uses both the SI system and the US Customary system
3.
Space
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Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, in Isaac Newtons view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space. Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley attempted to refute the visibility of spatial depth in his Essay Towards a New Theory of Vision. Kant referred to the experience of space in his Critique of Pure Reason as being a pure a priori form of intuition. In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in space is conceived as curved. According to Albert Einsteins theory of relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a model for the shape of space. In the seventeenth century, the philosophy of space and time emerged as an issue in epistemology. At its heart, Gottfried Leibniz, the German philosopher-mathematician, and Isaac Newton, unoccupied regions are those that could have objects in them, and thus spatial relations with other places. For Leibniz, then, space was an abstraction from the relations between individual entities or their possible locations and therefore could not be continuous but must be discrete. Space could be thought of in a way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people, but since there would be no observational way of telling these universes apart then, according to the identity of indiscernibles, there would be no real difference between them. According to the principle of sufficient reason, any theory of space that implied that there could be two possible universes must therefore be wrong. Newton took space to be more than relations between objects and based his position on observation and experimentation
4.
Time
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Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is often referred to as the dimension, along with the three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems. Two contrasting viewpoints on time divide prominent philosophers, one view is that time is part of the fundamental structure of the universe—a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is referred to as Newtonian time. This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, Time in physics is unambiguously operationally defined as what a clock reads. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities, Time is used to define other quantities—such as velocity—so defining time in terms of such quantities would result in circularity of definition. The operational definition leaves aside the question there is something called time, apart from the counting activity just mentioned, that flows. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Furthermore, it may be there is a subjective component to time. Temporal measurement has occupied scientists and technologists, and was a motivation in navigation. Periodic events and periodic motion have long served as standards for units of time, examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is also of significant social importance, having economic value as well as value, due to an awareness of the limited time in each day. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day, increasingly, personal electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of an event as to hour or date is obtained by counting from a fiducial epoch—a central reference point. Artifacts from the Paleolithic suggest that the moon was used to time as early as 6,000 years ago. Lunar calendars were among the first to appear, either 12 or 13 lunar months, without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months
5.
Angle
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In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane, Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation and this measure is the ratio of the length of a circular arc to its radius. In the case of an angle, the arc is centered at the vertex. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word angle comes from the Latin word angulus, meaning corner, cognate words are the Greek ἀγκύλος, meaning crooked, curved, both are connected with the Proto-Indo-European root *ank-, meaning to bend or bow. Euclid defines a plane angle as the inclination to each other, in a plane, according to Proclus an angle must be either a quality or a quantity, or a relationship. In mathematical expressions, it is common to use Greek letters to serve as variables standing for the size of some angle, lower case Roman letters are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples, in geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB, sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex. However, in geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant. Otherwise, a convention may be adopted so that ∠BAC always refers to the angle from B to C. Angles smaller than an angle are called acute angles. An angle equal to 1/4 turn is called a right angle, two lines that form a right angle are said to be normal, orthogonal, or perpendicular. Angles larger than an angle and smaller than a straight angle are called obtuse angles. An angle equal to 1/2 turn is called a straight angle, Angles larger than a straight angle but less than 1 turn are called reflex angles
6.
Radian
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The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement in radians of the angle that it subtends. The unit was formerly an SI supplementary unit, but this category was abolished in 1995, separately, the SI unit of solid angle measurement is the steradian. The radian is represented by the symbol rad, so for example, a value of 1.2 radians could be written as 1.2 rad,1.2 r,1. 2rad, or 1. 2c. Radian describes the angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Conversely, the length of the arc is equal to the radius multiplied by the magnitude of the angle in radians. As the ratio of two lengths, the radian is a number that needs no unit symbol, and in mathematical writing the symbol rad is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and it follows that the magnitude in radians of one complete revolution is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees, the concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. He described the radian in everything but name, and he recognized its naturalness as a unit of angular measure, the idea of measuring angles by the length of the arc was already in use by other mathematicians. For example, al-Kashi used so-called diameter parts as units where one part was 1/60 radian. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson at Queens College, Belfast. He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, in 1874, after a consultation with James Thomson, Muir adopted radian. As stated, one radian is equal to 180/π degrees, thus, to convert from radians to degrees, multiply by 180/π. The length of circumference of a circle is given by 2 π r, so, to convert from radians to gradians multiply by 200 / π, and to convert from gradians to radians multiply by π /200. This is because radians have a mathematical naturalness that leads to a more elegant formulation of a number of important results, most notably, results in analysis involving trigonometric functions are simple and elegant when the functions arguments are expressed in radians. Because of these and other properties, the trigonometric functions appear in solutions to problems that are not obviously related to the functions geometrical meanings
7.
Degree (angle)
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A degree, usually denoted by °, is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of measure is the radian. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians, the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the path over the course of the year. Some ancient calendars, such as the Persian calendar, used 360 days for a year, the use of a calendar with 360 days may be related to the use of sexagesimal numbers. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle, a chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree, Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes, eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. Furthermore, it is divisible by every number from 1 to 10 except 7 and this property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case more than one of these factors has come into play. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates, degree measurements may be written using decimal degrees, with the symbol behind the decimals. Alternatively, the sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes, and one minute into 60 seconds, use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are represented by a single and double prime. For example,40. 1875° = 40° 11′ 15″, or, using quotation mark characters, additional precision can be provided using decimals for the arcseconds component. The older system of thirds, fourths, etc. which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today
8.
Minute and second of arc
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A minute of arc, arcminute, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn, a second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 of a radian. To express even smaller angles, standard SI prefixes can be employed, the number of square arcminutes in a complete sphere is 4 π2 =466560000 π ≈148510660 square arcminutes. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted. One arcminute is thus written 1′ and it is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it. The standard symbol for the arcsecond is the prime, though a double quote is commonly used where only ASCII characters are permitted. One arcsecond is thus written 1″ and it is also abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations. This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the format by default. An arcsecond is approximately the angle subtended by a U. S. dime coin at a distance of 4 kilometres, a milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth, since antiquity the arcminute and arcsecond have been used in astronomy. The principal exception is Right ascension in equatorial coordinates, which is measured in units of hours, minutes. These small angles may also be written in milliarcseconds, or thousandths of an arcsecond, the unit of distance, the parsec, named from the parallax of one arcsecond, was developed for such parallax measurements. It is the distance at which the radius of the Earths orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia is hoped to measure star positions to 20 microarcseconds when it begins producing catalog positions sometime after 2016, there are about 1.3 trillion µas in a turn. Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond, space telescopes are not affected by the Earths atmosphere but are diffraction limited. For example, the Hubble space telescope can reach a size of stars down to about 0. 1″
9.
