1.
Maurice Quentin de La Tour
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Maurice Quentin de La Tour was a French Rococo portraitist who worked primarily with pastels. Among his most famous subjects were Voltaire, Rousseau, Louis XV and Madame de Pompadour. He was born in Saint-Quentin, Aisne, the son of a musician, François de La Tour, a Laonnois. François de La Tour apparently was successively a trumpet-player for the regiment of the duc du Maine. He is popularly said to have disapproved of his son taking up the arts, according to François Marandet in 2002, an apprenticeship was arranged for La Tour with a painter named Dupouch from 12 October 1719, but it is not known when this contract was terminated. After travelling briefly to England in 1725, he returned to Paris in 1727 and his earliest known portrait, of which only an engraving by Langlois of 1731 is testament, was that of Voltaire. Nevertheless, the painter Joseph Ducreux claimed to be his only student, on 25 May 1737 La Tour was officially recognised by the Royal Academy of Painting and Sculpture, and soon attracted the attention of the French court. According to Jeffares, he had an apartment in the palais du Louvre in 1745, contemporary accounts describe Quentin de La Tours nature as lively, good-humoured, but eccentric. However, of a nervous disposition, and an exacting practitioner, he has also been accused of over-engineering his work. He was also advisor and benefactor to the Royal Academy of Painting and Sculpture in Paris, jean-François de La Tour, chevalier de lordre royal militaire de Saint-Louis, was the natural heir to his estate. Issue of regular 50 Francs French Banknotes during the years 1976 to 1992 with de La Tours portrait, mariette et autres notes inédites de cet amateur sur les arts et les artistes. III, 1854–56, pp. 66–78. de Goncourt, Edmond and Jules
Maurice Quentin de La Tour
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Self-portrait with Lace Jabot (ca 1751)
Maurice Quentin de La Tour
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Voltaire
Maurice Quentin de La Tour
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Marquise de Pompadour
Maurice Quentin de La Tour
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Jean-Jacques Rousseau
2.
University of Paris
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The University of Paris, metonymically known as the Sorbonne, was a university in Paris, France. Emerging around 1150 as an associated with the cathedral school of Notre Dame de Paris. Vast numbers of popes, royalties, scientists and intellectuals were educated at the University of Paris, following the turbulence of the French Revolution, education was suspended in 1793 whereafter its faculties were partly reorganised by Napoleon as the University of France. In 1896, it was renamed again to the University of Paris, in 1970, following the May 1968 events, the university was divided into 13 autonomous universities. Others, like Panthéon-Sorbonne University, chose to be multidisciplinary, in 1150, the future University of Paris was a student-teacher corporation operating as an annex of the Notre-Dame cathedral school. The university had four faculties, Arts, Medicine, Law, the Faculty of Arts was the lowest in rank, but also the largest, as students had to graduate there in order to be admitted to one of the higher faculties. The students were divided into four nationes according to language or regional origin, France, Normandy, Picardy, the last came to be known as the Alemannian nation. Recruitment to each nation was wider than the names might imply, the faculty and nation system of the University of Paris became the model for all later medieval universities. Under the governance of the Church, students wore robes and shaved the tops of their heads in tonsure, students followed the rules and laws of the Church and were not subject to the kings laws or courts. This presented problems for the city of Paris, as students ran wild, students were often very young, entering the school at age 13 or 14 and staying for 6 to 12 years. Three schools were especially famous in Paris, the palatine or palace school, the school of Notre-Dame, the decline of royalty brought about the decline of the first. The other two were ancient but did not have much visibility in the early centuries, the glory of the palatine school doubtless eclipsed theirs, until it completely gave way to them. These two centres were much frequented and many of their masters were esteemed for their learning, the first renowned professor at the school of Ste-Geneviève was Hubold, who lived in the tenth century. Not content with the courses at Liège, he continued his studies at Paris, entered or allied himself with the chapter of Ste-Geneviève, and attracted many pupils via his teaching. Distinguished professors from the school of Notre-Dame in the century include Lambert, disciple of Fulbert of Chartres, Drogo of Paris, Manegold of Germany. Three other men who added prestige to the schools of Notre-Dame and Ste-Geneviève were William of Champeaux, Abélard, humanistic instruction comprised grammar, rhetoric, dialectics, arithmetic, geometry, music, and astronomy. To the higher instruction belonged dogmatic and moral theology, whose source was the Scriptures and it was completed by the study of Canon law. The School of Saint-Victor arose to rival those of Notre-Dame and Ste-Geneviève and it was founded by William of Champeaux when he withdrew to the Abbey of Saint-Victor
University of Paris
University of Paris
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University of Paris
University of Paris
University of Paris
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The Sorbonne covered by snow.
3.
Virtual work
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Virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement will be different for different displacements, among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed by the according to the principle of least action. The work of a force on a particle along a displacement is known as the virtual work. The principle of work had always been used in some form since antiquity in the study of statics. It was used by the Greeks, medieval Arabs and Latins, working with Leibnizian concepts, Johann Bernoulli systematized the virtual work principle and made explicit the concept of infinitesimal displacement. He was able to solve problems for both bodies as well as fluids. Bernoullis version of virtual work law appeared in his letter to Pierre Varignon in 1715 and this formulation of the principle is today known as the principle of virtual velocities and is commonly considered as the prototype of the contemporary virtual work principles. In 1743 DAlembert published his Traite de Dynamique where he applied the principle of work, based on the Bernoullis work. His idea was to convert a dynamical problem into static problem by introducing inertial force, consider a point particle that moves along a path which is described by a function r from point A, where r, to point B, where r. It is possible that the moves from A to B along a nearby path described by r + δr. The variation δr satisfies the requirement δr = δr =0, the components of the variation, δr1, δr2 and δr3, are called virtual displacements. This can be generalized to a mechanical system defined by the generalized coordinates qi. In which case, the variation of the qi is defined by the virtual displacements δqi. Virtual work is the work done by the applied forces. When considering forces applied to a body in equilibrium, the principle of least action requires the virtual work of these forces to be zero. Consider a particle P that moves from a point A to a point B along a trajectory r and it is important to notice that the value of the work W depends on the trajectory r. Suppose the force F is the same as F, the variation of the work δW associated with this nearby path, known as the virtual work, can be computed to be δ W = W ¯ − W = ∫ t 0 t 1 d t
Virtual work
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This is an engraving from Mechanics Magazine published in London in 1824.
Virtual work
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Illustration from Army Service Corps Training on Mechanical Transport, (1911), Fig. 112 Transmission of motion and force by gear wheels, compound train
4.
Fluid dynamics
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In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids. It has several subdisciplines, including aerodynamics and hydrodynamics, before the twentieth century, hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability, the foundational axioms of fluid dynamics are the conservation laws, specifically, conservation of mass, conservation of linear momentum, and conservation of energy. These are based on mechanics and are modified in quantum mechanics. They are expressed using the Reynolds transport theorem, in addition to the above, fluids are assumed to obey the continuum assumption. Fluids are composed of molecules that collide with one another and solid objects, however, the continuum assumption assumes that fluids are continuous, rather than discrete. The fact that the fluid is made up of molecules is ignored. The unsimplified equations do not have a general solution, so they are primarily of use in Computational Fluid Dynamics. The equations can be simplified in a number of ways, all of which make them easier to solve, some of the simplifications allow some simple fluid dynamics problems to be solved in closed form. Three conservation laws are used to solve fluid dynamics problems, the conservation laws may be applied to a region of the flow called a control volume. A control volume is a volume in space through which fluid is assumed to flow. The integral formulations of the laws are used to describe the change of mass, momentum. Mass continuity, The rate of change of fluid mass inside a control volume must be equal to the net rate of flow into the volume. Mass flow into the system is accounted as positive, and since the vector to the surface is opposite the sense of flow into the system the term is negated. The first term on the right is the net rate at which momentum is convected into the volume, the second term on the right is the force due to pressure on the volumes surfaces. The first two terms on the right are negated since momentum entering the system is accounted as positive, the third term on the right is the net acceleration of the mass within the volume due to any body forces. Surface forces, such as forces, are represented by F surf. The following is the form of the momentum conservation equation
Fluid dynamics
5.
Three-body problem
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The three-body problem is a special case of the n-body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth, in an extended modern sense, a three-body problem is a class of problems in classical or quantum mechanics that model the motion of three particles. The gravitational problem of three bodies in its traditional sense dates in substance from 1687, when Isaac Newton published his Principia. The physical problem was addressed by Amerigo Vespucci and subsequently by Galileo Galilei, however the accuracy of the lunar theory was low, due to the perturbing effect of the Sun and planets on the motion of the Moon around the Earth. They submitted their competing first analyses to the Académie Royale des Sciences in 1747 and it was in connection with these researches, in Paris, in the 1740s, that the name three-body problem began to be commonly used. An account published in 1761 by Jean le Rond dAlembert indicates that the name was first used in 1747, in 1887, mathematicians Heinrich Bruns and Henri Poincaré showed that there is no general analytical solution for the three-body problem given by algebraic expressions and integrals. The motion of three bodies is generally non-repeating, except in special cases, a prominent example of the classical three-body problem is the movement of a planet with a satellite around a star. In this case, the problem is simplified to two instances of the two-body problem, however, the effect of the star on the movement of the satellite around the planet can be considered as a perturbation. While a spaceflight involving a gravity assist tends to be at least a problem, once far away from the Earth when Earths gravity becomes negligible. The general statement for the three body problem is as follows, in the circular restricted three-body problem, two massive bodies move in circular orbits around their common center of mass, and the third mass is negligible with respect to the other two. It can be useful to consider the effective potential, in 1767 Leonhard Euler found three families of periodic solutions in which the three masses are collinear at each instant. In 1772 Lagrange found a family of solutions in which the three form an equilateral triangle at each instant. Together, these form the central configurations for the three-body problem. These solutions are valid for any mass ratios, and the move on Keplerian ellipses. These five families are the only solutions for which there are explicit analytic formulae. In 1893 Meissel stated what is called the Pythagorean three-body problem. Burrau further investigated this problem in 1913, in 1967 Victor Szebehely and coworkers established eventual escape for this problem using numerical integration, while at the same time finding a nearby periodic solution. In 1911, United States scientist William Duncan MacMillan found one special solution, in 1961, Russian mathematician Sitnikov improved this solution
Three-body problem
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Figure 1: Configuration of the Sitnikov Problem
Three-body problem
6.
Royal Society
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Founded in November 1660, it was granted a royal charter by King Charles II as The Royal Society. The society is governed by its Council, which is chaired by the Societys President, according to a set of statutes and standing orders. The members of Council and the President are elected from and by its Fellows, the members of the society. As of 2016, there are about 1,600 fellows, allowed to use the postnominal title FRS, there are also royal fellows, honorary fellows and foreign members, the last of which are allowed to use the postnominal title ForMemRS. The Royal Society President is Venkatraman Ramakrishnan, who took up the post on 30 November 2015, since 1967, the society has been based at 6–9 Carlton House Terrace, a Grade I listed building in central London which was previously used by the Embassy of Germany, London. The Royal Society started from groups of physicians and natural philosophers, meeting at variety of locations and they were influenced by the new science, as promoted by Francis Bacon in his New Atlantis, from approximately 1645 onwards. A group known as The Philosophical Society of Oxford was run under a set of rules still retained by the Bodleian Library, after the English Restoration, there were regular meetings at Gresham College. It is widely held that these groups were the inspiration for the foundation of the Royal Society, I will not say, that Mr Oldenburg did rather inspire the French to follow the English, or, at least, did help them, and hinder us. But tis well known who were the men that began and promoted that design. This initial royal favour has continued and, since then, every monarch has been the patron of the society, the societys early meetings included experiments performed first by Hooke and then by Denis Papin, who was appointed in 1684. These experiments varied in their area, and were both important in some cases and trivial in others. The Society returned to Gresham in 1673, there had been an attempt in 1667 to establish a permanent college for the society. Michael Hunter argues that this was influenced by Solomons House in Bacons New Atlantis and, to a lesser extent, by J. V. The first proposal was given by John Evelyn to Robert Boyle in a letter dated 3 September 1659, he suggested a scheme, with apartments for members. The societys ideas were simpler and only included residences for a handful of staff and these plans were progressing by November 1667, but never came to anything, given the lack of contributions from members and the unrealised—perhaps unrealistic—aspirations of the society. During the 18th century, the gusto that had characterised the early years of the society faded, with a number of scientific greats compared to other periods. The pointed lightning conductor had been invented by Benjamin Franklin in 1749, during the same time period, it became customary to appoint society fellows to serve on government committees where science was concerned, something that still continues. The 18th century featured remedies to many of the early problems
Royal Society
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The entrance to the Royal Society in Carlton House Terrace, London
Royal Society
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The President, Council, and Fellows of the Royal Society of London for Improving Natural Knowledge
Royal Society
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John Evelyn, who helped to found the Royal Society
Royal Society
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Mace granted by Charles II
7.
