The metre (British spelling and BIPM spelling^{[1]}) or meter (American spelling ^{[2]}) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in some metric systems, including the International System of Units (SI). The SI unit symbol is m. ^{[3]} The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 second.^{[1]}
The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole – as a result the Earth's circumference is approximately 40,000 km today. In 1799, it was redefined in terms of a prototype metre bar (the actual bar used was changed in 1889). In 1960, the metre was redefined in terms of a certain 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 (2.54 centimetres or 25.4 millimetres). One metre is about 3 ^{3}⁄_{8} inches longer than a yard, i.e. about 39 ^{3}⁄_{8} inches.
Metre | |
---|---|
Unit system | SI base unit |
Unit of | length |
Symbol | m |
Conversions | |
1 m in ... | ... is equal to ... |
SI units | 1000 mm 0.001 km |
imperial/US units | 1.0936 yd 3.2808 ft 39.370 in |
nautical units | 0.00053996 nmi |
Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States^{[4]}^{[5]}^{[6]} and the Philippines,^{[7]} which use meter. Other Germanic languages, such as German, Dutch, and the Scandinavian languages^{[8]} likewise spell the word meter.
Measuring devices (such as ammeter, speedometer) are spelled "-meter" in all variants of English.^{[9]} The suffix "-meter" has the same Greek origin as the unit of length.^{[10]}^{[11]}
The etymological roots of metre can be traced to the Greek verb μετρέω (metreo) (to measure, count or compare) and noun μέτρον (metron) (a measure), which were used for physical measurement, for poetic metre and by extension for moderation or avoiding extremism (as in "be measured in your response"). This range of uses is also found in Latin (metior, mensura), French (mètre, mesure), English and other languages. The motto ΜΕΤΡΩ ΧΡΩ (metro chro) in the seal of the International Bureau of Weights and Measures (BIPM), which was a saying of the Greek statesman and philosopher Pittacus of Mytilene and may be translated as "Use measure!", thus calls for both measurement and moderation.
In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, the universal measure or standard based on a pendulum with a two-second period.^{[12]} The use of the seconds pendulum to define length had been suggested to the Royal Society in 1660 by Christopher Wren. Christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches; that is, 997 mm.^{[12]}^{[13]}^{[14]} No official action was taken regarding these suggestions.
In 1670 Gabriel Mouton, Bishop of Lyon, also suggested a universal length standard with decimal multiples and divisions, to be based on a one-minute angle of the Earth's meridian arc or (as the Earth's circumference was not easy to measure) on a pendulum with a two-second period. In 1675, the Italian scientist Tito Livio Burattini, in his work Misura Universale, used the phrase metro cattolico ("universal measure"), derived from the Greek μέτρον καθολικόν (métron katholikón), to denote the standard unit of length derived from a pendulum.^{[15]} As a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. On 7 October 1790 that commission advised the adoption of a decimal system, and on 19 March 1791 advised the adoption of the term mètre ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the distance between the North Pole and the Equator.^{[16]}^{[17]}^{[18]}^{[19]} In 1793, the French National Convention adopted the proposal; this use of metre in English began at least as early as 1797.^{[20]}
In 1791, the French Academy of Sciences selected the meridional definition over the pendular definition because the force of gravity varies slightly over the surface of the Earth, which affects the period of a pendulum.
To establish a universally accepted foundation for the definition of the metre, more accurate measurements of this meridian were needed. The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from 1792 to 1799, which attempted to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle in Barcelona to estimate the length of the meridian arc through Dunkerque. This portion of the meridian, assumed to be the same 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. The problem with this approach is that the exact shape of the Earth is not a simple mathematical shape, such as a sphere or oblate spheroid, at the level of precision required for defining a standard of length. The irregular and particular shape of the Earth smoothed to sea level is represented by a mathematical model called a geoid, which literally means "Earth-shaped". Despite these issues, in 1793 France adopted this definition of the metre as its official unit of length based on provisional results from this expedition. However, it was later determined that the first prototype metre bar was short by about 200 micrometres because of miscalculation of the flattening of the Earth, making the prototype about 0.02% shorter than the original proposed definition of the metre. Regardless, this length became the French standard and was progressively adopted by other countries in Europe.