Solid angle
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In geometry, a solid angle is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the object appears to an observer looking from that point, in the International System of Units, a solid angle is expressed in a dimensionless unit called a steradian. A small object nearby may subtend the same angle as a larger object farther away. For example, although the Moon is much smaller than the Sun, indeed, as viewed from any point on Earth, both objects have approximately the same solid angle as well as apparent size. This is evident during a solar eclipse, an objects solid angle in steradians is equal to the area of the segment of a unit sphere, centered at the angles vertex, that the object covers. A solid angle in steradians equals the area of a segment of a sphere in the same way a planar angle in radians equals the length of an arc of a unit circle. Solid angles are used in physics, in particular astrophysics. The solid angle of an object that is far away is roughly proportional to the ratio of area to squared distance. Here area means the area of the object when projected along the viewing direction. The solid angle of a sphere measured from any point in its interior is 4π sr, Solid angles can also be measured in square degrees, in square minutes and square seconds, or in fractions of the sphere, also known as spat. In spherical coordinates there is a formula for the differential, d Ω = sin θ d θ d φ where θ is the colatitude, at the equator you see all of the celestial sphere, at either pole only one half. Let OABC be the vertices of a tetrahedron with an origin at O subtended by the triangular face ABC where a →, b →, c → are the positions of the vertices A, B and C. Define the vertex angle θa to be the angle BOC and define θb, let φab be the dihedral angle between the planes that contain the tetrahedral faces OAC and OBC and define φac, φbc correspondingly. When implementing the above equation care must be taken with the function to avoid negative or incorrect solid angles. One source of errors is that the scalar triple product can be negative if a, b, c have the wrong winding. Computing abs is a sufficient solution since no other portion of the equation depends on the winding, the other pitfall arises when the scalar triple product is positive but the divisor is negative. Indices are cycled, s0 = sn and s1 = sn +1, the solid angle of a latitude-longitude rectangle on a globe is s r, where φN and φS are north and south lines of latitude, and θE and θW are east and west lines of longitude. Mathematically, this represents an arc of angle φN − φS swept around a sphere by θE − θW radians, when longitude spans 2π radians and latitude spans π radians, the solid angle is that of a sphere
10.
Steradian
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The steradian or square radian is the SI unit of solid angle. It is used in geometry, and is analogous to the radian which quantifies planar angles. The name is derived from the Greek stereos for solid and the Latin radius for ray and it is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol sr is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian, the steradian was formerly an SI supplementary unit, but this category was abolished in 1995 and the steradian is now considered an SI derived unit. A steradian can be defined as the angle subtended at the center of a unit sphere by a unit area on its surface. For a general sphere of radius r, any portion of its surface with area A = r2 subtends one steradian, because the surface area A of a sphere is 4πr2, the definition implies that a sphere measures 4π steradians. By the same argument, the solid angle that can be subtended at any point is 4π sr. Since A = r2, it corresponds to the area of a cap. Therefore one steradian corresponds to the angle of the cross-section of a simple cone subtending the plane angle 2θ, with θ given by, θ = arccos = arccos = arccos ≈0.572 rad. This angle corresponds to the plane angle of 2θ ≈1.144 rad or 65. 54°. A steradian is also equal to the area of a polygon having an angle excess of 1 radian, to 1/4π of a complete sphere. The solid angle of a cone whose cross-section subtends the angle 2θ is, Ω =2 π s r. In two dimensions, an angle is related to the length of the arc that it spans, θ = l r r a d where l is arc length, r is the radius of the circle. For example, a measurement of the width of an object would be given in radians. At the same time its visible area over ones visible field would be given in steradians. Just as the area of a circle is related to its diameter or radius. One-dimensional circular measure has units of radians or degrees, while two-dimensional spherical measure is expressed in steradians, in higher dimensional mathematical spaces, units for analogous solid angles have not been explicitly named. When they are used, they are dealt with by analogy with the circular or spherical cases and that is, as a proportion of the relevant unit hypersphere taken up by the generalized angle, or point set expressed in spherical coordinates
11.
Length
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In geometric measurements, length is the most extended dimension of an object. In the International System of Quantities, length is any quantity with dimension distance, in other contexts length is the measured dimension of an object. For example, it is possible to cut a length of a wire which is shorter than wire thickness. Length may be distinguished from height, which is vertical extent, and width or breadth, length is a measure of one dimension, whereas area is a measure of two dimensions and volume is a measure of three dimensions. In most systems of measurement, the unit of length is a base unit, measurement has been important ever since humans settled from nomadic lifestyles and started using building materials, occupying land and trading with neighbours. As society has become more technologically oriented, much higher accuracies of measurement are required in a diverse set of fields. One of the oldest units of measurement used in the ancient world was the cubit which was the length of the arm from the tip of the finger to the elbow. This could then be subdivided into shorter units like the foot, hand or finger, the cubit could vary considerably due to the different sizes of people. After Albert Einsteins special relativity, length can no longer be thought of being constant in all reference frames. Thus a ruler that is one meter long in one frame of reference will not be one meter long in a frame that is travelling at a velocity relative to the first frame. This means length of an object is variable depending on the observer, in the physical sciences and engineering, when one speaks of units of length, the word length is synonymous with distance. There are several units that are used to measure length, in the International System of Units, the basic unit of length is the metre and is now defined in terms of the speed of light. The centimetre and the kilometre, derived from the metre, are commonly used units. In U. S. customary units, English or Imperial system of units, commonly used units of length are the inch, the foot, the yard, and the mile. Units used to denote distances in the vastness of space, as in astronomy, are longer than those typically used on Earth and include the astronomical unit, the light-year. Dimension Distance Orders of magnitude Reciprocal length Smoot Unit of length
12.
Metre
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The metre or meter, is the base unit of length in the International System of Units. The metre is defined as the length of the path travelled by light in a vacuum in 1/299792458 seconds, the metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a metre bar. In 1960, the metre was redefined in terms of a number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted, the imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use meter. Measuring devices are spelled -meter in all variants of English, the suffix -meter has the same Greek origin as the unit of length. This range of uses is found in Latin, French, English. Thus calls for measurement and moderation. In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, as a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. In 1668, Wilkins proposed using Christopher Wrens suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm, no official action was taken regarding this suggestion. In the 18th century, there were two approaches to the definition of the unit of length. One favoured Wilkins approach, to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth of the length of a quadrant along the Earths meridian, that is, the distance from the Equator to the North Pole. This means that the quadrant would have defined as exactly 10000000 metres at that time. To establish a universally accepted foundation for the definition of the metre, more measurements of this meridian were needed. This portion of the meridian, assumed to be the length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator
13.