Institut de France
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The Institut de France is a French learned society, grouping five académies, the most famous of which is the Académie française. The Institute, located in Paris, manages approximately 1,000 foundations, as well as museums and it also awards prizes and subsidies, which amounted to a total of €5,028,190.55 for 2002. Most of these prizes are awarded by the Institute on the recommendation of the académies, the Institut de France was established on 25 October 1795, by the French government. Académie française – initiated 1635, suppressed 1793, restored 1803 as a division of the institute, Académie des inscriptions et belles-lettres – initiated 1663. Académie des sciences – initiated 1666, the Royal Society of Canada, initiated 1882, was modeled after the Institut de France and the Royal Society of London
Institut de France
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Institut de France, from the
pont des Arts
Institut de France
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Cupola of the Institut de France
Institut de France
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Henri Grégoire was a founding member of the Institut de France.
Institut de France
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Esplanade in front of the Institut, 1898.
8.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
Mathematics
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Euclid (holding
calipers), Greek mathematician, 3rd century BC, as imagined by
Raphael in this detail from
The School of Athens.
Mathematics
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Greek mathematician
Pythagoras (c. 570 – c. 495 BC), commonly credited with discovering the
Pythagorean theorem
Mathematics
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Leonardo Fibonacci, the
Italian mathematician who established the Hindu–Arabic numeral system to the Western World
Mathematics
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Carl Friedrich Gauss, known as the prince of mathematicians
9.
Mechanics
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Mechanics is an area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The scientific discipline has its origins in Ancient Greece with the writings of Aristotle, during the early modern period, scientists such as Khayaam, Galileo, Kepler, and Newton, laid the foundation for what is now known as classical mechanics. It is a branch of physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as a branch of science which deals with the motion of, historically, classical mechanics came first, while quantum mechanics is a comparatively recent invention. Classical mechanics originated with Isaac Newtons laws of motion in Philosophiæ Naturalis Principia Mathematica, both are commonly held to constitute the most certain knowledge that exists about physical nature. Classical mechanics has especially often been viewed as a model for other so-called exact sciences, essential in this respect is the relentless use of mathematics in theories, as well as the decisive role played by experiment in generating and testing them. Quantum mechanics is of a scope, as it encompasses classical mechanics as a sub-discipline which applies under certain restricted circumstances. According to the principle, there is no contradiction or conflict between the two subjects, each simply pertains to specific situations. The correspondence principle states that the behavior of systems described by quantum theories reproduces classical physics in the limit of quantum numbers. Quantum mechanics has superseded classical mechanics at the level and is indispensable for the explanation and prediction of processes at the molecular, atomic. However, for macroscopic processes classical mechanics is able to solve problems which are difficult in quantum mechanics and hence remains useful. Modern descriptions of such behavior begin with a definition of such quantities as displacement, time, velocity, acceleration, mass. Until about 400 years ago, however, motion was explained from a different point of view. He showed that the speed of falling objects increases steadily during the time of their fall and this acceleration is the same for heavy objects as for light ones, provided air friction is discounted. The English mathematician and physicist Isaac Newton improved this analysis by defining force and mass, for objects traveling at speeds close to the speed of light, Newton’s laws were superseded by Albert Einstein’s theory of relativity. For atomic and subatomic particles, Newton’s laws were superseded by quantum theory, for everyday phenomena, however, Newton’s three laws of motion remain the cornerstone of dynamics, which is the study of what causes motion. In analogy to the distinction between quantum and classical mechanics, Einsteins general and special theories of relativity have expanded the scope of Newton, the differences between relativistic and Newtonian mechanics become significant and even dominant as the velocity of a massive body approaches the speed of light. Relativistic corrections are also needed for quantum mechanics, although general relativity has not been integrated, the two theories remain incompatible, a hurdle which must be overcome in developing a theory of everything
Mechanics
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Arabic Machine Manuscript. Unknown date (at a guess: 16th to 19th centuries).
10.
Physics
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Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy
Physics
–
Further information:
Outline of physics
Physics
–
Ancient
Egyptian astronomy is evident in monuments like the
ceiling of Senemut's tomb from the
Eighteenth Dynasty of Egypt.
Physics
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Sir Isaac Newton (1643–1727), whose
laws of motion and
universal gravitation were major milestones in classical physics
Physics
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Albert Einstein (1879–1955), whose work on the
photoelectric effect and the
theory of relativity led to a revolution in 20th century physics
11.
Pierre-Simon Laplace
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Pierre-Simon, marquis de Laplace was an influential French scholar whose work was important to the development of mathematics, statistics, physics and astronomy. He summarized and extended the work of his predecessors in his five-volume Mécanique Céleste and this work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace, Laplace formulated Laplaces equation, and pioneered the Laplace transform which appears in many branches of mathematical physics, a field that he took a leading role in forming. The Laplacian differential operator, widely used in mathematics, is named after him. Laplace is remembered as one of the greatest scientists of all time, sometimes referred to as the French Newton or Newton of France, he has been described as possessing a phenomenal natural mathematical faculty superior to that of any of his contemporaries. Laplace became a count of the Empire in 1806 and was named a marquis in 1817, Laplace was born in Beaumont-en-Auge, Normandy on 23 March 1749, a village four miles west of Pont lEveque in Normandy. According to W. W. Rouse Ball, His father, Pierre de Laplace and his great-uncle, Maitre Oliver de Laplace, had held the title of Chirurgien Royal. It would seem that from a pupil he became an usher in the school at Beaumont, however, Karl Pearson is scathing about the inaccuracies in Rouse Balls account and states, Indeed Caen was probably in Laplaces day the most intellectually active of all the towns of Normandy. It was here that Laplace was educated and was provisionally a professor and it was here he wrote his first paper published in the Mélanges of the Royal Society of Turin, Tome iv. 1766–1769, at least two years before he went at 22 or 23 to Paris in 1771, thus before he was 20 he was in touch with Lagrange in Turin. He did not go to Paris a raw self-taught country lad with only a peasant background, the École Militaire of Beaumont did not replace the old school until 1776. His parents were from comfortable families and his father was Pierre Laplace, and his mother was Marie-Anne Sochon. The Laplace family was involved in agriculture until at least 1750, Pierre Simon Laplace attended a school in the village run at a Benedictine priory, his father intending that he be ordained in the Roman Catholic Church. At sixteen, to further his fathers intention, he was sent to the University of Caen to read theology, at the university, he was mentored by two enthusiastic teachers of mathematics, Christophe Gadbled and Pierre Le Canu, who awoke his zeal for the subject. Here Laplaces brilliance as a mathematician was recognised and while still at Caen he wrote a memoir Sur le Calcul integral aux differences infiniment petites et aux differences finies. About this time, recognizing that he had no vocation for the priesthood, in this connection reference may perhaps be made to the statement, which has appeared in some notices of him, that he broke altogether with the church and became an atheist. Laplace did not graduate in theology but left for Paris with a letter of introduction from Le Canu to Jean le Rond dAlembert who at time was supreme in scientific circles. According to his great-great-grandson, dAlembert received him rather poorly, and to get rid of him gave him a mathematics book
Pierre-Simon Laplace
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Pierre-Simon Laplace (1749–1827). Posthumous portrait by
Jean-Baptiste Paulin Guérin, 1838.
Pierre-Simon Laplace
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Laplace's house at Arcueil.
Pierre-Simon Laplace
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Laplace.
Pierre-Simon Laplace
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Tomb of Pierre-Simon Laplace
12.
Physicist
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A physicist is a scientist who has specialized knowledge in the field of physics, the exploration of the interactions of matter and energy across the physical universe. A physicist is a scientist who specializes or works in the field of physics, physicists generally are interested in the root or ultimate causes of phenomena, and usually frame their understanding in mathematical terms. Physicists can also apply their knowledge towards solving real-world problems or developing new technologies, some physicists specialize in sectors outside the science of physics itself, such as engineering. The study and practice of physics is based on a ladder of discoveries. Many mathematical and physical ideas used today found their earliest expression in ancient Greek culture and Asian culture, the bulk of physics education can be said to flow from the scientific revolution in Europe, starting with the work of Galileo and Kepler in the early 1600s. New knowledge in the early 21st century includes an increase in understanding physical cosmology. The term physicist was coined by William Whewell in his 1840 book The Philosophy of the Inductive Sciences, many physicist positions require an undergraduate degree in applied physics or a related science or a Masters degree like MSc, MPhil, MPhys or MSci. In a research oriented level, students tend to specialize in a particular field, Physics students also need training in mathematics, and also in computer science and programming. For being employed as a physicist a doctoral background may be required for certain positions, undergraduate students like BSc Mechanical Engineering, BSc Electrical and Computer Engineering, BSc Applied Physics. etc. With physics orientation are chosen as research assistants with faculty members, the highest honor awarded to physicists is the Nobel Prize in Physics, awarded since 1901 by the Royal Swedish Academy of Sciences. The three major employers of career physicists are academic institutions, laboratories, and private industries, with the largest employer being the last, physicists in academia or government labs tend to have titles such as Assistants, Professors, Sr. /Jr. As per the American Institute for Physics, some 20% of new physics Ph. D. s holds jobs in engineering development programs, while 14% turn to computer software, a majority of physicists employed apply their skills and training to interdisciplinary sectors. For industry or self-employment. and also in science and programming. Hence a majority of Physics bachelors degree holders are employed in the private sector, other fields are academia, government and military service, nonprofit entities, labs and teaching
Physicist
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Albert Einstein, physicist who developed the theory of general relativity.
13.
Music theorist
–
Music theory is the study of the practices and possibilities of music. The term is used in three ways in music, though all three are interrelated. The first is what is otherwise called rudiments, currently taught as the elements of notation, of key signatures, of time signatures, of rhythmic notation, Theory in this sense is treated as the necessary preliminary to the study of harmony, counterpoint, and form. The second is the study of writings about music from ancient times onwards, Music theory is frequently concerned with describing how musicians and composers make music, including tuning systems and composition methods among other topics. However, this medieval discipline became the basis for tuning systems in later centuries, Music theory as a practical discipline encompasses the methods and concepts composers and other musicians use in creating music. The development, preservation, and transmission of music theory in this sense may be found in oral and written music-making traditions, musical instruments, and other artifacts. In ancient and living cultures around the world, the deep and long roots of music theory are clearly visible in instruments, oral traditions, and current music making. Many cultures, at least as far back as ancient Mesopotamia and ancient China, have also considered music theory in more formal ways such as written treatises, in modern academia, music theory is a subfield of musicology, the wider study of musical cultures and history. Etymologically, music theory is an act of contemplation of music, from the Greek θεωρία, a looking at, viewing, contemplation, speculation, theory, also a sight, a person who researches, teaches, or writes articles about music theory is a music theorist. University study, typically to the M. A. or Ph. D level, is required to teach as a music theorist in a US or Canadian university. Methods of analysis include mathematics, graphic analysis, and especially analysis enabled by Western music notation, comparative, descriptive, statistical, and other methods are also used. See for instance Paleolithic flutes, Gǔdí, and Anasazi flute, several surviving Sumerian and Akkadian clay tablets include musical information of a theoretical nature, mainly lists of intervals and tunings. The scholar Sam Mirelman reports that the earliest of these dates from before 1500 BCE. Further, All the Mesopotamian texts are united by the use of a terminology for music that, much of Chinese music history and theory remains unclear. The earliest texts about Chinese music theory are inscribed on the stone and they include more than 2800 words describing theories and practices of music pitches of the time. The bells produce two intertwined pentatonic scales three tones apart with additional pitches completing the chromatic scale, Chinese theory starts from numbers, the main musical numbers being twelve, five and eight. Twelve refers to the number of pitches on which the scales can be constructed, the Lüshi chunqiu from about 239 BCE recalls the legend of Ling Lun. On order of the Yellow Emperor, Ling Lun collected twelve bamboo lengths with thick, blowing on one of these like a pipe, he found its sound agreeable and named it huangzhong, the Yellow Bell
Music theorist
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Ancient Egyptian musicians playing lutes in an ensemble.