The expedition was fictionalised in Denis Guedj, Le mètre du Monde.^{[21]} Ken Alder wrote factually about the expedition in The Measure of All Things: the seven year odyssey and hidden error that transformed the world.^{[22]}
In 1867 at the second general conference of the International Association of Geodesy held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth.^{[23]}^{[24]}^{[25]} The conference recommended the adoption of the metre and the creation of an international metre commission, according to the proposal of Johann Jacob Baeyer, Adolphe Hirsch and Carlos Ibáñez e Ibáñez de Ibero.^{[23]}
In the 1870s and in light of modern precision, a series of international conferences was held to devise new metric standards. The Metre Convention (Convention du Mètre) of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, France. This new organisation was to construct and preserve a prototype metre bar, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation created such a bar in 1889 at the first General Conference on Weights and Measures (CGPM: Conférence Générale des Poids et Mesures), establishing the International Prototype Metre as the distance between two lines on a standard bar composed of an alloy of 90% platinum and 10% iridium, measured at the melting point of ice.^{[26]}
The original international prototype of the metre is still kept at the BIPM under the conditions specified in 1889.
In 1893, the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using some particular wavelength of light as a standard of length. By 1925, interferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standard until 1960, when the eleventh CGPM defined the metre in the new International System of Units (SI) as equal to 1 650 763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum.^{[27]}
To further reduce uncertainty, the 17th CGPM in 1983 replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the second and the speed of light:^{[1]}
This definition fixed the speed of light in vacuum at exactly 299792458 metres per second (≈300000 km/s). An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare lasers accurately using frequency, resulting in wavelengths with one-fifth the uncertainty involved in the direct comparison of wavelengths, because interferometer errors were eliminated. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised helium–neon laser "a recommended radiation" for realising the metre.^{[28]} For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, λ_{HeNe}, to be 632.99121258 nm with an estimated relative standard uncertainty (U) of 2.1×10^{−11}.^{[28]}^{[29]}^{[30]} This uncertainty is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain atomic clock (U = 5×10^{−16}).^{[31]} Consequently, a realisation of the metre is usually delineated (not defined) today in labs as 1579800.762042(33) wavelengths of helium-neon laser light in a vacuum, the error stated being only that of frequency determination.^{[28]} This bracket notation expressing the error is explained in the article on measurement uncertainty.
Practical realisation of the metre is subject to uncertainties in characterising the medium, to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source.^{[32]} A commonly used medium is air, and the National Institute of Standards and Technology (NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air.^{[33]} As described by NIST, in air, the uncertainties in characterising the medium are dominated by errors in measuring temperature and pressure. Errors in the theoretical formulas used are secondary.^{[34]} By implementing a refractive index correction such as this, an approximate realisation of the metre can be implemented in air, for example, using the formulation of the metre as 1579800.762042(33) wavelengths of helium–neon laser light in vacuum, and converting the wavelengths in a vacuum to wavelengths in air. Air is only one possible medium to use in a realisation of the metre, and any partial vacuum can be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented.^{[35]}
The metre is defined as the path length travelled by light in a given time and practical laboratory length measurements in metres are determined by counting the number of wavelengths of laser light of one of the standard types that fit into the length,^{[38]} and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement:^{[32]}^{[39]}
Of these, the last is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in metres is based upon the relation
which converts the unit of wavelength λ to metres using c, the speed of light in vacuum in m/s. Here n is the refractive index of the medium in which the measurement is made, and f is the measured frequency of the source. Although conversion from wavelengths to metres introduces an additional error in the overall length due to measurement error in determining the refractive index and the frequency, the measurement of frequency is one of the most accurate measurements available.^{[39]}
Basis of definition | Date | Absolute uncertainty |
Relative uncertainty |
---|---|---|---|
1/10 000 000 part of the quadrant along the meridian, measurement by Delambre and Méchain (443.296 lines) | 1795 | 500–100 μm | 10^{−4} |
First prototype Mètre des Archives platinum bar standard | 1799 | 50–10 μm | 10^{−5} |
Platinum-iridium bar at melting point of ice (1st CGPM) | 1889 | 0.2–0.1 μm (200–100 nm) | 10^{−7} |
Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM) | 1927 | n.a. | n.a. |
Hyperfine atomic transition; 1650763.73 wavelengths of light from a specified transition in krypton-86 (11th CGPM) | 1960 | 4 nm | 4×10^{−9}^{[44]} |
Length of the path travelled by light in a vacuum in 1/299 792 458 second (17th CGPM) | 1983 | 0.1 nm | 10^{−10} |
SI prefixes are often employed to denote decimal multiples and submultiples of the metre, as shown in the table below. As indicated in the table, some are commonly used, while others are not. Long distances are usually expressed in km, astronomical units (149.6 Gm), light-years (10 Pm), or parsecs (31 Pm), rather than in Mm, Gm, Tm, Pm, Em, Zm or Ym; "30 cm", "30 m", and "300 m" are more common than "3 dm", "3 dam", and "3 hm", respectively.