Speed of light
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The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299792458 metres per second, it is exact because the unit of length, the metre, is defined from this constant, according to special relativity, c is the maximum speed at which all matter and hence information in the universe can travel. It is the speed at which all particles and changes of the associated fields travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the reference frame of the observer. In the theory of relativity, c interrelates space and time, the speed at which light propagates through transparent materials, such as glass or air, is less than c, similarly, the speed of radio waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the index n of the material. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, the light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light limits the theoretical maximum speed of computers. The speed of light can be used time of flight measurements to measure large distances to high precision. Ole Rømer first demonstrated in 1676 that light travels at a speed by studying the apparent motion of Jupiters moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, in 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 299792458 m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units as the distance travelled by light in vacuum in 1/299792458 of a second, as a result, the numerical value of c in metres per second is now fixed exactly by the definition of the metre. The speed of light in vacuum is usually denoted by a lowercase c, historically, the symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant later shown to equal √2 times the speed of light in vacuum, in 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum. This article uses c exclusively for the speed of light in vacuum, since 1983, the metre has been defined in the International System of Units as the distance light travels in vacuum in 1⁄299792458 of a second
14.
Height
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Height is the measure of vertical distance, either how tall something is, or how high up it is. For example The height of the building is 50 m or The height of the airplane is 10,000 m, when used to describe how high something like an airplane or mountain peak is from sea level, height is more often called altitude. Height is measured along the axis between a specified point and another. English high is derived from Old English hēah, ultimately from Proto-Germanic *xauxa-z, the derived noun height, also the obsolete forms heighth and highth, is from Old English híehþo, later héahþu, as it were from Proto-Germanic *xaux-iþa. In elementary models of space, height may indicate the third dimension, height is normal to the plane formed by the length and width. Height is also used as a name for more abstract definitions. Although height is relative to a plane of reference, most measurements of height in the world are based upon a zero surface. Both altitude and elevation, two synonyms for height, are defined as the position of a point above the mean sea level. One can extend the surface under the continents, naively. In practice, the sea level under a continent has to be computed from gravity measurements, instead of using the sea level, geodesists often prefer to define height from the surface of a reference ellipsoid, see Geodetic system, vertical datum. Defining the height of geographic landmarks becomes a question of reference, in aviation terminology, the terms height, altitude, and elevation are not synonyms. Usually, the altitude of an aircraft is measured from sea level, Elevation is also measured from sea level, but is most often regarded as a property of the ground. Thus, elevation plus height can equal altitude, but the term altitude has several meanings in aviation, Human height is one of the areas of study within anthropometry. While height variations within a population are largely genetic, height variations between populations are mostly environmental, the United Nations uses height to monitor changes in the nutrition of developing nations. In human populations, average height can distill down complex data about the birth, upbringing, social class, diet. Acrophobia Centimetre–gram–second system of units Chinese units of measurement Elevation Human height Imperial units International System of Units United States customary units
15.
Diameter
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In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle, both definitions are also valid for the diameter of a sphere. In more modern usage, the length of a diameter is called the diameter. In this sense one speaks of the rather than a diameter, because all diameters of a circle or sphere have the same length. Both quantities can be calculated efficiently using rotating calipers, for a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance. For an ellipse, the terminology is different. A diameter of an ellipse is any chord passing through the midpoint of the ellipse, for example, conjugate diameters have the property that a tangent line to the ellipse at the endpoint of one of them is parallel to the other one. The longest diameter is called the major axis, the word diameter is derived from Greek διάμετρος, diameter of a circle, from διά, across, through and μέτρον, measure. It is often abbreviated DIA, dia, d, or ⌀, the definitions given above are only valid for circles, spheres and convex shapes. However, they are cases of a more general definition that is valid for any kind of n-dimensional convex or non-convex object. The diameter of a subset of a space is the least upper bound of the set of all distances between pairs of points in the subset. So, if A is the subset, the diameter is sup, if the distance function d is viewed here as having codomain R, this implies that the diameter of the empty set equals −∞. Some authors prefer to treat the empty set as a case, assigning it a diameter equal to 0. For any solid object or set of scattered points in n-dimensional Euclidean space, in medical parlance concerning a lesion or in geology concerning a rock, the diameter of an object is the supremum of the set of all distances between pairs of points in the object. In differential geometry, the diameter is an important global Riemannian invariant, the symbol or variable for diameter, ⌀, is similar in size and design to ø, the Latin small letter o with stroke. In Unicode it is defined as U+2300 ⌀ Diameter sign, on an Apple Macintosh, the diameter symbol can be entered via the character palette, where it can be found in the Technical Symbols category. The character will not display correctly, however, since many fonts do not include it. In many situations the letter ø is a substitute, which in Unicode is U+00F8 ø
16.
Displacement (vector)
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A displacement is a vector that is the shortest distance from the initial to the final position of a point P. It quantifies both the distance and direction of an imaginary motion along a line from the initial position to the final position of the point. The velocity then is distinct from the speed which is the time rate of change of the distance traveled along a specific path. The velocity may be defined as the time rate of change of the position vector. For motion over an interval of time, the displacement divided by the length of the time interval defines the average velocity. In dealing with the motion of a body, the term displacement may also include the rotations of the body. In this case, the displacement of a particle of the body is called linear displacement, for a position vector s that is a function of time t, the derivatives can be computed with respect to t. These derivatives have common utility in the study of kinematics, control theory, vibration sensing and other sciences, by extension, the higher order derivatives can be computed in a similar fashion. Study of these higher order derivatives can improve approximations of the displacement function. Such higher-order terms are required in order to represent the displacement function as a sum of an infinite series, enabling several analytical techniques in engineering. The fourth order derivative is called jounce
17.
Distance
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Distance is a numerical description of how far apart objects are. In physics or everyday usage, distance may refer to a physical length, in most cases, distance from A to B is interchangeable with distance from B to A. In mathematics, a function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to a set of rules. The circumference of the wheel is 2π × radius, and assuming the radius to be 1, in engineering ω = 2πƒ is often used, where ƒ is the frequency. Chessboard distance, formalized as Chebyshev distance, is the number of moves a king must make on a chessboard to travel between two squares. Distance measures in cosmology are complicated by the expansion of the universe, the term distance is also used by analogy to measure non-physical entities in certain ways. In computer science, there is the notion of the distance between two strings. For example, the dog and dot, which vary by only one letter, are closer than dog and cat. In this way, many different types of distances can be calculated, such as for traversal of graphs, comparison of distributions and curves, distance cannot be negative, and distance travelled never decreases. Distance is a quantity or a magnitude, whereas displacement is a vector quantity with both magnitude and direction. Directed distance is a positive, zero, or negative scalar quantity, the distance covered by a vehicle, person, animal, or object along a curved path from a point A to a point B should be distinguished from the straight-line distance from A to B. For example, whatever the distance covered during a trip from A to B and back to A. In general the straight-line distance does not equal distance travelled, except for journeys in a straight line, directed distances are distances with a directional sense. They can be determined along straight lines and along curved lines, for instance, just labelling the two endpoints as A and B can indicate the sense, if the ordered sequence is assumed, which implies that A is the starting point. A displacement is a kind of directed distance defined in mechanics. A directed distance is called displacement when it is the distance along a line from A and B. This implies motion of the particle, the distance traveled by a particle must always be greater than or equal to its displacement, with equality occurring only when the particle moves along a straight path
18.