Music theorist
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Pythagoras and
Philolaus engaged in theoretical investigations, in a woodcut from
Franchinus Gaffurius, Theorica musicæ (1492)
Music theorist
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A set of bells from China, 5th Century BCE.
Music theorist
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Barbershop quartets, such as this US Navy group, sing 4-part pieces, made up of a melody line (normally the second-highest voice, called the "lead") and 3 harmony parts.
14.
Denis Diderot
–
Denis Diderot was a French philosopher, art critic, and writer. He was a prominent figure during the Enlightenment and is best known for serving as co-founder, chief editor, Denis Diderot was born in Langres, Champagne, and began his formal education at a Jesuit collège in Langres. His parents were Didier Diderot a cutler, maître coutelier, three of five siblings survived to adulthood, Denise Diderot and their youngest brother Pierre-Didier Diderot, and finally their sister Angélique Diderot. According to Arthur McCandless Wilson, Denis Diderot greatly admired his sister Denise, in 1732 Denis Diderot earned the Master of Arts degree in philosophy. Then he entered the Collège dHarcourt of the University of Paris and he abandoned the idea of entering the clergy and decided instead to study at the Paris Law Faculty. His study of law was short-lived however and in 1734 Diderot decided to become a writer, because of his refusal to enter one of the learned professions, he was disowned by his father, and for the next ten years he lived a bohemian existence. In 1742 he befriended Jean-Jacques Rousseau, in 1743 he further alienated his father by marrying Antoinette Champion, a devout Roman Catholic. The match was considered due to Champions low social standing, poor education, fatherless status. She was about three years older than Diderot, the marriage in October 1743 produced one surviving child, a girl. Her name was Angélique, after both Diderots dead mother and sister, the death of his sister, a nun, from overwork in the convent may have affected Diderots opinion of religion. Babuti, Madeleine de Puisieux, Sophie Volland and Mme de Maux and his letters to Sophie Volland are known for their candor and are regarded to be among the literary treasures of the eighteenth century. Though his work was broad as well as rigorous, it did not bring Diderot riches, when the time came for him to provide a dowry for his daughter, he saw no alternative than to sell his library. When Empress Catherine II of Russia heard of his financial troubles she commissioned an agent in Paris to buy the library and she then requested that the philosopher retain the books in Paris until she required them, and act as her librarian with a yearly salary. Between October 1773 and March 1774, the sick Diderot spent a few months at the court in Saint Petersburg. Diderot died of thrombosis in Paris on 31 July 1784. His heirs sent his vast library to Catherine II, who had it deposited at the National Library of Russia and this idea seems to have been shelved. In 1745, he published a translation of Shaftesburys Inquiry Concerning Virtue and Merit, in 1746, Diderot wrote his first original work, the Philosophical Thoughts. In this book, Diderot argued for a reconciliation of reason with feeling so as to establish harmony, according to Diderot, without feeling there would be a detrimental effect on virtue and no possibility of creating sublime work
Denis Diderot
–
n° 9 de la place dans le centre ville de Langres in the background on the right side the birthplace of Denis Diderot
Denis Diderot
–
Diderot, by
Louis-Michel van Loo, 1767.
Denis Diderot
–
Title page of the
Encyclopédie
Denis Diderot
–
Statue of Denis Diderot in the city of
Langres, his birthplace
15.
Wave equation
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The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in physics—such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics, historically, the problem of a vibrating string such as that of a musical instrument was studied by Jean le Rond dAlembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange. In 1746, d’Alembert discovered the wave equation, and within ten years Euler discovered the three-dimensional wave equation. The wave equation is a partial differential equation. It typically concerns a time t, one or more spatial variables x1, x2, …, xn, and a scalar function u = u, whose values could model, for example. The wave equation for u is ∂2 u ∂ t 2 = c 2 ∇2 u where ∇2 is the Laplacian, therefore, the sum of any two solutions is again a solution, in physics this property is called the superposition principle. The wave equation, and modifications of it, are found in elasticity, quantum mechanics, plasma physics. The wave equation in one dimension can be written as follows. This equation is described as having only one space dimension x. The wave equation in one dimension can be derived in a variety of different physical settings. Most famously, it can be derived for the case of a string that is vibrating in a two-dimensional plane, another physical setting for derivation of the wave equation in one space dimension utilizes Hookes Law. The wave equation in the case can be derived from Hookes Law in the following way. In the case of a stress pulse propagating through a beam the beam acts much like a number of springs in series. A beam of constant cross section made from an elastic material has a stiffness K given by K = E A L Where A is the cross sectional area. Traveling means that the shape of these individual arbitrary functions with respect to x stays constant, however the functions are translated left and this was derived by Jean le Rond dAlembert. However, the waveforms F and G may also be generalized functions, in that case, the solution may be interpreted as an impulse that travels to the right or the left. The basic wave equation is a differential equation and so it will adhere to the superposition principle. This means that the net displacement caused by two or more waves is the sum of the displacements which would have been caused by each wave individually
Wave equation
–
French scientist
Jean-Baptiste le Rond d'Alembert (b. 1717) discovered the wave equation in one space dimension.
Wave equation
Wave equation
–
Swiss Mathematician and Physicist
Leonhard Euler (b. 1707) discovered the wave equation in three space dimensions.
16.
Illegitimate child
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Legitimacy, in traditional Western common law, is the status of a child born to parents who are legally married to each other, and of a child conceived before the parents obtain a legal divorce. Conversely, illegitimacy is the status of a child born outside marriage, depending on the cultural context, legitimacy can affect a childs rights of inheritance to the putative fathers estate and the childs right to bear the fathers surname or title. Illegitimacy has also had consequences for the mothers and childs right to support from the putative father, in medieval Wales, a bastard was defined simply as a child not acknowledged by its father. All children, whether born in or out of wedlock, that were acknowledged by the father enjoyed the legal rights. Englands Statute of Merton stated, regarding illegitimacy, He is a bastard that is born before the marriage of his parents and this definition also applied to situations when a childs parents could not marry, as when one or both were already married or when the relationship was incestuous. The Poor Law of 1576 formed the basis of English bastardy law and its purpose was to punish a bastard childs mother and putative father, and to relieve the parish from the cost of supporting mother and child. By an act of 1576, it was ordered that bastards should be supported by their putative fathers, if the genitor could be found, then he was put under very great pressure to accept responsibility and to maintain the child. Under English law, a bastard was unable to be an heir to real property, in contrast to the situation under civil law, a younger non-bastard brother would have no claim to the land. The Legitimacy Act 1926 of England and Wales legitimized the birth of a if the parents subsequently married each other. The Legitimacy Act 1959 extended the legitimization even if the parents had married others in the meantime, neither the 1926 nor 1959 Acts changed the laws of succession to the British throne and succession to peerage titles. The Family Law Reform Act 1969 allowed a bastard to inherit on the intestacy of his parents, in canon and in civil law, the offspring of putative marriages have also been considered legitimate. Since 2003 in England and Wales,2002 in Northern Ireland and 2006 in Scotland, still, children born out of wedlock may not be eligible for certain federal benefits unless the child has been legitimized in the appropriate jurisdiction. Many other countries have abolished by any legal disabilities of a child born out of wedlock. In France, legal reforms regarding illegitimacy began in the 1970s, the European Convention on the Legal Status of Children Born out of Wedlock came into force in 1978. Countries which ratify it must ensure that children born outside marriage are provided with legal rights as stipulated in the text of this Convention, the Convention was ratified by the UK in 1981 and by Ireland in 1988. Use of the illegitimate child is now rare, even in legal contexts. It has been stricken from passports and legal documents as needlessly insulting and stigmatizing to the child, terms such as extra-marital child, love child and child born out of wedlock are more commonly used. Also used in Britain and other English-speaking countries is bastard, though such as natural child are preferred in polite society
Illegitimate child
–
Elizabeth I of England
Illegitimate child
–
The Outcast, by
Richard Redgrave, 1851. A patriarch casts his daughter and her illegitimate baby out of the family home.
Illegitimate child
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Magdalene laundries were institutions that existed from the 18th to the late 20th centuries, throughout Europe and North America, where "fallen women", including unmarried mothers, were detained. Photo: Magdalene laundry in
Ireland, ca. early twentieth century.
Illegitimate child
–
Edwin Booth
17.
Artillery
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Artillery is a class of large military weapons built to fire munitions far beyond the range and power of infantrys small arms. Early artillery development focused on the ability to breach fortifications, and led to heavy, as technology improved, lighter, more mobile field artillery developed for battlefield use. This development continues today, modern self-propelled artillery vehicles are highly mobile weapons of great versatility providing the largest share of an armys total firepower, in its earliest sense, the word artillery referred to any group of soldiers primarily armed with some form of manufactured weapon or armour. In common speech, the artillery is often used to refer to individual devices, along with their accessories and fittings. However, there is no generally recognised generic term for a gun, howitzer, mortar, and so forth, the United States uses artillery piece, the projectiles fired are typically either shot or shell. Shell is a widely used term for a projectile, which is a component of munitions. By association, artillery may also refer to the arm of service that customarily operates such engines, in the 20th Century technology based target acquisition devices, such as radar, and systems, such as sound ranging and flash spotting, emerged to acquire targets, primarily for artillery. These are usually operated by one or more of the artillery arms, Artillery originated for use against ground targets—against infantry, cavalry and other artillery. An early specialist development was coastal artillery for use against enemy ships, the early 20th Century saw the development of a new class of artillery for use against aircraft, anti-aircraft guns. Artillery is arguably the most lethal form of land-based armament currently employed, the majority of combat deaths in the Napoleonic Wars, World War I, and World War II were caused by artillery. In 1944, Joseph Stalin said in a speech that artillery was the God of War, although not called as such, machines performing the role recognizable as artillery have been employed in warfare since antiquity. The first references in the historical tradition begin at Syracuse in 399 BC. From the Middle Ages through most of the era, artillery pieces on land were moved by horse-drawn gun carriages. In the contemporary era, the artillery and crew rely on wheeled or tracked vehicles as transportation, Artillery used by naval forces has changed significantly also, with missiles replacing guns in surface warfare. The engineering designs of the means of delivery have likewise changed significantly over time, in some armies, the weapon of artillery is the projectile, not the equipment that fires it. The process of delivering fire onto the target is called gunnery, the actions involved in operating the piece are collectively called serving the gun by the detachment or gun crew, constituting either direct or indirect artillery fire. The term gunner is used in armed forces for the soldiers and sailors with the primary function of using artillery. The gunners and their guns are usually grouped in teams called either crews or detachments, several such crews and teams with other functions are combined into a unit of artillery, usually called a battery, although sometimes called a company
Artillery
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French naval piece of the late 19th century
Artillery
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French soldiers in the
Franco-Prussian War 1870–71.
Artillery
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British 64 Pounder Rifled Muzzle-Loaded (RML) Gun on a Moncrieff disappearing mount, at Scaur Hill Fort,
Bermuda. This is a part of a fixed battery, meant to protect against over-land attack and to serve as coastal artillery.
Artillery
–
7-person gun crew firing a US
M777 Light Towed Howitzer,
War in Afghanistan, 2009.
18.
Patron saint
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Catholics believe that patron saints, having already transcended to the metaphysical, are able to intercede effectively for the needs of their special charges. Historically, a practice has also occurred in many Islamic lands. With regard to the omnipresence of this belief, the late Martin Lings wrote. Traditionally, it has been understood that the saint of a particular place prays for that places wellbeing and for the health. Saints often become the patrons of places where they were born or had been active, professions sometimes have a patron saint owing to that individual being involved somewhat with it, although some of the connections were tenuous. Lacking such a saint, an occupation would have a patron whose acts or miracles in some way recall the profession and it is, however, generally discouraged in some Protestant branches such as Calvinism, where the practice is considered a form of idolatry. In Islam, the veneration or commemoration and recognition of saints is found in many branches of traditional Sunnism
Patron saint
–
Saint Matthew the Apostle, depicted with an angel, is the patron saint of
Salerno, Italy, bankers and tax collectors
Patron saint
–
A branch of
Saint Honore Cake Shop, a
Hong Kong chain bakery, in Hong Kong.
Saint Honorius (Honoré) is the patron saint of bakers and confectioners.
19.