The terms micron and (occasionally) millimicron are often used instead of micrometre (μm) and nanometre (nm), but this practice is officially discouraged.^{[45]}
Submultiples | Multiples | |||||
---|---|---|---|---|---|---|
Value | SI symbol | Name | Value | SI symbol | Name | |
10^{−1} m | dm | decimetre | 10^{1} m | dam | decametre | |
10^{−2} m | cm | centimetre | 10^{2} m | hm | hectometre | |
10^{−3} m | mm | millimetre | 10^{3} m | km | kilometre | |
10^{−6} m | µm | micrometre | 10^{6} m | Mm | megametre | |
10^{−9} m | nm | nanometre | 10^{9} m | Gm | gigametre | |
10^{−12} m | pm | picometre | 10^{12} m | Tm | terametre | |
10^{−15} m | fm | femtometre | 10^{15} m | Pm | petametre | |
10^{−18} m | am | attometre | 10^{18} m | Em | exametre | |
10^{−21} m | zm | zeptometre | 10^{21} m | Zm | zettametre | |
10^{−24} m | ym | yoctometre | 10^{24} m | Ym | yottametre | |
Common prefixed units are in bold face. |
Metric unit expressed in non-SI units |
Non-SI unit expressed in metric units | |||||||
---|---|---|---|---|---|---|---|---|
1 metre | ≈ | 1.0936 | yard | 1 yard | ≡ | 0.9144 | metre | |
1 metre | ≈ | 39.370 | inches | 1 inch | ≡ | 0.0254 | metre | |
1 centimetre | ≈ | 0.39370 | inch | 1 inch | ≡ | 2.54 | centimetres | |
1 millimetre | ≈ | 0.039370 | inch | 1 inch | ≡ | 25.4 | millimetres | |
1 metre | ≡ | 1 × 10^{10} | ångström | 1 ångström | ≡ | 1 × 10^{−10} | metre | |
1 nanometre | ≡ | 10 | ångström | 1 ångström | ≡ | 100 | picometres |
Within this table, "inch" and "yard" mean "international inch" and "international yard"^{[46]} respectively, though approximate conversions in the left column hold for both international and survey units.
One metre is exactly equivalent to 10 000/254 inches and to 10 000/9 144 yards.
A simple mnemonic aid exists to assist with conversion, as three "3"s:
The ancient Egyptian cubit was about 0.5 m (surviving rods are 523–529 mm). Scottish and English definitions of the ell (two cubits) were 941 mm (0.941 m) and 1143 mm (1.143 m) respectively. The ancient Parisian toise (fathom) was slightly shorter than 2 m and was standardised at exactly 2 m in the mesures usuelles system, such that 1 m was exactly ^{1}⁄_{2} toise. The Russian verst was 1.0668 km. The Swedish mil was 10.688 km, but was changed to 10 km when Sweden converted to metric units.
The spelling of English words is in accordance with the United States Government Printing Office Style Manual, which follows Webster's Third New International Dictionary rather than the Oxford Dictionary. Thus the spellings “meter,”…rather than “metre,”...as in the original BIPM English text...
An identical metric system to that introduced in France was proposed in 1668 by Bishop John Wilkins, a founder of the Royal Society in England. ... he proposed an integrated system of measurement based on a decimal system and almost identical to the modern metric system. His unit of measurement was 997 millimeters - almost exactly a meter.
he [Wilkins] proposed essentially what became ... the French decimal metric system
The error [introduced by using air] can be reduced tenfold if the chamber is filled with an atmosphere of helium rather than air.
Data from Giacomo, P., Du platine à la lumière [From platinum to light], Bull. Bur. Nat. Metrologie, 102 (1995) 5–14.
