fundamental and derived quantities and units of measurement
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In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position
English units of measurement principal system of weights and measures used in a few nations, the only major industrial one being the United States. It actually consists of two related systemsâ€”the U.S. Customary System of units, used in the United States and dependencies, and the British Imperial System. The names of the units and the relationships between them are generally the same in both systems, but the sizes of the units differ, sometimes considerably. Customary Units of Weights and Measures Units of Weight The pound (lb) is the basic unit of weight (which is proportional to mass). Within the English units of measurement there are three different systems of weights. In the avoirdupois system, the most widely used of the three, the pound is divided into 16 ounces (oz) and the ounce into 16 drams. The ton, used to measure large masses, is equal to 2,000 lb (short ton) or 2,240 lb (long ton). In Great Britain the stone, equal to 14 lb, is also used. The troy system (named for Troyes, France, where it is said to have originated) is used only for precious metals. The troy pound is divided into 12 ounces and the troy ounce into 20 pennyweights or 480 grains; the troy pound is thus 5,760 grains. The grain is also a unit in the avoirdupois system, 1 avoirdupois pound being 7,000 grains, so that the troy pound is 5,760/7,000 of an avoirdupois pound. Apothecaries' weights are based on troy weights; in addition to the pound, ounce, and grain, which are equal to the troy units of the same name, other units are the dram (1/8 oz) and the scruple (1/24 oz or 1/3 dram). Units of Length and Area The basic unit of length is the yard (yd); fractions of the yard are the inch (1/36 yd) and the foot (1/3 yd), and commonly used multiples are the rod (5 1/2 yd), the furlong (220 yd), and the mile (1,760 yd). The acre, equal to 4,840 square yards or 160 square rods, is used for measuring land area. Units of Liquid Measure For liquid measure, or liquid capacity, the basic unit is the gallon, which is divided into 4 quarts, 8 pints, or 32 gills. The U.S. gallon, or wine gallon, is 231 cubic inches (cu in.); the British imperial gallon is the volume of 10 lb of pure water at 62Â°F and is equal to 277.42 cu in. The British units of liquid capacity are thus about 20% larger than the corresponding American units. The U.S. fluid ounce is 1/16 of a U.S. pint; the British unit of the same name is 1/20 of an imperial pint and is thus slightly smaller than the U.S. fluid ounce. Units of Dry Measure For dry measure, or dry capacity, the basic unit is the bushel, which is divided into 4 pecks, 32 dry quarts, or 64 dry pints. The U.S. bushel, or Winchester bushel, is 2,150.42 cu in. and is about 3% smaller than the British imperial bushel of 2,219.36 cu in., with a similar difference existing between U.S. and British subdivisions. The barrel is a unit for measuring the capacity of larger quantities and has various legal definitions depending on the quantity being measured, the most common value being 105 dry quarts. Differences between American and British Systems Many American units of weights and measures are based on units in use in Great Britain before 1824, when the British Imperial System was established. Since the Mendenhall Order of 1893, the U.S. yard and pound and all other units derived from them have been defined in terms of the metric units of length and mass, the meter and the kilogram ; thus, there is no longer any direct relationship between American units and British units of the same name. In 1959 an international agreement was reached among English-speaking nations to use the same metric equivalents for the yard and pound for purposes of science and technology; these values are 1 yd=0.9144 meter (m) and 1 lb=0.45359237 kilogram (kg). In the United States, the older definition of the yard as 3,600/3,937 m is still used for surveying, the corresponding foot (1,200/3,937 m) being known as the survey foot. The English units of measurement have many drawbacks: the complexity of converting from one unit to another, the differences between American and British units, the use of the same name for different units (e.g., ounce for both weight and liquid capacity, quart and pint for both liquid and dry capacity), and the existence of three different systems of weights (avoirdupois, troy, and apothecaries'). Because of these disadvantages and because of the wide use of the much simpler metric system in most other parts of the world, there have been proposals to do away with the U.S. Customary System and replace it with the metric system. Bibliography See L. J. Chisholm, Units of Weights and Measure: International and U.S. Customary (U.S. National Bureau of Standards, 1967).