Orphanage
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An orphanage is a residential institution devoted to the care of orphans—children whose biological parents are deceased or otherwise unable or unwilling to care for them. It is frequently used to describe institutions abroad, where it is an accurate term. Most children who live in orphanages are not orphans, four out of five children in orphanages having at least one living parent, most orphanages have been closed in Europe and North America. Few large international charities continue to fund orphanages, however, they are still commonly founded by smaller charities, especially in developing countries, orphanages may prey on vulnerable families at risk of breakdown and actively recruit children to ensure continued funding. Orphanages in developing countries are run by the state. Other residential institutions for children can be called group homes, childrens homes, refuges, rehabilitation centers, night shelters, the Romans formed their first orphanages around 400 AD. Jewish law prescribed care for the widow and the orphan, plato says, Orphans should be placed under the care of public guardians. Men should have a fear of the loneliness of orphans and of the souls of their departed parents, a man should love the unfortunate orphan of whom he is guardian as if he were his own child. He should be as careful and as diligent in the management of the property as of his own or even more careful still. The care of orphans was referred to bishops and, during the Middle Ages, as soon as they were old enough, children were often given as apprentices to households to ensure their support and to learn an occupation. In medieval Europe, care for orphans tended to reside with the Church, the Elizabethan Poor Laws were enacted at the time of the Reformation, and placed public responsibility on individual parishes to care for the indigent poor. The growth of sentimental philanthropy in the 18th century, led to the establishment of the first charitable institutions catering for the orphan, the first children were admitted into a temporary house located in Hatton Garden. At first, no questions were asked about child or parent, on reception, children were sent to wet nurses in the countryside, where they stayed until they were about four or five years old. At sixteen, girls were apprenticed as servants for four years, at fourteen, boys were apprenticed into variety of occupations. There was a benevolent fund for adults. A basket was accordingly hung outside the hospital, the age for admission was raised from two months to twelve, and a flood of children poured in from country workhouses. Parliament soon came to the conclusion that the indiscriminate admission should be discontinued, the hospital adopted a system of receiving children only with considerable sums. This practice was stopped in 1801, and it henceforth became a fundamental rule that no money was to be received
Orphanage
Orphanage
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Former Jewish orphanage in
Berlin-Pankow
Orphanage
–
St. Nicholas Orphanage in
Novosibirsk, Russia
Orphanage
–
Caring for orphans, by Dutch artist
Jan de Bray, 1663
20.
Child abandonment
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Child abandonment is the practice of relinquishing interests and claims over ones offspring in an extralegal way with the intent of never again resuming or reasserting them. Causes include many social and cultural factors as well as mental illness, an abandoned child is called a foundling. Baby dumping refers to parents abandoning or discarding a child younger than 12 months in a public or private place with the intent of disposing of them and it is also known as rehoming in cases of failed adoptions. Poverty is often a cause of child abandonment. People in cultures with poor social welfare systems who are not financially capable of taking care of a child are more likely to abandon them, another common reason for baby dumping is teenage pregnancies. Pregnant teenagers experience problems during and after due to social and psychological distress. Regardless of age, parents may abandon a child because they are unprepared to raise them, other reasons include unpreferred gender, appearance, or other characteristics of the child as well as mental or physical handicaps of the child. Education, family planning, government support, and post-natal services, historically, many cultures practiced abandonment of infants, called infant exposure. Although such children would survive if taken up by others, exposure is considered a form of infanticide—as described by Tertullian in his Apology. By exposure to cold and hunger and dogs, medieval laws in Europe governing child abandonment, as for example the Visigothic Code, often prescribed that the person who had taken up the child was entitled to the childs service as a slave. Conscripting or enslaving children into armies and labor pools often occurred as a consequence of war or pestilence when many children were left parentless, abandoned children then became the ward of the state, military organization, or religious group. When this practice happened en masse, it had the advantage of ensuring the strength and continuity of cultural, the largest migration of abandoned children in history took place in the United States between 1854 and 1929. Over two hundred thousand orphans were forced onto railroad cars and shipped west, where any family desiring their services as laborers, maids, orphan trains were highly popular as a source of free labor. The sheer size of the displacement and degree of exploitation that occurred gave rise to new agencies, eventually, adoption became a quintessential American institution, embodying faith in social engineering and mobility. By 1945, adoption was formulated as an act with consideration of the child’s best interests. Brace feared the impact of the poverty and their Catholic religion, in particular. Reformers during the Progressive Era later carried on this tradition of secrecy when drafting American laws. Today, abandonment of a child is considered to be a crime in many jurisdictions because it can be considered malum in se due to the direct harm to the child
Child abandonment
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A modern Baby box or Baby hatch in the Czech Republic where a baby can be anonymously abandoned while ensuring that the child will be cared for.
Child abandonment
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The children of Queen Blondine and of her sister, Princess Brunette, picked up by a Corsair after seven days at sea; illustration by
Walter Crane to the fairy tale
Princess Belle-Etoile
21.
Glazier
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A glazier is a skilled tradesman responsible for cutting, installing, and removing glass. Glaziers may work with glass in various surfaces and settings, such as windows, doors, shower doors, skylights, storefronts, display cases, mirrors, facades, interior walls, ceilings, the Occupational Outlook Handbook of the U. S. Uses and maintains tools and equipment 2, performs routine activities Block B – Commercial Window and Door Systems 4. Fabricates commercial window and door systems 5, installs commercial window and door systems Block C – Residential Window and Door Systems 6. Installs residential door systems Block D – Specialty Glass and Products 8, fabricates and installs specialty glass and products 9. Installs glass systems on vehicles Block E – Servicing 10, services commercial window and door systems 11. Services residential window and door systems 12, tools used by glaziers include cutting boards, glass-cutting blades, straightedges, glazing knives, saws, drills, grinders, putty, and glazing compounds. Some glaziers work specifically with glass in motor vehicles, other work specifically with the safety glass used in aircraft. Glaziers are typically educated at the high school diploma or equivalent level and learn the skills of the trade through an apprenticeship program, in the U. S. apprenticeship programs are offered through the National Glass Association as well as trade associations and local contractors associations. Construction-industry glaziers are frequently members of the International Union of Painters, in Ontario, Canada, apprenticeships are offered at the provincial level and certified through the Ontario College of Trades. Other provinces manage their own apprenticeship programs, the Trade of Glazier is a designated Red Seal Trade in Canada. Occupational hazards encountered by glaziers include the risks of being cut by glass or tools, according to the Occupational Outlook Handbook, there are some 45,300 glaziers in the United States, with median pay of $38,410 per year in 2014. Among the 50 states, only Connecticut and Florida require glaziers to hold a license, architectural glass Glazing in architecture Insulated glazing Stained glass Glass manufacturing Glassblowing Media related to Glaziers at Wikimedia Commons
Glazier
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glazier
Glazier
–
glazier trailer
22.
French livre
–
The livre was the currency of France from 781 to 1794. Several different livres existed, some concurrently, the livre was the name of both units of account and coins. The livre was established by Charlemagne as a unit of account equal to one pound of silver and it was subdivided into 20 sous, each of 12 deniers. The word livre came from the Latin word libra, a Roman unit of weight and this system and the denier itself served as the model for many of Europes currencies, including the British pound, Italian lira, Spanish dinero and the Portuguese dinheiro. This first livre is known as the livre carolingienne, only deniers were initially minted, but debasement led to larger denominations being issued. Different mints in different regions used different weights for the denier, livre is a homonym of the French word for book, the distinction being that the two have a different gender. The monetary unit is feminine, la/une livre, while book is masculine, for much of the Middle Ages, different duchies of France were semi-autonomous if not practically independent from the weak Capetian kings, and thus each minted their own currency. Charters would need to specify which region or mint was being used, the first steps towards standardization came under the first strong Capetian monarch, Philip II Augustus. Philip II conquered much of the continental Angevin Empire from King John of England, including Normandy, Anjou and this was a slow process lasting many decades and not completed within Philip IIs lifetime. Until the thirteenth century and onwards, only deniers were actually minted as coin money, both livres and sous did not actually exist as coins but were used only for accounting purposes. Between 1360 and 1641, coins worth 1 livre tournois were minted known as francs and this name persisted in common parlance for 1 livre tournois but was not used on coins or paper money. The official use of the livre tournois accounting unit in all contracts in France was legislated in 1549, however, in 1577, the livre tournois accounting unit was officially abolished and replaced by the écu, which was at that time the major French gold coin in actual circulation. In 1602, the livre tournois accounting unit was brought back, Louis XIII of France stopped minting the franc in 1641, replacing it with coins based on the silver écu and gold Louis dor. The écu and louis dor fluctuated in value, with the écu varying between three and six livres tournois until 1726 when it was fixed at six livres, the louis was initially worth ten livres, and fluctuated too, until its value was fixed at twenty-four livres in 1726. In 1667, the livre parisis was officially abolished, however, the sole remaining livre was still frequently referred to as the livre tournois until its demise. The first French paper money was issued in 1701 and was denominated in livres tournois, however, the notes did not hold their value relative to silver due to massive over–production. The Banque Royale crashed in 1720, rendering the banknotes worthless, in 1726, under Louis XVs minister Cardinal Fleury, a system of monetary stability was put in place. Eight ounces of gold was worth 740 livres,9 sols,8 ounces of silver was worth 51 livres,2 sols,3 deniers
French livre
–
French 1793 24-Livre gold coin.
French livre
–
10 livres Tournois note issued by La Banque Royale (1720)
French livre
–
Assignat for 125 livres (1793)
23.
Jansenism
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Jansenism was a Catholic heretical theological movement, primarily in France, that emphasized original sin, human depravity, the necessity of divine grace, and predestination. The movement originated from the published work of the Dutch theologian Cornelius Jansen. It was first popularized by Jansens friend Abbot Jean Duvergier de Hauranne, of Saint-Cyran-en-Brenne Abbey, through the 17th and into the 18th centuries, Jansenism was a distinct movement within the Catholic Church. The theological centre of the movement was the convent of Port-Royal Abbey, Paris, which was a haven for writers including Duvergier, Arnauld, Pierre Nicole, Blaise Pascal, Jansenism was opposed by many in the Catholic hierarchy, especially the Jesuits. Although the Jansenists identified themselves only as rigorous followers of Augustine of Hippos teachings, Jansenist leaders endeavored to accommodate the popes pronouncements while retaining their uniqueness, and enjoyed a measure of peace in the late 17th century under Pope Clement IX. However, further controversy led to the apostolic constitution Unigenitus Dei Filius, promulgated by Pope Clement XI in 1713, the origins of Jansenism lie in the friendship of Jansen and Duvergier, who met in the early 17th century when both were studying theology at the University of Leuven. Duvergier was Jansens patron for a number of years, getting Jansen a job as a tutor in Paris in 1606, two years later, he got Jansen a position teaching at the bishops college in Duvergiers hometown of Bayonne. The duo studied the Church Fathers together, with a focus on the thought of Augustine of Hippo. Duvergier became abbot of Saint Cyran Abbey in Brenne and was known as the Abbé de Saint-Cyran for the rest of his life, Jansen returned to the University of Leuven, where he completed his doctorate in 1619 and was named professor of exegesis. Jansen and Duvergier continued to correspond about Augustine, especially Augustines teachings on grace, upon the recommendation of King Philip IV of Spain, Jansen was consecrated as bishop of Ypres in 1636. Jansen died in a 1638 epidemic and this manuscript, published in 1640 as Augustinus, expounded Augustines system and formed the basis for the subsequent Jansenist Controversy. Jansen emphasized a particular reading of Augustines idea of efficacious grace which stressed that only a portion of humanity were predestined to be saved. Jansen insisted that the love of God was fundamental, and that only perfect contrition, Duvergier was not released until after Richelieus death in 1642, and he died shortly thereafter, in 1643. Jansen also insisted on justification by faith, although he did not contest the necessity of revering saints, of confession, Jansens opponents condemned his teachings for their alleged similarities to Calvinism. Pascal himself claimed that Molinists were correct concerning the state of humanity before the Fall, the heresy of Jansenism, as stated by subsequent Roman Catholic doctrine, lay in denying the role of free will in the acceptance and use of grace. Jansenism asserts that Gods role in the infusion of grace cannot be resisted, Catholic doctrine, in the Catechism of the Catholic Church, is that Gods free initiative demands mans free response—that is, humans freely assent or refuse Gods gift of grace. However, on August 1,1642, the Holy Office issued a decree condemning Augustinus, in 1602, Marie Angélique Arnauld become abbess of Port-Royal-des-Champs, a Cistercian convent in Magny-les-Hameaux. There, she reformed discipline after an experience in 1608
Jansenism
–
Abbé de Saint-Cyran –
Jean Duvergier de Hauranne, abbot of Saint Cyran Abbey in Brenne (1581–1643), one of the intellectual fathers of Jansenism.