Cartesian coordinates
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Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair. The coordinates can also be defined as the positions of the projections of the point onto the two axis, expressed as signed distances from the origin. One can use the principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes. In general, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n and these coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes. The invention of Cartesian coordinates in the 17th century by René Descartes revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes can be described by Cartesian equations, algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2, centered at the origin of the plane, a familiar example is the concept of the graph of a function. Cartesian coordinates are also tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering. They are the most common system used in computer graphics, computer-aided geometric design. Nicole Oresme, a French cleric and friend of the Dauphin of the 14th Century, used similar to Cartesian coordinates well before the time of Descartes. The adjective Cartesian refers to the French mathematician and philosopher René Descartes who published this idea in 1637 and it was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery. Both authors used a single axis in their treatments and have a length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes La Géométrie was translated into Latin in 1649 by Frans van Schooten and these commentators introduced several concepts while trying to clarify the ideas contained in Descartes work. Many other coordinate systems have developed since Descartes, such as the polar coordinates for the plane. The development of the Cartesian coordinate system would play a role in the development of the Calculus by Isaac Newton. The two-coordinate description of the plane was later generalized into the concept of vector spaces. Choosing a Cartesian coordinate system for a one-dimensional space – that is, for a straight line—involves choosing a point O of the line, a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by O is the positive, and which is negative, we say that the line is oriented from the negative half towards the positive half
19.
Radius of curvature
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In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof, in the case of a space curve, the radius of curvature is the length of the curvature vector. Heuristically, this result can be interpreted as R = | v |3 | v × v ˙ |, where | v | = | | = R d φ d t. As a special case, if f is a function from ℝ to ℝ, then the curvature of its graph, let γ be as above, and fix t. We want to find the radius ρ of a circle which matches γ in its zeroth, first. Clearly the radius will not depend on the position γ, only on the velocity γ′, there are only three independent scalars that can be obtained from two vectors v and w, namely v · v, v · w, and w · w. Thus the radius of curvature must be a function of the three scalars | γ′2 |, | γ″2 | and γ′ · γ″, for a semi-circle of radius a in the lower half-plane y = − a 2 − x 2, R = | a | = a. The circle of radius a has a radius of curvature equal to a, for the use in differential geometry, see Cesàro equation. For the radius of curvature of the earth, see Radius of curvature of the earth, Radius of curvature is also used in a three part equation for bending of beams. Radius of curvature Stress in the semiconductor structure involving evaporated thin films usually results from the expansion during the manufacturing process. Thermal stress occurs because film depositions are usually made above room temperature, upon cooling from the deposition temperature to room temperature, the difference in the thermal expansion coefficients of the substrate and the film cause thermal stress. Intrinsic stress results from the microstructure created in the film as atoms are deposited on the substrate, tensile stress results from microvoids in the thin film, because of the attractive interaction of atoms across the voids. The stress in thin film semiconductor structures results in the buckling of the wafers, the radius of the curvature of the stressed structure is related to stress tensor in the structure, and can be described by modified Stoney formula. The topography of the structure including radii of curvature can be measured using optical scanner methods. Differential Geometry of Curves and Surfaces, the Geometry Center, Principal Curvatures 15.3 Curvature and Radius of Curvature Weisstein, Eric W. Principal Curvatures. Weisstein, Eric W. Principal Radius of Curvature
20.
Curvature
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In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry. This article deals primarily with extrinsic curvature and its canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius everywhere. Smaller circles bend more sharply, and hence have higher curvature, the curvature of a smooth curve is defined as the curvature of its osculating circle at each point. Curvature is normally a scalar quantity, but one may define a curvature vector that takes into account the direction of the bend in addition to its magnitude. The curvature of more objects is described by more complex objects from linear algebra. This article sketches the mathematical framework which describes the curvature of a curve embedded in a plane, the curvature of C at a point is a measure of how sensitive its tangent line is to moving the point to other nearby points. There are a number of equivalent ways that this idea can be made precise and it is natural to define the curvature of a straight line to be constantly zero. The curvature of a circle of radius R should be large if R is small and small if R is large, thus the curvature of a circle is defined to be the reciprocal of the radius, κ =1 R. Given any curve C and a point P on it, there is a circle or line which most closely approximates the curve near P. The curvature of C at P is then defined to be the curvature of that circle or line, the radius of curvature is defined as the reciprocal of the curvature. Another way to understand the curvature is physical, suppose that a particle moves along the curve with unit speed. Taking the time s as the parameter for C, this provides a natural parametrization for the curve, the unit tangent vector T also depends on time. The curvature is then the magnitude of the rate of change of T. Symbolically and this is the magnitude of the acceleration of the particle and the vector dT/ds is the acceleration vector. Geometrically, the curvature κ measures how fast the unit tangent vector to the curve rotates. If a curve close to the same direction, the unit tangent vector changes very little and the curvature is small, where the curve undergoes a tight turn. These two approaches to the curvature are related geometrically by the following observation, in the first definition, the curvature of a circle is equal to the ratio of the angle of an arc to its length. e. For such a curve, there exists a reparametrization with respect to arc length s. This is a parametrization of C such that ∥ γ ′ ∥2 = x ′2 + y ′2 =1, the velocity vector T is the unit tangent vector
21.
Area
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Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the surface of a three-dimensional object. It is the analog of the length of a curve or the volume of a solid. The area of a shape can be measured by comparing the shape to squares of a fixed size, in the International System of Units, the standard unit of area is the square metre, which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the area as three such squares. In mathematics, the square is defined to have area one. There are several formulas for the areas of simple shapes such as triangles, rectangles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles, for shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a motivation for the historical development of calculus. For a solid such as a sphere, cone, or cylinder. Formulas for the areas of simple shapes were computed by the ancient Greeks. Area plays an important role in modern mathematics, in addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, in general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers and it can be proved that such a function exists. An approach to defining what is meant by area is through axioms, area can be defined as a function from a collection M of special kind of plane figures to the set of real numbers which satisfies the following properties, For all S in M, a ≥0. If S and T are in M then so are S ∪ T and S ∩ T, if S and T are in M with S ⊆ T then T − S is in M and a = a − a. If a set S is in M and S is congruent to T then T is also in M, every rectangle R is in M. If the rectangle has length h and breadth k then a = hk, let Q be a set enclosed between two step regions S and T
22.