The 100 metres, or 100 metre dash, is a sprint race in track and field competitions. The shortest common outdoor running distance, it is one of the most popular and prestigious events in the sport of athletics. It has been contested at the Summer Olympics since 1896 for men and since 1928 for women.
The reigning 100 m Olympic champion is often named "the fastest man in the world". The World Championships 100 metres has been contested since 1983. Justin Gatlin and Tori Bowie are the reigning world champions; Usain Bolt and Elaine Thompson are the men's and women's Olympic champions.
On an outdoor 400 metres running track, the 100 m is run on the home straight, with the start usually being set on an extension to make it a straight-line race. Runners begin in the starting blocks and the race begins when an official fires the starter's pistol. Sprinters typically reach top speed after somewhere between 50 and 60 m. Their speed then slows towards the finish line.
The 10-second barrier has historically been a barometer of fast men's performances, while the best female sprinters take eleven seconds or less to complete the race. The current men's world record is 9.58 seconds, set by Jamaica's Usain Bolt in 2009, while the women's world record of 10.49 seconds set by American Florence Griffith-Joyner in 1988 remains unbroken.The 100 m (109.361 yards) emerged from the metrication of the 100 yards (91.44 m), a now defunct distance originally contested in English-speaking countries. The event is largely held outdoors as few indoor facilities have a 100 m straight.
US athletes have won the men's Olympic 100 metres title more times than any other country, 16 out of the 28 times that it has been run. US women have also dominated the event winning 9 out of 21 times.
110 metres hurdlesThe 110 metres hurdles, or 110-meter hurdles, is a hurdling track and field event for men. It is included in the athletics programme at the Summer Olympic Games. The female counterpart is the 100 metres hurdles. As part of a racing event, ten hurdles of 1.067 metres (3.5 ft or 42 inches) in height are evenly spaced along a straight course of 110 metres. They are positioned so that they will fall over if bumped into by the runner. Fallen hurdles do not carry a fixed time penalty for the runners, but they have a significant pull-over weight which slows down the run. Like the 100 metres sprint, the 110 metres hurdles begins in the starting blocks.
For the 110 m hurdles, the first hurdle is placed after a run-up of 13.72 metres (45 ft) from the starting line. The next nine hurdles are set at a distance of 9.14 metres (30 ft) from each other, and the home stretch from the last hurdle to the finish line is 14.02 metres (46 ft) long.
The Olympic Games have included the 110 metre hurdles in their program since 1896. The equivalent hurdles race for women was run over a course of 80 metres from 1932 to 1968. Starting with the 1972 Summer Olympics, the women's race was set at 100 metres. In the early 20th century, the race was often contested as 120 yard hurdles, thus the imperial units distances between hurdles.
The fastest 110 metre hurdlers run the distance in around 13 seconds. Aries Merritt of the United States holds the current world record of 12.80 seconds, set at the Memorial Van Damme meet on 7 September 2012 in Belgium.
1500 metresThe 1500 metres or 1,500-metre run (typically pronounced 'fifteen-hundred metres') is the foremost middle distance track event in athletics. The distance has been contested at the Summer Olympics since 1896 and the World Championships in Athletics since 1983. It is equivalent to 1.5 kilometers or approximately 15⁄16 miles.
The demands of the race are similar to that of the 800 metres, but with a slightly higher emphasis on aerobic endurance and a slightly lower sprint speed requirement. The 1500 metre race is predominantly aerobic, but anaerobic conditioning is also required.Each lap run during the world-record race run by Hicham El Guerrouj of Morocco in 1998 in Rome, Italy averaged just under 55 seconds (or under 13.8 seconds per 100 metres). 1,500 metres is three and three-quarter laps around a 400-metre track. During the 1970s and 1980s this race was dominated by British runners, along with an occasional Finn, American, or New Zealander, but through the 1990s a large number of African runners began to take over in being the masters of this race, with runners from Kenya, Morocco, and Algeria winning the Olympic gold medals.