Jansenism
–
Jansenism:
Cornelius Jansen (1585–1638), professor at the
Old University of Louvain
Jansenism
–
The title page of Augustinus by
Cornelius Jansen, published posthumously in 1640. The book formed the foundation of the subsequent Jansenist controversy.
Jansenism
–
La mère –
Marie Angélique Arnauld (1591–1661),
abbess of
Port-Royal-des-Champs.
24.
Bachelor of Arts
–
A Bachelor of Arts is a bachelors degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both. Bachelor of Arts degree programs take three to four years depending on the country, academic institution, and specific specializations, majors or minors. The word baccalaureus or baccalarium should not be confused with baccalaureatus, degree diplomas generally are printed on high-quality paper or parchment, individual institutions set the preferred abbreviation for their degrees. In Pakistan, the Bachelor of Arts degree can also be attained within two years as an external degree, in colleges and universities in Australia, New Zealand, Nepal and South Africa, the BA degree can be taken over three years of full-time study. Unlike in other countries, students do not receive a grade for their Bachelor of Arts degree with varying levels of honours. Qualified students may be admitted, after they have achieved their Bachelors program with an overall grade point average. Thus, to achieve a Bachelor Honours degree, a postgraduate year. A student who holds a Honours degree is eligible for entry to either a Doctorate or a very high research Master´s degree program. Education in Canada is controlled by the Provinces and can be different depending on the province in Canada. Canadian universities typically offer a 3-year Bachelor of Arts degrees, in many universities and colleges, Bachelor of Arts degrees are differentiated either as Bachelors of Arts or as honours Bachelor of Arts degree. The honours degrees are designated with the abbreviation in brackets of. It should not be confused with the consecutive Bachelor of Arts degree with Honours, Latin Baccalaureatus in Artibus Cum Honore, BA hon. de jure without brackets and with a dot. It is a degree, which is considered to be the equivalent of a corresponding maîtrise degree under the French influenced system. Going back in history, a three-year Bachelor of Arts degree was called a pass degree or general degree. Students may be required to undertake a long high-quality research empirical thesis combined with a selection of courses from the relevant field of studies. The consecutive B. cum Honore degree is essential if students ultimate goal is to study towards a two- or three-year very high research masters´ degree qualification. A student holding a Baccalaureatus Cum Honore degree also may choose to complete a Doctor of Philosophy program without the requirement to first complete a masters degree, over the years, in some universities certain Baccalaureatus cum Honore programs have been changed to corresponding master´s degrees. In general, in all four countries, the B. A. degree is the standard required for entry into a masters programme, in science, a BA hons degree is generally a prerequisite for entrance to a Ph. D program or a very-high-research-activity master´s programme
Bachelor of Arts
–
A certificate or diploma evidencing the granting of a bachelor's degree
25.
Ecclesiastical
–
The word ecclesiology was defined in the 19th century as the science of the building and decoration of church buildings and at least one publication still uses the word in this sense. The Ecclesiologist was first published in October 1841 and dealt with the study of the building and its successor Ecclesiology Today is still, as of 2017, being published by The Ecclesiological Society. The situation regarding the etymology has been summed up by Alister McGrath, is it a visible or earthly corporation, or a unified and visible society — a church in the sense of a specific denomination or institution, for instance. Or is it the body of all believing Christians, regardless of their denominational differences, what is the relationship between living Christians and departed Christians —do they constitute together the Church. What is the relationship between a believer and the Church and that is, what is the role of corporate worship in the spiritual lives of believers. Can salvation be found outside of formal membership in a faith community. What is the authority of the Church, who gets to interpret the doctrines of the Church. Is the organizational structure itself, either in a corporate body, or generally within the range of formal church structures. For example, is the Bible a written part of a wider revelation entrusted to the Church as faith community, or is the Bible the revelation itself, and the Church is to be defined as a group of people who claim adherence to it. What are the sacraments, divine ordinances, and liturgies, in the context of the Church, what is the comparative emphasis and relationship between worship service, spiritual formation, and mission, and is the Churchs role to create disciples of Christ or some other function. Is the Eucharist the defining element of the rest of the sacramental system, is the Church to be understood as the vehicle for salvation, or the salvific presence in the world, or as a community of those already saved. How should the Church be governed, what was the mission and authority of the Apostles, and is this handed down through the sacraments today. What are the methods of choosing clergy such as bishops and priests. Who are the leaders of a church, must there be a policy-making board of leaders within a church and what are the qualifications for this position, and by what process do these members become official, ordained leaders. Must leaders and clergy be ordained, and is possible only by those who have been ordained by others. What are the roles of spiritual gifts in the life of the church, how does the Churchs New Covenant relate to the covenants expressed in scripture with Gods chosen people, the Jewish people. What is the destiny of the Church in Christian eschatology. This shift is most clearly marked by the encyclical Divino afflante Spiritu in 1943, avery Robert Cardinal Dulles, S. J. contributed greatly to the use of models in understanding ecclesiology
Ecclesiastical
–
Washington National Cathedral
Ecclesiastical
–
Jesus
26.
Lawyer
–
A lawyer is a person who practices law, as an advocate, barrister, attorney, counselor or solicitor or chartered legal executive. The role of the lawyer varies greatly across legal jurisdictions, in practice, legal jurisdictions exercise their right to determine who is recognized as being a lawyer. As a result, the meaning of the lawyer may vary from place to place. In Australia, the lawyer is used to refer to both barristers and solicitors. In Canada, the word lawyer refers to individuals who have been called to the bar or. Common law lawyers in Canada are formally and properly called barristers and solicitors, however, in Quebec, civil law advocates often call themselves attorney and sometimes barrister and solicitor in English. The Legal Services Act 2007 defines the activities that may only be performed by a person who is entitled to do so pursuant to the Act. Lawyer is not a protected title, in India, the term lawyer is often colloquially used, but the official term is advocate as prescribed under the Advocates Act,1961. In Scotland, the word refers to a more specific group of legally trained people. It specifically includes advocates and solicitors, in a generic sense, it may also include judges and law-trained support staff. In the United States, the term refers to attorneys who may practice law. It is never used to refer to patent agents or paralegals, in fact, there are regulatory restrictions on non-lawyers like paralegals practicing law. Other nations tend to have terms for the analogous concept. In most countries, particularly civil law countries, there has been a tradition of giving many legal tasks to a variety of civil law notaries, clerks, and scriveners. Several countries that originally had two or more legal professions have since fused or united their professions into a type of lawyer. Most countries in this category are common law countries, though France, in countries with fused professions, a lawyer is usually permitted to carry out all or nearly all the responsibilities listed below. Arguing a clients case before a judge or jury in a court of law is the province of the barrister in England. However, the boundary between barristers and solicitors has evolved, in England today, the barrister monopoly covers only appellate courts, and barristers must compete directly with solicitors in many trial courts
Lawyer
–
Dr Alberico Gentili (1552-1608), one of the best known lawyers.
Lawyer
–
A French lawyer
Lawyer
–
Law Faculty of
Comenius University in
Bratislava (Slovakia).
Lawyer
–
U.S. President Abraham Lincoln is a famous example of a lawyer who became a politician.
27.
Frederick the Great
–
Frederick II was King of Prussia from 1740 until 1786, the longest reign of any Hohenzollern king. Frederick was the last titled King in Prussia and declared himself King of Prussia after achieving full sovereignty for all historical Prussian lands, Prussia had greatly increased its territories and became a leading military power in Europe under his rule. He became known as Frederick the Great and was affectionately nicknamed Der Alte Fritz by the Prussian, in his youth, Frederick was more interested in music and philosophy than the art of war. Upon ascending to the Prussian throne, he attacked Austria and claimed Silesia during the Silesian Wars, winning acclaim for himself. Near the end of his life, Frederick physically connected most of his realm by conquering Polish territories in the First Partition of Poland and he was an influential military theorist whose analysis emerged from his extensive personal battlefield experience and covered issues of strategy, tactics, mobility and logistics. Considering himself the first servant of the state, Frederick was a proponent of enlightened absolutism and he modernized the Prussian bureaucracy and civil service and pursued religious policies throughout his realm that ranged from tolerance to segregation. He reformed the system and made it possible for men not of noble stock to become judges. Frederick also encouraged immigrants of various nationalities and faiths to come to Prussia, some critics, however, point out his oppressive measures against conquered Polish subjects during the First Partition. Frederick supported arts and philosophers he favored, as well as allowing complete freedom of the press, Frederick is buried at his favorite residence, Sanssouci in Potsdam. Because he died childless, Frederick was succeeded by his nephew, Frederick William II, son of his brother, historian Leopold von Ranke was unstinting in his praise of Fredericks Heroic life, inspired by great ideas, filled with feats of arms. Immortalized by the raising of the Prussian state to the rank of a power, Johann Gustav Droysen was even more extolling. However, by the 21st century, a re-evaluation of his legacy as a great warrior, Frederick, the son of Frederick William I and his wife, Sophia Dorothea of Hanover, was born in Berlin on 24 January 1712. The birth of Frederick was welcomed by his grandfather, Frederick I, with more than usual pleasure, with the death of his father in 1713, Frederick William became King of Prussia, thus making young Frederick the crown prince. The new king wished for his sons and daughters to be educated not as royalty and he had been educated by a Frenchwoman, Madame de Montbail, who later became Madame de Rocoulle, and he wished that she educate his children. However, he possessed a violent temper and ruled Brandenburg-Prussia with absolute authority. As Frederick grew, his preference for music, literature and French culture clashed with his fathers militarism, in contrast, Fredericks mother Sophia was polite, charismatic and learned. Her father, George Louis of Brunswick-Lüneburg, succeeded to the British throne as King George I in 1714, Frederick was brought up by Huguenot governesses and tutors and learned French and German simultaneously. Although Frederick William I was raised a Calvinist, he feared he was not of the elect, to avoid the possibility of Frederick being motivated by the same concerns, the king ordered that his heir not be taught about predestination
Frederick the Great
–
Portrait of Frederick the Great; By
Anton Graff, 1781
Frederick the Great
–
Baptism of Frederick, 1712 (Harper's Magazine, 1870)
Frederick the Great
–
Frederick as Crown Prince (1739)
Frederick the Great
–
Rheinsberg Palace, Frederick's residence 1736-1740
28.
Classical mechanics
–
In physics, classical mechanics is one of the two major sub-fields of mechanics, along with quantum mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology. Classical mechanics describes the motion of objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars. Within classical mechanics are fields of study that describe the behavior of solids, liquids and gases, Classical mechanics also provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When both quantum and classical mechanics cannot apply, such as at the level with high speeds. Since these aspects of physics were developed long before the emergence of quantum physics and relativity, however, a number of modern sources do include relativistic mechanics, which in their view represents classical mechanics in its most developed and accurate form. Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and these advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newtons work, particularly through their use of analytical mechanics. The following introduces the concepts of classical mechanics. For simplicity, it often models real-world objects as point particles, the motion of a point particle is characterized by a small number of parameters, its position, mass, and the forces applied to it. Each of these parameters is discussed in turn, in reality, the kind of objects that classical mechanics can describe always have a non-zero size. Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the degrees of freedom. However, the results for point particles can be used to such objects by treating them as composite objects. The center of mass of a composite object behaves like a point particle, Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space, non-relativistic mechanics also assumes that forces act instantaneously. The position of a point particle is defined with respect to a fixed reference point in space called the origin O, in space. A simple coordinate system might describe the position of a point P by means of a designated as r. In general, the point particle need not be stationary relative to O, such that r is a function of t, the time
Classical mechanics
–
Sir
Isaac Newton (1643–1727), an influential figure in the history of physics and whose
three laws of motion form the basis of classical mechanics
Classical mechanics
–
Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors.
Classical mechanics
–
Hamilton 's greatest contribution is perhaps the reformulation of
Newtonian mechanics, now called
Hamiltonian mechanics.
29.