Hectare
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The hectare is an SI accepted metric system unit of area equal to 100 ares and primarily used in the measurement of land as a metric replacement for the imperial acre. An acre is about 0.405 hectare and one hectare contains about 2.47 acres, in 1795, when the metric system was introduced, the are was defined as 100 square metres and the hectare was thus 100 ares or 1⁄100 km2. When the metric system was further rationalised in 1960, resulting in the International System of Units, the are was not included as a recognised unit. The hectare, however, remains as a non-SI unit accepted for use with the SI units, the metric system of measurement was first given a legal basis in 1795 by the French Revolutionary government. At the first meeting of the CGPM in 1889 when a new standard metre, manufactured by Johnson Matthey & Co of London was adopted, in 1960, when the metric system was updated as the International System of Units, the are did not receive international recognition. The units that were catalogued replicated the recommendations of the CGPM, many farmers, especially older ones, still use the acre for everyday calculations, and convert to hectares only for official paperwork. Farm fields can have long histories which are resistant to change, with names such as the six acre field stretching back hundreds of years. The names centiare, deciare, decare and hectare are derived by adding the standard metric prefixes to the base unit of area. The centiare is a synonym for one square metre, the deciare is ten square metres. The are is a unit of area, equal to 100 square metres and it was defined by older forms of the metric system, but is now outside of the modern International System of Units. It is commonly used to measure real estate, in particular in Indonesia, India, and in French-, Portuguese-, Slovakian-, Serbian-, Czech-, Polish-, Dutch-, in Russia and other former Soviet Union states, the are is called sotka. It is used to describe the size of suburban dacha or allotment garden plots or small city parks where the hectare would be too large, the decare is derived from deka, the prefix for 10 and are, and is equal to 10 ares or 1000 square metres. It is used in Norway and in the former Ottoman areas of the Middle East, the hectare, although not strictly a unit of SI, is the only named unit of area that is accepted for use within the SI. The United Kingdom, United States, Burma, and to some extent Canada instead use the acre, others, such as South Africa, published conversion factors which were to be used particularly when preparing consolidation diagrams by compilation. In many countries, metrication redefined or clarified existing measures in terms of metric units, non-SI units accepted for use with the International System of Units
23.
Volume
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Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre, three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, Volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shapes boundary. Where a variance in shape and volume occurs, such as those that exist between different human beings, these can be calculated using techniques such as the Body Volume Index. One-dimensional figures and two-dimensional shapes are assigned zero volume in the three-dimensional space, the volume of a solid can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas, the combined volume of two substances is usually greater than the volume of one of the substances. However, sometimes one substance dissolves in the other and the volume is not additive. In differential geometry, volume is expressed by means of the volume form, in thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure. Any unit of length gives a unit of volume, the volume of a cube whose sides have the given length. For example, a cubic centimetre is the volume of a cube whose sides are one centimetre in length, in the International System of Units, the standard unit of volume is the cubic metre. The metric system also includes the litre as a unit of volume, thus 1 litre =3 =1000 cubic centimetres =0.001 cubic metres, so 1 cubic metre =1000 litres. Small amounts of liquid are often measured in millilitres, where 1 millilitre =0.001 litres =1 cubic centimetre. Capacity is defined by the Oxford English Dictionary as the applied to the content of a vessel, and to liquids, grain, or the like. Capacity is not identical in meaning to volume, though closely related, Units of capacity are the SI litre and its derived units, and Imperial units such as gill, pint, gallon, and others. Units of volume are the cubes of units of length, in SI the units of volume and capacity are closely related, one litre is exactly 1 cubic decimetre, the capacity of a cube with a 10 cm side. In other systems the conversion is not trivial, the capacity of a fuel tank is rarely stated in cubic feet, for example. The density of an object is defined as the ratio of the mass to the volume, the inverse of density is specific volume which is defined as volume divided by mass. Specific volume is an important in thermodynamics where the volume of a working fluid is often an important parameter of a system being studied
24.
Cubic metre
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The cubic metre or cubic meter is the SI derived unit of volume. It is the volume of a cube with one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère, another alternative name, no longer widely used, was the kilolitre. A cubic metre of water at the temperature of maximum density and standard atmospheric pressure has a mass of 1000 kg. At 0 °C, the point of water, a cubic metre of water has slightly less mass,999.972 kilograms. It is sometimes abbreviated to cu m, m3, M3, m^3, m**3, CBM, abbreviated CBM and cbm in the freight business and MTQ in international trade. See Orders of magnitude for a comparison with other volumes
25.
Litre
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The litre or liter is an SI accepted metric system unit of volume equal to 1 cubic decimetre,1,000 cubic centimetres or 1/1,000 cubic metre. A cubic decimetre occupies a volume of 10×10×10 centimetres and is equal to one-thousandth of a cubic metre. The original French metric system used the litre as a base unit. The word litre is derived from an older French unit, the litron, whose name came from Greek — where it was a unit of weight, not volume — via Latin, and which equalled approximately 0.831 litres. The litre was also used in subsequent versions of the metric system and is accepted for use with the SI. The spelling used by the International Bureau of Weights and Measures is litre, the less common spelling of liter is more predominantly used in American English. One litre of water has a mass of almost exactly one kilogram. Subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact, a litre is defined as a special name for a cubic decimetre or 10 centimetres ×10 centimetres ×10 centimetres. Hence 1 L ≡0.001 m3 ≡1000 cm3, from 1901 to 1964, the litre was defined as the volume of one kilogram of pure water at maximum density and standard pressure. The kilogram was in turn specified as the mass of a platinum/iridium cylinder held at Sèvres in France and was intended to be of the mass as the 1 litre of water referred to above. It was subsequently discovered that the cylinder was around 28 parts per million too large and thus, during this time, additionally, the mass-volume relationship of water depends on temperature, pressure, purity and isotopic uniformity. In 1964, the definition relating the litre to mass was abandoned in favour of the current one, although the litre is not an official SI unit, it is accepted by the CGPM for use with the SI. CGPM defines the litre and its acceptable symbols, a litre is equal in volume to the millistere, an obsolete non-SI metric unit customarily used for dry measure. The litre is often used in some calculated measurements, such as density. One litre of water has a mass of almost exactly one kilogram when measured at its maximal density, similarly,1 millilitre of water has a mass of about 1 g,1,000 litres of water has a mass of about 1,000 kg. It is now known that density of water depends on the isotopic ratios of the oxygen and hydrogen atoms in a particular sample. The litre, though not an official SI unit, may be used with SI prefixes, the most commonly used derived unit is the millilitre, defined as one-thousandth of a litre, and also often referred to by the SI derived unit name cubic centimetre. It is a commonly used measure, especially in medicine and cooking, Other units may be found in the table below, where the more often used terms are in bold
26.