In the Modern Olympic Games, the men's 1,500-metre race has been contested from the beginning, and at every Olympic Games since. The first winner, in 1896, was Edwin Flack of Australia, who also won the first gold medal in the 800-metre race. The women's 1,500-metre race was first added to the Summer Olympics in 1972, and the winner of the first gold medal was Lyudmila Bragina of the Soviet Union. During the Olympic Games of 1972 through 2008, the women's 1,500-metre race has been won by three Soviets plus one Russian, one Italian, one Romanian, one Briton, one Kenyan, and two Algerians. The 2012 Olympic results are still undecided as a result of multiple doping cases. The best women's times for the race were controversially set by Chinese runners, all set in the same race on just two dates 4 years apart at the Chinese National Games. At least one of those top Chinese athletes has admitted to being part of a doping program. The women's record was finally surpassed by Genzebe Dibaba of Ethiopia in 2015.
In American high schools, the mile run (which is 1609.344 metres in length) and the 1,600-metre run, also colloquially referred to as "metric mile", are more frequently run than the 1,500-metre run, since US customary units are better-known in America. Which distance is used depends on which state the high school is in, and, for convenience, national rankings are standardized by converting all 1,600-metre run times to their mile run equivalents.
400 metresThe 400 metres, or 400 metre dash, is a sprinting event in track and field competitions. It has been featured in the athletics programme at the Summer Olympics since 1896 for men and since 1964 for women. On a standard outdoor running track, it is one lap around the track. Runners start in staggered positions and race in separate lanes for the entire course. In many countries, athletes previously competed in the 440 yard dash (402.336 m)—which is a quarter of a mile and was referred to as the 'quarter-mile'—instead of the 400 m (437.445 yards), though this distance is now obsolete.
Maximum sprint speed capability is a significant contributing factor to success in the event, but athletes also require substantial speed endurance and the ability to cope well with high amounts of lactic acid to sustain a fast speed over a whole lap. While considered to be predominantly an anaerobic event, there is some aerobic involvement and the degree of aerobic training required for 400 metre athletes is open to debate.The current men's world record is held by Wayde van Niekerk of South Africa, with a time of 43.03 seconds; van Niekerk is also the reigning world and Olympic champion. The world indoor record holder is Michael Norman, in 44.52 seconds. The current women's world record is held by Marita Koch, with a time of 47.60 seconds. Phyllis Francis is the reigning women's world champion, while Shaunae Miller holds the women's Olympic title. The men's T43 Paralympic world record of 45.07 seconds is held by Oscar Pistorius.An Olympic double of 200 metres and 400 m was first achieved by Valerie Brisco-Hooks in 1984, and later by Marie-José Pérec of France and Michael Johnson from the United States on the same evening in 1996. Alberto Juantorena of Cuba at the 1976 Summer Olympics became the first and so far the only athlete to win both the 400 m and 800 m Olympic titles. Pérec became the first to defend the Olympic title in 1996, Johnson became the first and only man to do so in 2000.
The Olympic champion has frequently won a second gold medal in the 4 × 400 metres relay. This has been accomplished 14 times by men; Charles Reidpath, Ray Barbuti, Bill Carr, George Rhoden, Charles Jenkins, Otis Davis, Mike Larrabee, Lee Evans, Viktor Markin, Alonzo Babers, Steve Lewis, Quincy Watts, Jeremy Wariner and LaShawn Merritt; and 4 times by women; Monika Zehrt, Valerie Brisco-Hooks, Olga Bryzgina and Sanya Richards-Ross. All but Rhoden, Markin, Zehrt and Bryzgina ran on American relay teams. Injured after his double in 1996, Johnson also accomplished the feat in 2000 only to have it disqualified when his teammate Antonio Pettigrew admitted to doping.
Cubic metreThe cubic metre (in British English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the SI derived unit of volume. Its SI symbol is m3. It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère, still sometimes used for dry measure (for instance, in reference to wood). Another alternative name, no longer widely used, was the kilolitre.
International System of UnitsThe International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the ampere, kelvin, second, metre, kilogram, candela, mole, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.
The base units are derived from invariant constants of nature, such as the speed of light in vacuum and the triple point of water, which can be observed and measured with great accuracy, and one physical artefact. The artefact is the international prototype kilogram, certified in 1889, and consisting of a cylinder of platinum-iridium, which nominally has the same mass as one litre of water at the freezing point. Its stability has been a matter of significant concern, culminating in a revision of the definition of the base units entirely in terms of constants of nature, scheduled to be put into effect on 20 May 2019.Derived units may be defined in terms of base units or other derived units. They are adopted to facilitate measurement of diverse quantities. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. The most recent derived unit, the katal, was defined in 1999.