Second law of motion
–
Newtons laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a measure of the force. These three laws have been expressed in different ways, over nearly three centuries, and can be summarised as follows. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, Newton used them to explain and investigate the motion of many physical objects and systems. For example, in the volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation. Newtons laws are applied to objects which are idealised as single point masses, in the sense that the size and this can be done when the object is small compared to the distances involved in its analysis, or the deformation and rotation of the body are of no importance. In this way, even a planet can be idealised as a particle for analysis of its orbital motion around a star, in their original form, Newtons laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalisation of Newtons laws of motion for rigid bodies called Eulers laws of motion, if a body is represented as an assemblage of discrete particles, each governed by Newtons laws of motion, then Eulers laws can be derived from Newtons laws. Eulers laws can, however, be taken as axioms describing the laws of motion for extended bodies, Newtons laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Other authors do treat the first law as a corollary of the second, the explicit concept of an inertial frame of reference was not developed until long after Newtons death. In the given mass, acceleration, momentum, and force are assumed to be externally defined quantities. This is the most common, but not the interpretation of the way one can consider the laws to be a definition of these quantities. Newtonian mechanics has been superseded by special relativity, but it is useful as an approximation when the speeds involved are much slower than the speed of light. The first law states that if the net force is zero, the first law can be stated mathematically when the mass is a non-zero constant, as, ∑ F =0 ⇔ d v d t =0. Consequently, An object that is at rest will stay at rest unless a force acts upon it, an object that is in motion will not change its velocity unless a force acts upon it. This is known as uniform motion, an object continues to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest, if an object is moving, it continues to move without turning or changing its speed
Second law of motion
–
Newton's First and Second laws, in Latin, from the original 1687
Principia Mathematica.
Second law of motion
–
Isaac Newton (1643–1727), the physicist who formulated the laws
30.
Continuum mechanics
–
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century, research in the area continues till today. Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies, Continuum mechanics deals with physical properties of solids and fluids which are independent of any particular coordinate system in which they are observed. These physical properties are represented by tensors, which are mathematical objects that have the required property of being independent of coordinate system. These tensors can be expressed in coordinate systems for computational convenience, Materials, such as solids, liquids and gases, are composed of molecules separated by space. On a microscopic scale, materials have cracks and discontinuities, a continuum is a body that can be continually sub-divided into infinitesimal elements with properties being those of the bulk material. More specifically, the continuum hypothesis/assumption hinges on the concepts of an elementary volume. This condition provides a link between an experimentalists and a viewpoint on constitutive equations as well as a way of spatial and statistical averaging of the microstructure. The latter then provide a basis for stochastic finite elements. The levels of SVE and RVE link continuum mechanics to statistical mechanics, the RVE may be assessed only in a limited way via experimental testing, when the constitutive response becomes spatially homogeneous. Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made, consider car traffic on a highway---with just one lane for simplicity. Somewhat surprisingly, and in a tribute to its effectiveness, continuum mechanics effectively models the movement of cars via a differential equation for the density of cars. The familiarity of this situation empowers us to understand a little of the continuum-discrete dichotomy underlying continuum modelling in general. To start modelling define that, x measure distance along the highway, t is time, ρ is the density of cars on the highway, cars do not appear and disappear. Consider any group of cars, from the car at the back of the group located at x = a to the particular car at the front located at x = b. The total number of cars in this group N = ∫ a b ρ d x, since cars are conserved d N / d t =0. The only way an integral can be zero for all intervals is if the integrand is zero for all x, consequently, conservation derives the first order nonlinear conservation PDE ∂ ρ ∂ t + ∂ ∂ x =0 for all positions on the highway. This conservation PDE applies not only to car traffic but also to fluids, solids, crowds, animals, plants, bushfires, financial traders and this PDE is one equation with two unknowns, so another equation is needed to form a well posed problem
Continuum mechanics
–
Figure 1. Configuration of a continuum body
31.
Kinematics
–
Kinematics as a field of study is often referred to as the geometry of motion and as such may be seen as a branch of mathematics. The study of the influence of forces acting on masses falls within the purview of kinetics, for further details, see analytical dynamics. Kinematics is used in astrophysics to describe the motion of celestial bodies, in mechanical engineering, robotics, and biomechanics kinematics is used to describe the motion of systems composed of joined parts such as an engine, a robotic arm or the human skeleton. Kinematic analysis is the process of measuring the quantities used to describe motion. In addition, kinematics applies geometry to the study of the mechanical advantage of a mechanical system or mechanism. The term kinematic is the English version of A. M, ampères cinématique, which he constructed from the Greek κίνημα kinema, itself derived from κινεῖν kinein. Kinematic and cinématique are related to the French word cinéma, particle kinematics is the study of the trajectory of a particle. The position of a particle is defined to be the vector from the origin of a coordinate frame to the particle. If the tower is 50 m high, then the vector to the top of the tower is r=. In the most general case, a coordinate system is used to define the position of a particle. However, if the particle is constrained to move in a surface, all observations in physics are incomplete without those observations being described with respect to a reference frame. The position vector of a particle is a vector drawn from the origin of the frame to the particle. It expresses both the distance of the point from the origin and its direction from the origin, the magnitude of the position vector |P| gives the distance between the point P and the origin. | P | = x P2 + y P2 + z P2, the direction cosines of the position vector provide a quantitative measure of direction. It is important to note that the vector of a particle isnt unique. The position vector of a particle is different relative to different frames of reference. The velocity of a particle is a quantity that describes the direction of motion. More mathematically, the rate of change of the vector of a point
Kinematics
–
Each particle on the wheel travels in a planar circular trajectory (Kinematics of Machinery, 1876).
Kinematics
–
Kinematic quantities of a classical particle: mass m, position r, velocity v, acceleration a.
Kinematics
–
Illustration of a four-bar linkage from http://en.wikisource.org/wiki/The_Kinematics_of_Machinery Kinematics of Machinery, 1876
32.
Statics
–
When in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of mass moves at constant velocity. The application of Newtons second law to a system gives, F = m a, where bold font indicates a vector that has magnitude and direction. F is the total of the acting on the system, m is the mass of the system. The summation of forces will give the direction and the magnitude of the acceleration will be proportional to the mass. The assumption of static equilibrium of a =0 leads to, the summation of forces, one of which might be unknown, allows that unknown to be found. Likewise the application of the assumption of zero acceleration to the summation of moments acting on the leads to. The summation of moments, one of which might be unknown and these two equations together, can be applied to solve for as many as two loads acting on the system. From Newtons first law, this implies that the net force, the net forces equaling zero is known as the first condition for equilibrium, and the net torque equaling zero is known as the second condition for equilibrium. A scalar is a quantity which only has a magnitude, such as mass or temperature, a vector has a magnitude and a direction. There are several notations to identify a vector, including, A bold faced character V An underlined character V A character with an arrow over it V →, vectors are added using the parallelogram law or the triangle law. Vectors contain components in orthogonal bases, unit vectors i, j, and k are, by convention, along the x, y, and z axes, respectively. Force is the action of one body on another, a force is either a push or a pull. A force tends to move a body in the direction of its action, the action of a force is characterized by its magnitude, by the direction of its action, and by its point of application. Thus, force is a quantity, because its effect depends on the direction as well as on the magnitude of the action. Forces are classified as either contact or body forces, a contact force is produced by direct physical contact, an example is the force exerted on a body by a supporting surface. A body force is generated by virtue of the position of a body within a field such as a gravitational, electric. An example of a force is the weight of a body in the Earths gravitational field. In addition to the tendency to move a body in the direction of its application, the axis may be any line which neither intersects nor is parallel to the line of action of the force
Statics
–
Example of a beam in static equilibrium. The sum of force and moment is zero.
33.
Statistical mechanics
–
Statistical mechanics is a branch of theoretical physics using probability theory to study the average behaviour of a mechanical system, where the state of the system is uncertain. A common use of mechanics is in explaining the thermodynamic behaviour of large systems. This branch of mechanics, which treats and extends classical thermodynamics, is known as statistical thermodynamics or equilibrium statistical mechanics. Statistical mechanics also finds use outside equilibrium, an important subbranch known as non-equilibrium statistical mechanics deals with the issue of microscopically modelling the speed of irreversible processes that are driven by imbalances. Examples of such processes include chemical reactions or flows of particles, in physics there are two types of mechanics usually examined, classical mechanics and quantum mechanics. Statistical mechanics fills this disconnection between the laws of mechanics and the experience of incomplete knowledge, by adding some uncertainty about which state the system is in. The statistical ensemble is a probability distribution over all states of the system. In classical statistical mechanics, the ensemble is a probability distribution over phase points, in quantum statistical mechanics, the ensemble is a probability distribution over pure states, and can be compactly summarized as a density matrix. These two meanings are equivalent for many purposes, and will be used interchangeably in this article, however the probability is interpreted, each state in the ensemble evolves over time according to the equation of motion. Thus, the ensemble itself also evolves, as the systems in the ensemble continually leave one state. The ensemble evolution is given by the Liouville equation or the von Neumann equation, one special class of ensemble is those ensembles that do not evolve over time. These ensembles are known as equilibrium ensembles and their condition is known as statistical equilibrium, Statistical equilibrium occurs if, for each state in the ensemble, the ensemble also contains all of its future and past states with probabilities equal to the probability of being in that state. The study of equilibrium ensembles of isolated systems is the focus of statistical thermodynamics, non-equilibrium statistical mechanics addresses the more general case of ensembles that change over time, and/or ensembles of non-isolated systems. The primary goal of thermodynamics is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles. Whereas statistical mechanics proper involves dynamics, here the attention is focussed on statistical equilibrium, Statistical equilibrium does not mean that the particles have stopped moving, rather, only that the ensemble is not evolving. A sufficient condition for statistical equilibrium with a system is that the probability distribution is a function only of conserved properties. There are many different equilibrium ensembles that can be considered, additional postulates are necessary to motivate why the ensemble for a given system should have one form or another. A common approach found in textbooks is to take the equal a priori probability postulate
Statistical mechanics
–
Statistical mechanics
34.
Acceleration
–
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
Acceleration
–
Components of acceleration for a curved motion. The tangential component a t is due to the change in speed of traversal, and points along the curve in the direction of the velocity vector (or in the opposite direction). The normal component (also called centripetal component for circular motion) a c is due to the change in direction of the velocity vector and is normal to the trajectory, pointing toward the center of curvature of the path.
Acceleration
–
Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time t is found in the limit as
time interval Δt → 0 of Δ v / Δt
35.
Angular momentum
–
In physics, angular momentum is the rotational analog of linear momentum. It is an important quantity in physics because it is a conserved quantity – the angular momentum of a system remains constant unless acted on by an external torque. The definition of momentum for a point particle is a pseudovector r×p. This definition can be applied to each point in continua like solids or fluids, unlike momentum, angular momentum does depend on where the origin is chosen, since the particles position is measured from it. The angular momentum of an object can also be connected to the angular velocity ω of the object via the moment of inertia I. However, while ω always points in the direction of the rotation axis, Angular momentum is additive, the total angular momentum of a system is the vector sum of the angular momenta. For continua or fields one uses integration, torque can be defined as the rate of change of angular momentum, analogous to force. Applications include the gyrocompass, control moment gyroscope, inertial systems, reaction wheels, flying discs or Frisbees. In general, conservation does limit the motion of a system. In quantum mechanics, angular momentum is an operator with quantized eigenvalues, Angular momentum is subject to the Heisenberg uncertainty principle, meaning only one component can be measured with definite precision, the other two cannot. Also, the spin of elementary particles does not correspond to literal spinning motion, Angular momentum is a vector quantity that represents the product of a bodys rotational inertia and rotational velocity about a particular axis. Angular momentum can be considered an analog of linear momentum. Thus, where momentum is proportional to mass m and linear speed v, p = m v, angular momentum is proportional to moment of inertia I. Unlike mass, which only on amount of matter, moment of inertia is also dependent on the position of the axis of rotation. Unlike linear speed, which occurs in a line, angular speed occurs about a center of rotation. Therefore, strictly speaking, L should be referred to as the angular momentum relative to that center and this simple analysis can also apply to non-circular motion if only the component of the motion which is perpendicular to the radius vector is considered. In that case, L = r m v ⊥, where v ⊥ = v sin θ is the component of the motion. It is this definition, × to which the moment of momentum refers
Angular momentum
–
This
gyroscope remains upright while spinning due to the conservation of its angular momentum.
Angular momentum
–
An
ice skater conserves angular momentum – her
rotational speed increases as her
moment of inertia decreases by drawing in her arms and legs.
36.