Second
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The second is the base unit of time in the International System of Units. It is qualitatively defined as the division of the hour by sixty. SI definition of second is the duration of 9192631770 periods of the corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. Seconds may be measured using a mechanical, electrical or an atomic clock, SI prefixes are combined with the word second to denote subdivisions of the second, e. g. the millisecond, the microsecond, and the nanosecond. Though SI prefixes may also be used to form multiples of the such as kilosecond. The second is also the unit of time in other systems of measurement, the centimetre–gram–second, metre–kilogram–second, metre–tonne–second. Absolute zero implies no movement, and therefore zero external radiation effects, the second thus defined is consistent with the ephemeris second, which was based on astronomical measurements. The realization of the second is described briefly in a special publication from the National Institute of Standards and Technology. 1 international second is equal to, 1⁄60 minute 1⁄3,600 hour 1⁄86,400 day 1⁄31,557,600 Julian year 1⁄, more generally, = 1⁄, the Hellenistic astronomers Hipparchus and Ptolemy subdivided the day into sixty parts. They also used an hour, simple fractions of an hour. No sexagesimal unit of the day was used as an independent unit of time. The modern second is subdivided using decimals - although the third remains in some languages. The earliest clocks to display seconds appeared during the last half of the 16th century, the second became accurately measurable with the development of mechanical clocks keeping mean time, as opposed to the apparent time displayed by sundials. The earliest spring-driven timepiece with a hand which marked seconds is an unsigned clock depicting Orpheus in the Fremersdorf collection. During the 3rd quarter of the 16th century, Taqi al-Din built a clock with marks every 1/5 minute, in 1579, Jost Bürgi built a clock for William of Hesse that marked seconds. In 1581, Tycho Brahe redesigned clocks that displayed minutes at his observatory so they also displayed seconds, however, they were not yet accurate enough for seconds. In 1587, Tycho complained that his four clocks disagreed by plus or minus four seconds, in 1670, London clockmaker William Clement added this seconds pendulum to the original pendulum clock of Christiaan Huygens. From 1670 to 1680, Clement made many improvements to his clock and this clock used an anchor escapement mechanism with a seconds pendulum to display seconds in a small subdial
27.
Hyperfine levels
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In atomic physics, hyperfine structure is the different effects leading to small shifts and splittings in the energy levels of atoms, molecules and ions. The name is a reference to the structure, which results from the interaction between the magnetic moments associated with electron spin and the electrons orbital angular momentum. The optical hyperfine structure was observed in 1881 by Albert Abraham Michelson and it could, however, only be explained in terms of quantum mechanics when Wolfgang Pauli proposed the existence of a small nuclear magnetic moment in 1924. In 1935, H. Schüler and Theodor Schmidt proposed the existence of a quadrupole moment in order to explain anomalies in the hyperfine structure. The theory of structure comes directly from electromagnetism, consisting of the interaction of the nuclear multipole moments with internally generated fields. The theory is derived first for the case, but can be applied to each nucleus in a molecule. Following this there is a discussion of the additional effects unique to the molecular case, the dominant term in the hyperfine Hamiltonian is typically the magnetic dipole term. Atomic nuclei with a nuclear spin I have a magnetic dipole moment, given by, μ I = g I μ N I. There is an associated with a magnetic dipole moment in the presence of a magnetic field. For a nuclear magnetic moment, μI, placed in a magnetic field, B. Electron orbital angular momentum results from the motion of the electron about some fixed point that we shall take to be the location of the nucleus. Written in terms of the Bohr magneton, this gives, B el l = −2 μ B μ04 π1 r 3 r × m e v ℏ. Recognizing that mev is the momentum, p, and that r×p/ħ is the orbital angular momentum in units of ħ, l, we can write. The electron spin angular momentum is a different property that is intrinsic to the particle. Nonetheless it is angular momentum and any angular momentum associated with a charged particle results in a dipole moment. The magnetic field of a moment, μs, is given by. The first term gives the energy of the dipole in the field due to the electronic orbital angular momentum. The second term gives the energy of the finite distance interaction of the dipole with the field due to the electron spin magnetic moments
28.
Ground state
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The ground state of a quantum mechanical system is its lowest-energy state, the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with greater than the ground state. In the quantum theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate, many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state, according to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state, thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a crystal lattice, have a unique ground state. It is also possible for the highest excited state to have zero temperature for systems that exhibit negative temperature. In 1D, the state of the Schrödinger equation has no nodes. This can be proved considering the energy of a state with a node at x =0, i. e. ψ =0. Consider the average energy in this state ⟨ ψ | H | ψ ⟩ = ∫ d x where V is the potential, now consider a small interval around x =0, i. e. x ∈. Take a new wave function ψ ′ to be defined as ψ ′ = ψ, x < − ϵ and ψ ′ = − ψ, x > ϵ, if ϵ is small enough then this is always possible to do so that ψ ′ is continuous. Note that the energy density | d ψ ′ d x |2 < | d ψ d x |2 everywhere because of the normalization. For definiteness let us choose V ≥0, then it is clear that outside the interval x ∈ the potential energy density is smaller for the ψ ′ because | ψ ′ | < | ψ | there. Therefore, the energy is unchanged up to order ϵ2 if we deform the state with a node ψ into a state without a node ψ ′. We can therefore remove all nodes and reduce the energy, which implies that the wave function cannot have a node. The wave function of the state of a particle in a one-dimensional well is a half-period sine wave which goes to zero at the two edges of the well. The wave function of the state of a hydrogen atom is a spherically-symmetric distribution centred on the nucleus. The electron is most likely to be found at a distance from the equal to the Bohr radius
29.
Caesium
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Caesium or cesium is a chemical element with symbol Cs and atomic number 55. It is a soft, silvery-gold alkali metal with a point of 28.5 °C. Caesium is a metal and has physical and chemical properties similar to those of rubidium and potassium. The metal is extremely reactive and pyrophoric, reacting with water even at −116 °C, Caesium is one of the most reactive elements of all, even more reactive than fluorine, the most reactive nonmetal. It is the least electronegative element, with a value of 0.79 on the Pauling scale and it has only one stable isotope, caesium-133. Caesium is mined mostly from pollucite, while the radioisotopes, especially caesium-137, the German chemist Robert Bunsen and physicist Gustav Kirchhoff discovered caesium in 1860 by the newly developed method of flame spectroscopy. The first small-scale applications for caesium were as a getter in vacuum tubes, since then, caesium has been widely used in highly accurate atomic clocks. The radioactive isotope caesium-137 has a half-life of about 30 years and is used in applications, industrial gauges. Although the element is only toxic, the metal is a hazardous material. It is a ductile, pale metal, which darkens in the presence of trace amounts of oxygen. When in the presence of oil, it loses its metallic lustre and takes on a duller. It has a point of 28.4 °C, making it one of the few elemental metals that are liquid near room temperature. Mercury is the elemental metal with a known melting point lower than caesium. In addition, the metal has a low boiling point,641 °C. Its compounds burn with a blue or violet colour, Caesium forms alloys with the other alkali metals, gold, and mercury. At temperatures below 650 °C, it does not alloy with cobalt, iron, molybdenum, nickel, platinum, tantalum and it forms well-defined intermetallic compounds with antimony, gallium, indium, and thorium, which are photosensitive. It mixes with all the alkali metals, the alloy with a molar distribution of 41% caesium, 47% potassium. A few amalgams have been studied, CsHg 2 is black with a metallic lustre, while CsHg is golden-coloured
30.