Fundamental particles are the elementary entities from which all matter is made. They have no known smaller parts. As recently as 1900 most people believed that atoms were the tiniest particles in the universe. By the 1930s, however, it was clear that atoms were made up of even smaller particlesâ€”protons, neutrons, and electrons, then considered to be the fundamental particles of matter. (A proton is a positively charged particle that weighs about one atomic mass unit [1.0073 AMU]; a neutron has about the same mass [1.0087 AMU] but no charge; and an electron has a much smaller mass [0.0005 AMU] and a negative charge.) Protons and neutrons make up the tiny nucleus of an atom, while electrons exist outside the atomic nucleus in discrete energy levels within an electron "cloud." By 1970 it began to appear that matter might contain even smaller particles, an idea suggested in 1963 by American physicist Murray Gell-Mann (who called the particles quarks ) and independently by American physicist George Zweig (who called them aces ). There are in actuality hundreds of subatomic particles that have been observed, but many of them are unstable. At the start of the twenty-first century, scientists believe that all matter is made up of tiny particles called fermions (named after American physicist Enrico Fermi). Fermions include quarks and leptons. Leptons include electrons (along with muons and neutrinos); they have no measurable size, and they are not affected by the strong nuclear force. Quarks, on the other hand, are influenced by the strong nuclear force. They are the fundamental particles that make up protons and neutrons (as well as mesons and some other particles). Both protons and neutrons are classified as baryons, composite particles each made up of three quarks. Quarks come in six different types, or "flavors": up and down, top and bottom, and charm and strange. Protons and neutrons are made of up (u) quarks (which have a charge of +â…”) and down (d) quarks (which have a charge of âˆ’â…“). A proton is made from two u quarks (+â…”)(+â…”) and one d quark (âˆ’â…“), giving a total charge of +1. A neutron contains one u quark (+â…”) and two d quarks (âˆ’â…“)(âˆ’â…“) for a total charge of zero. There are also fundamental forces acting on matter; these have their own sets of fundamental particles. The forces are the strong nuclear force (or strong interaction), the weak nuclear force (or weak interaction), and electromagnetism (which includes light, x rays, and all the other electromagnetic forces). All these forces are transmitted by particles called fundamental bosons (named after Indian physicist S. N. Bose). Fundamental bosons differ from fermions in spin and the number of quarks they contain. Fermions have spins measured in half numbers, and they contain an odd number of quarks. Bosons have whole integer spins, and they contain an even number of quarks. The bosons that transmit the strong nuclear force are called gluons, those that transmit electromagnetic forces are photons, and those transmitting the weak force are known as weak bosons. A fourth force, the gravitational force, is believed to be transmitted by particles called gravitons; however, the particles have not yet been observed. Still another kind of boson, called a Higgs boson, is thought to be the source of mass in other particles, but this particle also has not actually been observed. The study of fundamental particles often involves speeding up charged particles, such as protons or electrons, and then letting them collide with targets so as to produce other particles for further study. The particle accelerators used to do this are devices that force the charged particles to jump over longer and longer space gaps per unit of time, until the particles are moving at speeds approaching the speed of light. The earliest of such devices were the linear Cockcroft-Walton accelerator (1929), the circular cyclotron (1930), and the Van de Graaff generator (1931). Modern synchrotrons are large machines that have both linear and curved sections. The most powerful synchrotron is the Tevatron proton accelerator at the Fermilab located near Batavia, Illinois (just outside of Chicago); it lies inside an underground circular tunnel that measures almost 6.4 kilometers (4.0 miles) around. The longest accelerator is the collider at the CERN research center in Geneva, Switzerlandâ€”it has a circumference of about 27.3 kilometers (17.0 miles). Detection of fundamental particles is difficult because the particles are so extremely tiny. The earliest detector was just photographic film, since particles passing through would expose the film and become evident when it was developed. The first device designed for the purpose of detecting tiny particles was the "cloud chamber" (invented by Scottish physicist Charles