Couple (mechanics)
–
In mechanics, a couple is a system of forces with a resultant moment but no resultant force. A better term is force couple or pure moment and its effect is to create rotation without translation, or more generally without any acceleration of the centre of mass. In rigid body mechanics, force couples are free vectors, meaning their effects on a body are independent of the point of application, the resultant moment of a couple is called a torque. This is not to be confused with the term torque as it is used in physics, instead, torque is a special case of moment. Torque has special properties that moment does not have, in particular the property of being independent of reference point, definition A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance or moment. The simplest kind of couple consists of two equal and opposite forces whose lines of action do not coincide and this is called a simple couple. The forces have an effect or moment called a torque about an axis which is normal to the plane of the forces. The SI unit for the torque of the couple is newton metre. When d is taken as a vector between the points of action of the forces, then the couple is the product of d and F, i. e. τ = | d × F |. The moment of a force is defined with respect to a certain point P, and in general when P is changed. However, the moment of a couple is independent of the reference point P, in other words, a torque vector, unlike any other moment vector, is a free vector. The proof of claim is as follows, Suppose there are a set of force vectors F1, F2, etc. that form a couple, with position vectors r1, r2. The moment about P is M = r 1 × F1 + r 2 × F2 + ⋯ Now we pick a new reference point P that differs from P by the vector r. The new moment is M ′ = × F1 + × F2 + ⋯ Now the distributive property of the cross product implies M ′ = + r ×, however, the definition of a force couple means that F1 + F2 + ⋯ =0. Therefore, M ′ = r 1 × F1 + r 2 × F2 + ⋯ = M This proves that the moment is independent of reference point, which is proof that a couple is a free vector. A force F applied to a body at a distance d from the center of mass has the same effect as the same force applied directly to the center of mass. The couple produces an acceleration of the rigid body at right angles to the plane of the couple. The force at the center of mass accelerates the body in the direction of the force without change in orientation, conversely, a couple and a force in the plane of the couple can be replaced by a single force, appropriately located
Couple (mechanics)
–
Classical mechanics
37.
Energy
–
In physics, energy is the property that must be transferred to an object in order to perform work on – or to heat – the object, and can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the transferred to an object by the mechanical work of moving it a distance of 1 metre against a force of 1 newton. Mass and energy are closely related, for example, with a sensitive enough scale, one could measure an increase in mass after heating an object. Living organisms require available energy to stay alive, such as the humans get from food. Civilisation gets the energy it needs from energy resources such as fuels, nuclear fuel. The processes of Earths climate and ecosystem are driven by the radiant energy Earth receives from the sun, the total energy of a system can be subdivided and classified in various ways. It may also be convenient to distinguish gravitational energy, thermal energy, several types of energy, electric energy. Many of these overlap, for instance, thermal energy usually consists partly of kinetic. Some types of energy are a mix of both potential and kinetic energy. An example is energy which is the sum of kinetic. Whenever physical scientists discover that a phenomenon appears to violate the law of energy conservation. Heat and work are special cases in that they are not properties of systems, in general we cannot measure how much heat or work are present in an object, but rather only how much energy is transferred among objects in certain ways during the occurrence of a given process. Heat and work are measured as positive or negative depending on which side of the transfer we view them from, the distinctions between different kinds of energy is not always clear-cut. In contrast to the definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness. The modern analog of this property, kinetic energy, differs from vis viva only by a factor of two, in 1807, Thomas Young was possibly the first to use the term energy instead of vis viva, in its modern sense. Gustave-Gaspard Coriolis described kinetic energy in 1829 in its modern sense, the law of conservation of energy was also first postulated in the early 19th century, and applies to any isolated system. It was argued for years whether heat was a physical substance, dubbed the caloric, or merely a physical quantity. In 1845 James Prescott Joule discovered the link between mechanical work and the generation of heat and these developments led to the theory of conservation of energy, formalized largely by William Thomson as the field of thermodynamics
Energy
–
In a typical
lightning strike, 500
megajoules of
electric potential energy is converted into the same amount of energy in other forms, mostly
light energy,
sound energy and
thermal energy.
Energy
–
Thermal energy is energy of microscopic constituents of matter, which may include both
kinetic and
potential energy.
Energy
–
Thomas Young – the first to use the term "energy" in the modern sense.
Energy
–
A
Turbo generator transforms the energy of pressurised steam into electrical energy
38.
Kinetic energy
–
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes, the same amount of work is done by the body in decelerating from its current speed to a state of rest. In classical mechanics, the energy of a non-rotating object of mass m traveling at a speed v is 12 m v 2. In relativistic mechanics, this is an approximation only when v is much less than the speed of light. The standard unit of energy is the joule. The adjective kinetic has its roots in the Greek word κίνησις kinesis, the dichotomy between kinetic energy and potential energy can be traced back to Aristotles concepts of actuality and potentiality. The principle in classical mechanics that E ∝ mv2 was first developed by Gottfried Leibniz and Johann Bernoulli, Willem s Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, Émilie du Châtelet recognized the implications of the experiment and published an explanation. The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century, early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled Du Calcul de lEffet des Machines outlining the mathematics of kinetic energy. William Thomson, later Lord Kelvin, is given the credit for coining the term kinetic energy c, energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, and rest energy. These can be categorized in two classes, potential energy and kinetic energy. Kinetic energy is the movement energy of an object, Kinetic energy can be transferred between objects and transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to, for example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance, the chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms, for example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling, the energy is not destroyed, it has only been converted to another form by friction
Kinetic energy
–
The cars of a
roller coaster reach their maximum kinetic energy when at the bottom of their path. When they start rising, the kinetic energy begins to be converted to gravitational
potential energy. The sum of kinetic and potential energy in the system remains constant, ignoring losses to
friction.
39.
Potential energy
–
In physics, potential energy is energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule, the term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotles concept of potentiality. Potential energy is associated with forces that act on a body in a way that the work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, that are called potential forces, can be represented at every point in space by vectors expressed as gradients of a scalar function called potential. Potential energy is the energy of an object. It is the energy by virtue of a position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force that works against the force field of the potential. This work is stored in the field, which is said to be stored as potential energy. If the external force is removed the field acts on the body to perform the work as it moves the body back to the initial position. Suppose a ball which mass is m, and it is in h position in height, if the acceleration of free fall is g, the weight of the ball is mg. There are various types of energy, each associated with a particular type of force. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of mutual positions of electrons and nuclei in atoms and molecules. Thermal energy usually has two components, the energy of random motions of particles and the potential energy of their mutual positions. Forces derivable from a potential are also called conservative forces, the work done by a conservative force is W = − Δ U where Δ U is the change in the potential energy associated with the force. The negative sign provides the convention that work done against a force field increases potential energy, common notations for potential energy are U, V, also Ep. Potential energy is closely linked with forces, in this case, the force can be defined as the negative of the vector gradient of the potential field. If the work for a force is independent of the path, then the work done by the force is evaluated at the start
Potential energy
–
In the case of a
bow and arrow, when the archer does work on the bow, drawing the string back, some of the chemical energy of the archer's body is transformed into elastic potential-energy in the bent limbs of the bow. When the string is released, the force between the string and the arrow does work on the arrow. Thus, the potential energy in the bow limbs is transformed into the
kinetic energy of the arrow as it takes flight.
Potential energy
–
A
trebuchet uses the gravitational potential energy of the
counterweight to throw projectiles over two hundred meters
Potential energy
–
Springs are used for storing
elastic potential energy
Potential energy
–
Archery is one of humankind's oldest applications of elastic potential energy
40.
Force
–
In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity, force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity and it is measured in the SI unit of newtons and represented by the symbol F. The original form of Newtons second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. In an extended body, each part usually applies forces on the adjacent parts, such internal mechanical stresses cause no accelation of that body as the forces balance one another. Pressure, the distribution of small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of materials, or flow in fluids. In part this was due to an understanding of the sometimes non-obvious force of friction. A fundamental error was the belief that a force is required to maintain motion, most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years, the Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known, in order of decreasing strength, they are, strong, electromagnetic, weak, high-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotles view, the sphere contained four elements that come to rest at different natural places therein. Aristotle believed that objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground. He distinguished between the tendency of objects to find their natural place, which led to natural motion, and unnatural or forced motion
Force
–
Aristotle famously described a force as anything that causes an object to undergo "unnatural motion"
Force
–
Forces are also described as a push or pull on an object. They can be due to phenomena such as
gravity,
magnetism, or anything that might cause a mass to accelerate.
Force
–
Though
Sir Isaac Newton 's most famous equation is, he actually wrote down a different form for his second law of motion that did not use
differential calculus.
Force
–
Galileo Galilei was the first to point out the inherent contradictions contained in Aristotle's description of forces.
41.
Frame of reference
–
In physics, a frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements. In n dimensions, n+1 reference points are sufficient to define a reference frame. Using rectangular coordinates, a frame may be defined with a reference point at the origin. In Einsteinian relativity, reference frames are used to specify the relationship between an observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes observational frame of reference, a relativistic reference frame includes the coordinate time, which does not correspond across different frames moving relatively to each other. The situation thus differs from Galilean relativity, where all possible coordinate times are essentially equivalent, the need to distinguish between the various meanings of frame of reference has led to a variety of terms. For example, sometimes the type of system is attached as a modifier. Sometimes the state of motion is emphasized, as in rotating frame of reference, sometimes the way it transforms to frames considered as related is emphasized as in Galilean frame of reference. Sometimes frames are distinguished by the scale of their observations, as in macroscopic and microscopic frames of reference, in this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a system may be employed for many purposes where the state of motion is not the primary concern. For example, a system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs generalized coordinates, normal modes or eigenvectors and it seems useful to divorce the various aspects of a reference frame for the discussion below. A coordinate system is a concept, amounting to a choice of language used to describe observations. Consequently, an observer in a frame of reference can choose to employ any coordinate system to describe observations made from that frame of reference. A change in the choice of coordinate system does not change an observers state of motion. This viewpoint can be found elsewhere as well, which is not to dispute that some coordinate systems may be a better choice for some observations than are others. Choice of what to measure and with what observational apparatus is a separate from the observers state of motion. D. Norton, The discussion is taken beyond simple space-time coordinate systems by Brading, extension to coordinate systems using generalized coordinates underlies the Hamiltonian and Lagrangian formulations of quantum field theory, classical relativistic mechanics, and quantum gravity
Frame of reference
–
An observer O, situated at the origin of a local set of coordinates – a frame of reference F. The observer in this frame uses the coordinates (x, y, z, t) to describe a spacetime event, shown as a star.
42.
Impulse (physics)
–
In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Since force is a quantity, impulse is also a vector in the same direction. Impulse applied to an object produces an equivalent vector change in its linear momentum, the SI unit of impulse is the newton second, and the dimensionally equivalent unit of momentum is the kilogram meter per second. The corresponding English engineering units are the pound-second and the slug-foot per second, a resultant force causes acceleration and a change in the velocity of the body for as long as it acts. Conversely, a force applied for a long time produces the same change in momentum—the same impulse—as a larger force applied briefly. This is often called the impulse-momentum theorem, as a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied. Impulse has the units and dimensions as momentum. In the International System of Units, these are kg·m/s = N·s, in English engineering units, they are slug·ft/s = lbf·s. The term impulse is also used to refer to a force or impact. This type of impulse is often idealized so that the change in momentum produced by the force happens with no change in time and this sort of change is a step change, and is not physically possible. However, this is a model for computing the effects of ideal collisions. The application of Newtons second law for variable mass allows impulse, in the case of rockets, the impulse imparted can be normalized by unit of propellant expended, to create a performance parameter, specific impulse. This fact can be used to derive the Tsiolkovsky rocket equation, which relates the vehicles propulsive change in velocity to the specific impulse. Wave–particle duality defines the impulse of a wave collision, the preservation of momentum in the collision is then called phase matching. Applications include, Compton effect nonlinear optics Acousto-optic modulator Electron phonon scattering Serway, Raymond A. Jewett, John W. Physics for Scientists, Physics for Scientists and Engineers, Mechanics, Oscillations and Waves, Thermodynamics
Impulse (physics)
–
A large force applied for a very short duration, such as a golf shot, is often described as the club giving the ball an impulse.
Impulse (physics)
43.