The reliability of the SI depends not only on the precise measurement of standards for the base units in terms of various physical constants of nature, but also on precise definition of those constants. The set of underlying constants is modified as more stable constants are found, or may be more precisely measured. For example, in 1983 the metre was redefined as the distance that light propagates in vacuum in a given fraction of a second, thus making the value of the speed of light in terms of the defined units exact.
The motivation for the development of the SI was the diversity of units that had sprung up within the centimetre–gram–second (CGS) systems (specifically the inconsistency between the systems of electrostatic units and electromagnetic units) and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and standardise the rules for writing and presenting measurements. The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre–kilogram–second system of units (MKS) rather than any variant of the CGS. Since then, the SI has been adopted by all countries except the United States, Liberia and Myanmar.
JouleThe joule (/dʒuːl/; symbol: J) is a derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre (1 newton metre or N⋅m). It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).
In terms firstly of base SI units and then in terms of other SI units:
where kg is the kilogram, m is the metre, s is the second, N is the newton, Pa is the pascal, W is the watt, C is the coulomb, and V is the volt.
One joule can also be defined as:
LitreThe litre (international spelling) or liter (American spelling) (symbols L or l) is an SI accepted metric system unit of volume equal to 1 cubic decimetre (dm3), 1,000 cubic centimetres (cm3) or 1/1,000 cubic metre. A cubic decimetre (or litre) occupies a volume of 10 cm×10 cm×10 cm (see figure) and is thus 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 several subsequent versions of the metric system and is accepted for use with the SI, although not an SI unit — the SI unit of volume is the cubic metre (m3). The spelling used by the International Bureau of Weights and Measures is "litre", a spelling which is shared by almost all English-speaking countries. The spelling "liter" is predominantly used in American English.One litre of liquid water has a mass of almost exactly one kilogram, because the kilogram was originally defined in 1795 as the mass of one cubic decimetre of water at the temperature of melting ice. Subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact.
Metre-gauge railwayMetre-gauge railways are narrow-gauge railways with track gauge of 1,000 mm (3 ft 3 3⁄8 in) or 1 metre.
Metre (music)In music, metre (Am. meter) refers to the regularly recurring patterns and accents such as bars and beats. Unlike rhythm, metric onsets are not necessarily sounded, but are nevertheless expected by the listener.
A variety of systems exist throughout the world for organising and playing metrical music, such as the Indian system of tala and similar systems in Arabian and African music.
Western music inherited the concept of metre from poetry (Scholes 1977; Latham 2002b) where it denotes: the number of lines in a verse; the number of syllables in each line; and the arrangement of those syllables as long or short, accented or unaccented (Scholes 1977; Latham 2002b). The first coherent system of rhythmic notation in modern Western music was based on rhythmic modes derived from the basic types of metrical unit in the quantitative meter of classical ancient Greek and Latin poetry (Hoppin 1978, 221).
Later music for dances such as the pavane and galliard consisted of musical phrases to accompany a fixed sequence of basic steps with a defined tempo and time signature. The English word "measure", originally an exact or just amount of time, came to denote either a poetic rhythm, a bar of music, or else an entire melodic verse or dance (Merriam-Webster 2015) involving sequences of notes, words, or movements that may last four, eight or sixteen bars.
Metre (poetry)In poetry, metre (British) or meter (American; see spelling differences) is the basic rhythmic structure of a verse or lines in verse. Many traditional verse forms prescribe a specific verse metre, or a certain set of metres alternating in a particular order. The study and the actual use of metres and forms of versification are both known as prosody. (Within linguistics, "prosody" is used in a more general sense that includes not only poetic metre but also the rhythmic aspects of prose, whether formal or informal, that vary from language to language, and sometimes between poetic traditions.)
Metre per secondMetre per second (American English: meter per second) is an SI derived unit of both speed (scalar) and velocity (vector quantity which specifies both magnitude and a specific direction), defined by distance in metres divided by time in seconds.
The SI unit symbols are m·s−1, m s−1, m/s, or m/s, sometimes (unofficially) abbreviated as mps. Where metres per second are several orders of magnitude too slow to be convenient, such as in astronomical measurements, velocities may be given in kilometres per second, where 1 km/s is 1000 metres per second, sometimes unofficially abbreviated as "kps".