Wilson in 1911). It was a glass container filled with air saturated with water (or alcohol) vapor. Charged particles passing through the chamber formed ions leaving fog tracksâ€”the heavier the particles, the wider their tracks. The "bubble chamber" (invented by American physicist Donald Glaser in 1952) was similar to a cloud chamber, except that it was filled with a liquid (usually liquefied helium or hydrogen) held at a temperature just below its boiling point. Moving particles would disturb the liquid, causing bubbles to form along their paths. There was also a "spark chamber" (invented in Japan in 1959) that contained a series of parallel metal plates and produced an electrical discharge along the ion trail left by a charged particle. Although all of these devices were once important for detecting subatomic particles, they have largely been replaced by more modern detectors. In the twenty-first century fundamental particles are studied using detectors such as tracking chambers (which trace the path of a particle with electrical signals), sampling calorimeters (which track the particle's path by its energy of motion), scintillators (which give off light when particles strike them), or magnetic detectors (which cause charged particles to move in curved paths). Many instruments use combinations of these various kinds of detectors. The inspiration for C. T. R. Wilson's expansion, or cloud, chamber came from his interest in meteorological sciences. His initial intention was to recreate cloud formations. This led to an interest in studying atmospheric electric fields and the vapor trail of ions. For his work he shared the Nobel Prize in 1927. â€”Valerie Borek To further complicate the subject of subatomic particles, each kind of particle has an antiparticle. For example, for each kind of quark there is an antiquark of the same mass and spin, but of opposite charge. The first antiparticle to be observed was the positron, an electron with a positive charge. An antiproton is like a proton, but it has a negative charge. Antiparticles can be observed, and molecules of antimatter can even be generated. A positron orbiting an antiproton, for example, is an antihydrogen atom. Many scientists believe that there must be some areas of the universe that are completely made up of antimatter, the exact opposite of the kind of matter found on Earth. If that is true, such areas would not be very compatible with areas made of matterâ€”when a particle and its antiparticle make contact, they destroy each other and are converted into energy. According to Einstein's special theory, E = mc2, which means that energy is equivalent to mass times the speed of light, squared. In other words, a tiny speck of matter can be converted to a considerable amount of energy. The conversion can also go the other way. Large releases of energy that occur when high-energy particles collide can produce new particles and antiparticles of matter. Much modern research in particle physics involves high-energy collisions between beams of particles, such as protons, so as to generate other kinds of particles. Some collisions involve interactions of particles with antiparticles (e.g., electrons with positrons). Particle accelerators have been turned into giant colliders in which beams of particles moving at speeds approaching the speed of li
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Answers:Here are the seven fundamental quantities. I also included their definitions and SI units. length - meter (m) - the measurement or extent of something from end to end. mass - kilogram (kg) - a coherent body of matter with no definite shape. time - second (s) - the indefinite continued progress of existence and events. electric current - ampere (A) - flow of electric charge. thermodynamic temperature - kelvin (K) - A measure proportional to the thermal energy of a given body at equilibrium. amount of substance - mole (mol) - the number of specified group of entities present in a substance. luminous intensity - candela (cd) - an expression of the amount of light power emanating from a point source within a solid angle of one steradian.
Answers:A fundamental physical quantity is an actual measurable quantity, for example: speed of light, weight of an electron, charge of an electron. A Standard unit is a defined measurement unit like a meter, or a gram.
Answers:(I)fundamental units: those units which are the quantities which are independent of each other. All other quantities may be expressed in these units. It turns out that the number of fundamental units is 7. They are: (a)length (metre; m) (b)mass (kilogram, kg) (c)time (second, s) (d)luminous intensity (candela, cd) (e)electric intensity (ampere, A) (f)amount of substance (mole, mol) (g)thermodynamic temperature (Kelvin, K)
Answers:Derived from year and c