Inertia
–
Inertia is the resistance of any physical object to any change in its state of motion, this includes changes to its speed, direction, or state of rest. It is the tendency of objects to keep moving in a line at constant velocity. The principle of inertia is one of the principles of classical physics that are used to describe the motion of objects. Inertia comes from the Latin word, iners, meaning idle, Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. In common usage, the inertia may refer to an objects amount of resistance to change in velocity, or sometimes to its momentum. Thus, an object will continue moving at its current velocity until some force causes its speed or direction to change. On the surface of the Earth, inertia is often masked by the effects of friction and air resistance, both of which tend to decrease the speed of moving objects, and gravity. Aristotle explained the continued motion of projectiles, which are separated from their projector, by the action of the surrounding medium, Aristotle concluded that such violent motion in a void was impossible. Despite its general acceptance, Aristotles concept of motion was disputed on several occasions by notable philosophers over nearly two millennia, for example, Lucretius stated that the default state of matter was motion, not stasis. Philoponus proposed that motion was not maintained by the action of a surrounding medium, although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction. This view was opposed by Averroes and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the Islamic world, in the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named impetus, dissipated spontaneously. Buridans position was that an object would be arrested by the resistance of the air. Buridan also maintained that impetus increased with speed, thus, his idea of impetus was similar in many ways to the modern concept of momentum. Buridan also believed that impetus could be not only linear, but also circular in nature, buridans thought was followed up by his pupil Albert of Saxony and the Oxford Calculators, who performed various experiments that further undermined the classical, Aristotelian view. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of demonstrating laws of motion in the form of graphs, benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion. The law of inertia states that it is the tendency of an object to resist a change in motion. According to Newton, an object will stay at rest or stay in motion unless acted on by a net force, whether it results from gravity, friction, contact
Inertia
–
Galileo Galilei
44.
Moment of inertia
–
It depends on the bodys mass distribution and the axis chosen, with larger moments requiring more torque to change the bodys rotation. It is a property, the moment of inertia of a composite system is the sum of the moments of inertia of its component subsystems. One of its definitions is the moment of mass with respect to distance from an axis r, I = ∫ Q r 2 d m. For bodies constrained to rotate in a plane, it is sufficient to consider their moment of inertia about a perpendicular to the plane. When a body is rotating, or free to rotate, around an axis, the amount of torque needed to cause any given angular acceleration is proportional to the moment of inertia of the body. Moment of inertia may be expressed in units of kilogram metre squared in SI units, moment of inertia plays the role in rotational kinetics that mass plays in linear kinetics - both characterize the resistance of a body to changes in its motion. The moment of inertia depends on how mass is distributed around an axis of rotation, for a point-like mass, the moment of inertia about some axis is given by mr2, where r is the distance to the axis, and m is the mass. For an extended body, the moment of inertia is just the sum of all the pieces of mass multiplied by the square of their distances from the axis in question. For an extended body of a shape and uniform density. In 1673 Christiaan Huygens introduced this parameter in his study of the oscillation of a body hanging from a pivot, the term moment of inertia was introduced by Leonhard Euler in his book Theoria motus corporum solidorum seu rigidorum in 1765, and it is incorporated into Eulers second law. Comparison of this frequency to that of a simple pendulum consisting of a single point of mass provides a mathematical formulation for moment of inertia of an extended body. Moment of inertia appears in momentum, kinetic energy, and in Newtons laws of motion for a rigid body as a physical parameter that combines its shape. There is a difference in the way moment of inertia appears in planar. The moment of inertia of a flywheel is used in a machine to resist variations in applied torque to smooth its rotational output. Moment of inertia I is defined as the ratio of the angular momentum L of a system to its angular velocity ω around a principal axis, if the angular momentum of a system is constant, then as the moment of inertia gets smaller, the angular velocity must increase. This occurs when spinning figure skaters pull in their arms or divers curl their bodies into a tuck position during a dive. For a simple pendulum, this yields a formula for the moment of inertia I in terms of the mass m of the pendulum and its distance r from the pivot point as. Thus, moment of inertia depends on both the mass m of a body and its geometry, or shape, as defined by the distance r to the axis of rotation
Moment of inertia
–
Tightrope walker Samuel Dixon using the long rod's moment of inertia for balance while crossing the
Niagara River in 1890.
Moment of inertia
–
Flywheels have large moments of inertia to smooth out mechanical motion. This example is in a Russian museum.
Moment of inertia
–
Spinning figure skaters can reduce their moment of inertia by pulling in their arms, allowing them to spin faster due to
conservation of angular momentum.
Moment of inertia
–
Pendulums used in Mendenhall
gravimeter apparatus, from 1897 scientific journal. The portable gravimeter developed in 1890 by Thomas C. Mendenhall provided the most accurate relative measurements of the local gravitational field of the Earth.
45.
Mass
–
In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules. Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
Mass
–
Depiction of early
balance scales in the
Papyrus of Hunefer (dated to the
19th dynasty, ca. 1285 BC). The scene shows
Anubis weighing the heart of Hunefer.
Mass
–
The kilogram is one of the seven
SI base units and one of three which is defined ad hoc (i.e. without reference to another base unit).
Mass
–
Galileo Galilei (1636)
Mass
–
Distance traveled by a freely falling ball is proportional to the square of the elapsed time
46.
Power (physics)
–
In physics, power is the rate of doing work. It is the amount of energy consumed per unit time, having no direction, it is a scalar quantity. In the SI system, the unit of power is the joule per second, known as the watt in honour of James Watt, another common and traditional measure is horsepower. Being the rate of work, the equation for power can be written, because this integral depends on the trajectory of the point of application of the force and torque, this calculation of work is said to be path dependent. As a physical concept, power requires both a change in the universe and a specified time in which the change occurs. This is distinct from the concept of work, which is measured in terms of a net change in the state of the physical universe. The output power of a motor is the product of the torque that the motor generates. The power involved in moving a vehicle is the product of the force of the wheels. The dimension of power is divided by time. The SI unit of power is the watt, which is equal to one joule per second, other units of power include ergs per second, horsepower, metric horsepower, and foot-pounds per minute. One horsepower is equivalent to 33,000 foot-pounds per minute, or the required to lift 550 pounds by one foot in one second. Other units include dBm, a logarithmic measure with 1 milliwatt as reference, food calories per hour, Btu per hour. This shows how power is an amount of energy consumed per unit time. If ΔW is the amount of work performed during a period of time of duration Δt and it is the average amount of work done or energy converted per unit of time. The average power is simply called power when the context makes it clear. The instantaneous power is then the value of the average power as the time interval Δt approaches zero. P = lim Δ t →0 P a v g = lim Δ t →0 Δ W Δ t = d W d t. In the case of constant power P, the amount of work performed during a period of duration T is given by, W = P t
Power (physics)
–
Ansel Adams photograph of electrical wires of the Boulder Dam Power Units, 1941–1942
47.
Work (physics)
–
In physics, a force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force. For example, when a ball is held above the ground and then dropped, the SI unit of work is the joule. The SI unit of work is the joule, which is defined as the work expended by a force of one newton through a distance of one metre. The dimensionally equivalent newton-metre is sometimes used as the unit for work, but this can be confused with the unit newton-metre. Usage of N⋅m is discouraged by the SI authority, since it can lead to confusion as to whether the quantity expressed in newton metres is a torque measurement, or a measurement of energy. Non-SI units of work include the erg, the foot-pound, the foot-poundal, the hour, the litre-atmosphere. Due to work having the physical dimension as heat, occasionally measurement units typically reserved for heat or energy content, such as therm, BTU. The work done by a constant force of magnitude F on a point that moves a distance s in a line in the direction of the force is the product W = F s. For example, if a force of 10 newtons acts along a point that travels 2 meters and this is approximately the work done lifting a 1 kg weight from ground level to over a persons head against the force of gravity. Notice that the work is doubled either by lifting twice the weight the distance or by lifting the same weight twice the distance. Work is closely related to energy, the work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Conversely, a decrease in energy is caused by an equal amount of negative work done by the resultant force. From Newtons second law, it can be shown that work on a free, rigid body, is equal to the change in energy of the velocity and rotation of that body. The work of forces generated by a function is known as potential energy. These formulas demonstrate that work is the associated with the action of a force, so work subsequently possesses the physical dimensions. The work/energy principles discussed here are identical to Electric work/energy principles, constraint forces determine the movement of components in a system, constraining the object within a boundary. Constraint forces ensure the velocity in the direction of the constraint is zero and this only applies for a single particle system. For example, in an Atwood machine, the rope does work on each body, there are, however, cases where this is not true
Work (physics)
–
A
baseball pitcher does positive work on the ball by applying a force to it over the distance it moves while in his grip.
Work (physics)
–
A force of constant magnitude and perpendicular to the lever arm
Work (physics)
–
Gravity F = mg does work W = mgh along any descending path
Work (physics)
–
Lotus type 119B gravity racer at Lotus 60th celebration.
48.
Momentum
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In classical mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object, quantified in kilogram-meters per second. It is dimensionally equivalent to impulse, the product of force and time, Newtons second law of motion states that the change in linear momentum of a body is equal to the net impulse acting on it. If the truck were lighter, or moving slowly, then it would have less momentum. Linear momentum is also a quantity, meaning that if a closed system is not affected by external forces. In classical mechanics, conservation of momentum is implied by Newtons laws. It also holds in special relativity and, with definitions, a linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory. It is ultimately an expression of one of the symmetries of space and time. Linear momentum depends on frame of reference, observers in different frames would find different values of linear momentum of a system. But each would observe that the value of linear momentum does not change with time, momentum has a direction as well as magnitude. Quantities that have both a magnitude and a direction are known as vector quantities, because momentum has a direction, it can be used to predict the resulting direction of objects after they collide, as well as their speeds. Below, the properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations, the momentum of a particle is traditionally represented by the letter p. It is the product of two quantities, the mass and velocity, p = m v, the units of momentum are the product of the units of mass and velocity. In SI units, if the mass is in kilograms and the velocity in meters per second then the momentum is in kilogram meters/second, in cgs units, if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters/second. Being a vector, momentum has magnitude and direction, for example, a 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has a momentum of 1 kg m/s due north measured from the ground. The momentum of a system of particles is the sum of their momenta, if two particles have masses m1 and m2, and velocities v1 and v2, the total momentum is p = p 1 + p 2 = m 1 v 1 + m 2 v 2. If all the particles are moving, the center of mass will generally be moving as well, if the center of mass is moving at velocity vcm, the momentum is, p = m v cm. This is known as Eulers first law, if a force F is applied to a particle for a time interval Δt, the momentum of the particle changes by an amount Δ p = F Δ t
Momentum
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In a game of
pool, momentum is conserved; that is, if one ball stops dead after the collision, the other ball will continue away with all the momentum. If the moving ball continues or is deflected then both balls will carry a portion of the momentum from the collision.
49.
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
Space
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Gottfried Leibniz
Space
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A right-handed three-dimensional
Cartesian coordinate system used to indicate positions in space.
Space
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Isaac Newton
Space
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Immanuel Kant
50.
Speed
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In everyday use and in kinematics, the speed of an object is the magnitude of its velocity, it is thus a scalar quantity. Speed has the dimensions of distance divided by time, the SI unit of speed is the metre per second, but the most common unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour. For air and marine travel the knot is commonly used, the fastest possible speed at which energy or information can travel, according to special relativity, is the speed of light in a vacuum c =299792458 metres per second. Matter cannot quite reach the speed of light, as this would require an amount of energy. In relativity physics, the concept of rapidity replaces the classical idea of speed, italian physicist Galileo Galilei is usually credited with being the first to measure speed by considering the distance covered and the time it takes. Galileo defined speed as the distance covered per unit of time, in equation form, this is v = d t, where v is speed, d is distance, and t is time. A cyclist who covers 30 metres in a time of 2 seconds, objects in motion often have variations in speed. If s is the length of the path travelled until time t, in the special case where the velocity is constant, this can be simplified to v = s / t. The average speed over a time interval is the total distance travelled divided by the time duration. Speed at some instant, or assumed constant during a short period of time, is called instantaneous speed. By looking at a speedometer, one can read the speed of a car at any instant. A car travelling at 50 km/h generally goes for less than one hour at a constant speed, if the vehicle continued at that speed for half an hour, it would cover half that distance. If it continued for one minute, it would cover about 833 m. Different from instantaneous speed, average speed is defined as the distance covered divided by the time interval. For example, if a distance of 80 kilometres is driven in 1 hour, likewise, if 320 kilometres are travelled in 4 hours, the average speed is also 80 kilometres per hour. When a distance in kilometres is divided by a time in hours, average speed does not describe the speed variations that may have taken place during shorter time intervals, and so average speed is often quite different from a value of instantaneous speed. If the average speed and the time of travel are known, using this equation for an average speed of 80 kilometres per hour on a 4-hour trip, the distance covered is found to be 320 kilometres. Linear speed is the distance travelled per unit of time, while speed is the linear speed of something moving along a circular path
Speed
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Speed can be thought of as the rate at which an object covers
distance. A fast-moving object has a high speed and covers a relatively large distance in a given amount of time, while a slow-moving object covers a relatively small amount of distance in the same amount of time.