Minute
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The minute is a unit of time or of angle. As a unit of time, the minute is equal to 1⁄60 of an hour, in the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds. As a unit of angle, the minute of arc is equal to 1⁄60 of a degree, although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, the prime is also sometimes used informally to denote minutes of time. In contrast to the hour, the minute does not have a historical background. What is traceable only is that it started being recorded in the Middle Ages due to the ability of construction of precision timepieces, however, no consistent records of the origin for the division as 1⁄60 part of the hour have ever been found, despite many speculations. Historically, the word comes from the Latin pars minuta prima. This division of the hour can be refined with a second small part. For even further refinement, the third remains in some languages, for example Polish and Turkish. The symbol notation of the prime for minutes and double prime for seconds can be seen as indicating the first, international System of Units Latitude and longitude Orders of magnitude Henry Campbell Black, Blacks Law Dictionary, 6th Edition, entry on Minute. West Publishing Company, St. Paul, Minnesota,1991
31.
Hour
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An hour is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3, 599–3,601 seconds, depending on conditions. The seasonal, temporal, or unequal hour was established in the ancient Near East as 1⁄12 of the night or daytime, such hours varied by season, latitude, and weather. It was subsequently divided into 60 minutes, each of 60 seconds, the modern English word hour is a development of the Anglo-Norman houre and Middle English ure, first attested in the 13th century. It displaced the Old English tide and stound, the Anglo-Norman term was a borrowing of Old French ure, a variant of ore, which derived from Latin hōra and Greek hṓrā. Like Old English tīd and stund, hṓrā was originally a word for any span of time, including seasons. Its Proto-Indo-European root has been reconstructed as *yeh₁-, making hour distantly cognate with year, the time of day is typically expressed in English in terms of hours. Whole hours on a 12-hour clock are expressed using the contracted phrase oclock, Hours on a 24-hour clock are expressed as hundred or hundred hours. Fifteen and thirty minutes past the hour is expressed as a quarter past or after and half past, respectively, fifteen minutes before the hour may be expressed as a quarter to, of, till, or before the hour. Sumerian and Babylonian hours divided the day and night into 24 equal hours, the ancient Egyptians began dividing the night into wnwt at some time before the compilation of the Dynasty V Pyramid Texts in the 24th century BC. By 2150 BC, diagrams of stars inside Egyptian coffin lids—variously known as diagonal calendars or star clocks—attest that there were exactly 12 of these. The coffin diagrams show that the Egyptians took note of the risings of 36 stars or constellations. Each night, the rising of eleven of these decans were noted, the original decans used by the Egyptians would have fallen noticeably out of their proper places over a span of several centuries. By the time of Amenhotep III, the priests at Karnak were using water clocks to determine the hours and these were filled to the brim at sunset and the hour determined by comparing the water level against one of its twelve gauges, one for each month of the year. During the New Kingdom, another system of decans was used, the later division of the day into 12 hours was accomplished by sundials marked with ten equal divisions. The morning and evening periods when the failed to note time were observed as the first and last hours. The Egyptian hours were closely connected both with the priesthood of the gods and with their divine services, by the New Kingdom, each hour was conceived as a specific region of the sky or underworld through which Ras solar bark travelled. Protective deities were assigned to each and were used as the names of the hours, as the protectors and resurrectors of the sun, the goddesses of the night hours were considered to hold power over all lifespans and thus became part of Egyptian funerary rituals. The Egyptian for astronomer, used as a synonym for priest, was wnwty, the earliest forms of wnwt include one or three stars, with the later solar hours including the determinative hieroglyph for sun
32.
Day
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In common usage, it is either an interval equal to 24 hours or daytime, the consecutive period of time during which the Sun is above the horizon. The period of time during which the Earth completes one rotation with respect to the Sun is called a solar day, several definitions of this universal human concept are used according to context, need and convenience. In 1960, the second was redefined in terms of the motion of the Earth. The unit of measurement day, redefined in 1960 as 86400 SI seconds and symbolized d, is not an SI unit, but is accepted for use with SI. The word day may also refer to a day of the week or to a date, as in answer to the question. The life patterns of humans and many species are related to Earths solar day. In recent decades the average length of a day on Earth has been about 86400.002 seconds. A day, understood as the span of time it takes for the Earth to make one rotation with respect to the celestial background or a distant star, is called a stellar day. This period of rotation is about 4 minutes less than 24 hours, mainly due to tidal effects, the Earths rotational period is not constant, resulting in further minor variations for both solar days and stellar days. Other planets and moons have stellar and solar days of different lengths to Earths, besides the day of 24 hours, the word day is used for several different spans of time based on the rotation of the Earth around its axis. An important one is the day, defined as the time it takes for the Sun to return to its culmination point. Because the Earth orbits the Sun elliptically as the Earth spins on an inclined axis, on average over the year this day is equivalent to 24 hours. A day, in the sense of daytime that is distinguished from night-time, is defined as the period during which sunlight directly reaches the ground. The length of daytime averages slightly more than half of the 24-hour day, two effects make daytime on average longer than nights. The Sun is not a point, but has an apparent size of about 32 minutes of arc, additionally, the atmosphere refracts sunlight in such a way that some of it reaches the ground even when the Sun is below the horizon by about 34 minutes of arc. So the first light reaches the ground when the centre of the Sun is still below the horizon by about 50 minutes of arc, the difference in time depends on the angle at which the Sun rises and sets, but can amount to around seven minutes. Ancient custom has a new day start at either the rising or setting of the Sun on the local horizon, the exact moment of, and the interval between, two sunrises or sunsets depends on the geographical position, and the time of year. A more constant day can be defined by the Sun passing through the local meridian, the exact moment is dependent on the geographical longitude, and to a lesser extent on the time of the year
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Angular velocity
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This speed can be measured in the SI unit of angular velocity, radians per second, or in terms of degrees per second, degrees per hour, etc. Angular velocity is usually represented by the symbol omega, the direction of the angular velocity vector is perpendicular to the plane of rotation, in a direction that is usually specified by the right-hand rule. The angular velocity of a particle is measured around or relative to a point, called the origin. As shown in the diagram, if a line is drawn from the origin to the particle, then the velocity of the particle has a component along the radius, if there is no radial component, then the particle moves in a circle. On the other hand, if there is no cross-radial component, a radial motion produces no change in the direction of the particle relative to the origin, so, for the purpose of finding the angular velocity, the radial component can be ignored. Therefore, the rotation is completely produced by the perpendicular motion around the origin, the angular velocity in two dimensions is a pseudoscalar, a quantity that changes its sign under a parity inversion. The positive direction of rotation is taken, by convention, to be in the direction towards the y axis from the x axis, if the parity is inverted, but the orientation of a rotation is not, then the sign of the angular velocity changes. There are three types of angular velocity involved in the movement on an ellipse corresponding to the three anomalies, in three dimensions, the angular velocity becomes a bit more complicated. The angular velocity in case is generally thought of as a vector, or more precisely. It now has not only a magnitude, but a direction as well, the magnitude is the angular speed, and the direction describes the axis of rotation that Eulers rotation theorem guarantees must exist. The right-hand rule indicates the direction of the angular velocity pseudovector. Let u be a vector along the instantaneous rotation axis. This is the definition of a vector space, the only property that presents difficulties to prove is the commutativity of the addition. This can be proven from the fact that the velocity tensor W is skew-symmetric, therefore, R = e W t is a rotation matrix and in a time dt is an infinitesimal rotation matrix. Therefore, it can be expanded as R = I + W ⋅ d t +122 +, in such a frame, each vector is a particular case of the previous case, in which the module of the vector is constant. Though it just a case of a moving particle, this is a very important one for its relationship with the rigid body study. There are two ways to describe the angular velocity of a rotating frame, the angular velocity vector. Both entities are related and they can be calculated from each other, in a consistent way with the general definition, the angular velocity of a frame is defined as the angular velocity of each of the three vectors of the frame