Metric systemThe metric system is an internationally recognised decimalised system of measurement. It is in widespread use, and where it is adopted, it is the only or most common system of weights and measures (see metrication). It is now known as the International System of Units (SI). It is used to measure everyday things such as the mass of a sack of flour, the height of a person, the speed of a car, and the volume of fuel in its tank. It is also used in science, industry and trade.
In its modern form, it consists of a set of base units including metre for length, kilogram for mass, second for time and ampere for electrical current, and a few others, which together with their derived units, can measure any physical quantity. Metric system may also refer to other systems of related base and derived units defined before the middle of the 20th century, some of which are still in limited use today.
The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units. It is also a coherent system, which means that its units do not introduce conversion factors not already present in equations relating quantities. It has a property called rationalisation that eliminates certain constants of proportionality in equations of physics.
The units of the metric system, originally taken from observable features of nature, are now defined by phenomena such as the microwave frequency of a caesium atomic clock which accurately measures seconds. One unit, the kilogram, remains defined in terms of a man-made artefact, but scientists recently voted to change the definition to one based on Planck's constant via a Kibble balance. The new definition is expected to be formally propagated on 20 May 2019.
While there are numerous named derived units of the metric system, such as watt and lumen, other common quantities such as velocity and acceleration do not have their own unit, but are defined in terms of existing base and derived units such as metres per second for velocity.
Though other currently or formerly widespread systems of weights and measures continue to exist, such as the British imperial system and the US customary system of weights and measures, in those systems most or all of the units are now defined in terms of the metric system, such as the US foot which is now a defined decimal fraction of a metre.
The metric system is also extensible, and new base and derived units are defined as needed in fields such as radiology and chemistry. The most recent derived unit, the katal, for catalytic activity, was added in 1999. Recent changes are directed toward defining base units in terms of invariant constants of physics to provide more precise realisations of units for advances in science and industry.
NanometreThe nanometre (International spelling as used by the International Bureau of Weights and Measures; SI symbol: nm) or nanometer (American spelling) is a unit of length in the metric system, equal to one billionth (short scale) of a metre (0.000000001 m). The name combines the SI prefix nano- (from the Ancient Greek νάνος, nanos, "dwarf") with the parent unit name metre (from Greek μέτρον, metrοn, "unit of measurement"). It can be written in scientific notation as 1×10−9 m, in engineering notation as 1 E−9 m, and is simply 1/1000000000 metres. One nanometre equals ten ångströms. When used as a prefix for something other than a unit of measure (as in "nanoscience"), nano refers to nanotechnology,
or phenomena typically occurring on a scale of nanometres (see nanoscopic scale).The nanometre is often used to express dimensions on an atomic scale: the diameter of a helium atom, for example, is about 0.1 nm, and that of a ribosome is about 20 nm. The nanometre is also commonly used to specify the wavelength of electromagnetic radiation near the visible part of the spectrum: visible light ranges from around 400 to 700 nm. The ångström, which is equal to 0.1 nm, was formerly used for these purposes, but is still used in other fields. Since the late 1980s, in usages such as 32 nm and 22 nm, it has also been used to describe typical feature sizes in successive generations of the ITRS Roadmap for miniaturization in the semiconductor industry.
Orders of magnitude (length)The following are examples of orders of magnitude for different lengths.
SI derived unitSI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.
The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg m−3), the SI derived unit of density.
The names of SI derived units, when written in full, are in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz"; but the symbol for metre is "m".
Square metreThe square metre (International spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the SI derived unit of area with symbol m2.Adding and subtracting SI prefixes creates multiples and submultiples; however, as the unit is exponentiated, the quantities grow geometrically by the corresponding power of 10. For example, a kilometre is 103 (a thousand) times the length of a metre, but a square kilometre is 1032 (106, a million) times the area of a square metre, and a cubic kilometre is 1033 (109, a billion) cubic metres.
TorqueTorque, moment, or moment of force is the rotational equivalent of linear force. The concept originated with the studies of Archimedes on the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector connecting the origin to the point of force application, and the angle between the force and lever arm vectors. In symbols:
where
The SI unit for torque is N⋅m. For more on the units of torque, see Units.
VolumeVolume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container; i. e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.
Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.
The volume of a solid (whether regularly or irregularly shaped) 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 just one of the substances. However, sometimes one substance dissolves in the other and in such cases the combined volume is not additive.In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant.
In thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure.
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