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Velocity
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The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion, Velocity is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a vector quantity, both magnitude and direction are needed to define it. The scalar absolute value of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI system as metres per second or as the SI base unit of. For example,5 metres per second is a scalar, whereas 5 metres per second east is a vector, if there is a change in speed, direction or both, then the object has a changing velocity and is said to be undergoing an acceleration. To have a constant velocity, an object must have a constant speed in a constant direction, constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed. For example, a car moving at a constant 20 kilometres per hour in a path has a constant speed. Hence, the car is considered to be undergoing an acceleration, Speed describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving. If a car is said to travel at 60 km/h, its speed has been specified, however, if the car is said to move at 60 km/h to the north, its velocity has now been specified. The big difference can be noticed when we consider movement around a circle and this is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled. Velocity is defined as the rate of change of position with respect to time, average velocity can be calculated as, v ¯ = Δ x Δ t. The average velocity is less than or equal to the average speed of an object. This can be seen by realizing that while distance is always strictly increasing, from this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time is the displacement, x. In calculus terms, the integral of the velocity v is the displacement function x. In the figure, this corresponds to the area under the curve labeled s. Since the derivative of the position with respect to time gives the change in position divided by the change in time, although velocity is defined as the rate of change of position, it is often common to start with an expression for an objects acceleration. As seen by the three green tangent lines in the figure, an objects instantaneous acceleration at a point in time is the slope of the tangent to the curve of a v graph at that point. In other words, acceleration is defined as the derivative of velocity with respect to time, from there, we can obtain an expression for velocity as the area under an a acceleration vs. time graph
35.
Kilometres per hour
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The kilometre per hour is a unit of speed, expressing the number of kilometres travelled in one hour. Worldwide, it is the most commonly used unit of speed on road signs, the Dutch on the other hand adopted the kilometre in 1817 but gave it the local name of the mijl. The SI representations, classified as symbols, are km/h, km h−1 and km·h−1, the use of abbreviations dates back to antiquity, but abbreviations for kilometres per hour did not appear in the English language until the late nineteenth century. The kilometre, a unit of length, first appeared in English in 1810, kilometres per hour did not begin to be abbreviated in print until many years later, with several different abbreviations existing near-contemporaneously. For example, news organisations such as Reuters and The Economist require kph, in Australian unofficial usage, km/h is sometimes pronounced and written as klicks or clicks. The use of symbols to replace words dates back to at least the medieval era when Johannes Widman, writing in German in 1486. In the early 1800s Berzelius introduced a symbolic notation for the chemical elements derived from the elements Latin names, typically, Na was used for the element sodium and H2O for water. In 1879, four years after the signing of the Treaty of the Metre, among these were the use of the symbol km for kilometre. In 1948, as part of its work for the SI. The SI explicitly states that unit symbols are not abbreviations and are to be using a very specific set of rules. Hence the name of the unit can be replaced by a kind of algebraic symbol and this symbol is not merely an abbreviation but a symbol which, like chemical symbols, must be used in a precise and prescribed manner. SI, and hence the use of km/h has now been adopted around the world in areas related to health and safety. It is also the system of measure in academia and in education. During the early years of the car, each country developed its own system of road signs. In 1968 the Vienna Convention on Road Signs and Signals was drawn up under the auspices of the United Nations Economic, many countries have since signed the convention and adopted its proposals. The use of SI implicitly required that states use km/h as the shorthand for kilometres per hour on official documents. Examples include, Dutch, kilometer per uur, Portuguese, quilómetro por hora Greek, in 1988 the United States National Highway Traffic Safety Administration promulgated a rule stating that MPH and/or km/h were to be used in speedometer displays. On May 15,2000 this was clarified to read MPH, or MPH, however, the Federal Motor Vehicle Safety Standard number 101 allows any combination of upper- and lowercase letters to represent the units
36.
Acceleration
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Acceleration, in physics, is the rate of change of velocity of an object with respect to time. An objects acceleration is the net result of any and all forces acting on the object, the SI unit for acceleration is metre per second squared. Accelerations are vector quantities and add according to the parallelogram law, as a vector, the calculated net force is equal to the product of the objects mass and its acceleration. For example, when a car starts from a standstill and travels in a line at increasing speeds. If the car turns, there is an acceleration toward the new direction, in this example, we can call the forward acceleration of the car a linear acceleration, which passengers in the car might experience as a force pushing them back into their seats. When changing direction, we call this non-linear acceleration, which passengers might experience as a sideways force. If the speed of the car decreases, this is an acceleration in the direction from the direction of the vehicle. Passengers may experience deceleration as a force lifting them forwards, mathematically, there is no separate formula for deceleration, both are changes in velocity. Each of these accelerations might be felt by passengers until their velocity matches that of the car, an objects average acceleration over a period of time is its change in velocity divided by the duration of the period. Mathematically, a ¯ = Δ v Δ t, instantaneous acceleration, meanwhile, is the limit of the average acceleration over an infinitesimal interval of time. The SI unit of acceleration is the metre per second squared, or metre per second per second, as the velocity in metres per second changes by the acceleration value, every second. An object moving in a circular motion—such as a satellite orbiting the Earth—is accelerating due to the change of direction of motion, in this case it is said to be undergoing centripetal acceleration. Proper acceleration, the acceleration of a relative to a free-fall condition, is measured by an instrument called an accelerometer. As speeds approach the speed of light, relativistic effects become increasingly large and these components are called the tangential acceleration and the normal or radial acceleration. Geometrical analysis of space curves, which explains tangent, normal and binormal, is described by the Frenet–Serret formulas. Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an amount in every equal time period. A frequently cited example of uniform acceleration is that of an object in free fall in a gravitational field. The acceleration of a body in the absence of resistances to motion is dependent only on the gravitational field strength g