1.
MV Christiaan Huygens
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Christiaan Huygens was a Dutch ocean liner that was built in 1927 by the Nederlandsche Scheepsbouw Maatschappij for the Stoomvaart Maatschappij Nederland. She was employed on the Amsterdam – Batavia route until the outbreak of the Second World War, requisitioned as a troopship, she was employed in the Mediterranean Sea and Indian Ocean. Surviving the end of the war in Europe, she struck a mine in the Scheldt on 26 August 1945 and was beached and she broke in two on 5 September and was declared a total loss. The ship was 168.05 metres long, with a beam of 20.22 metres and she had a depth of 20.22 metres and a draught of 12.12 metres. The ship was powered by two ten-cylinder two-stroke Single Cycle Single Action diesel engines, They were rated at 2,490 nhp,5,800 bhp, each engine drove a single screw propeller, giving the ship a speed of 16 knots. The engines were built by Sulzer Brothers, Winterthur, Switzerland and her auxiliary engines were three Sulzer 5S38 and a Sulzer 6RKH30 diesel engine, together rated at 2,250 bhp. Accommodation for 638 passengers was provided, Christiaan Huygens was built as yard number 186 by the Nederlandsche Scheepsbouw Maatschappij, Amsterdam, North Holland, Netherlands for Stoomvaart Maatschappij Nederland. She was launched on 28 September 1927 and completed in January 1928 and her port of registry was Amsterdam and the code letters NJWV were allocated. In 1934, her letters were changed to PDKD. Christiaan Huygens completed her sea trials on 28 January 1928 and she departed from Amsterdam on her maiden voyage on 28 February, bound for Batavia, Netherlands East Indies. She called at Southampton, Hampshire, United Kingdom on 1 March and she arrived at Batavia on 30 March, a day ahead of schedule. She departed for Amsterdam on 18 April, arriving on 18 May, on a voyage in November 1928, she arrived at Amsterdam three days ahead of schedule. On 13 August 1933, the Norwegian cargo ship Fernglen ran aground south of Cape Guardafui, Christiaan Huygens was one of the vessels that went to her aid. With the outbreak of the Second World War in 1939, Christiaan Huygens route was altered, in 1940, her port of registry was changed to Batavia. She was placed under the management of the Orient Line and served as a troopship, carrying 1,290 troops, Christiaan Huygens sailed from Fremantle, Western Australia on 22 September with Convoy US5, arriving at Suez, Egypt on 12 October. She sailed from Suez on 28 October 1940 as a member of Convoy SW 2A, Christiaan Huygens departed from Bombay on 12 November with Convoy BN 8A, which arrived at Suez on 23 November. She then joined Convoy BN 9A, which sailed on 30 November, Christiaan Huygens then sailed to Colombo, Ceylon, from where she departed on 16 January 1941 with Convoy US8, which arrived at Suez on 28 January. She departed on 17 February as a member of Convoy BSF2, on 5 April, she joined Convoy SL70, which had departed from Freetown, Sierra Leone on 29 March
MV Christiaan Huygens
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History
2.
Caspar Netscher
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Caspar Netscher was a Dutch portrait and genre painter. He was a master in depicting oriental rugs, silk and brocade, according to Arnold Houbrakens 17th century biographical study of Dutch painters he was born in Heidelberg or Prague. His father Johann Netscher was a sculptor from Stuttgart, the elder Netscher married Elizabet Vetter, the daughter of a mayor in Heidelberg, against her fathers wishes. He died in Poland when Caspar was two years of age and it has been suggested that Caspar may have been the son of a Rotterdam painter. When Heidelberg was attacked during the war, Caspars mother fled with four children to an estate outside the city. When the castle was laid siege, the people there suffered from hunger. Caspars mother fled in the night, carrying the young Caspar in her arms and with her daughter on foot, staying at almshouses for widows. They travelled in this way to Arnhem, where they found safe quarter. In Arnhem Caspar was adopted by a physician named A. Tullekens. He was Ter Borchs most gifted pupil, probably worked as an assistant as well, when he came of age, he first worked for the Dutch keelbeulen until he had enough money to make a grand tour. In 1658 he set out for Italy to complete his education, from Bordeaux he planned to proceed overland to Italy. However, while in Bordeaux he met the mathematician and fountain designer Godijn, and married his daughter Margaretha Godijn on 25 November 1659, in Bordeaux he toiled hard to earn a livelihood by painting small cabinet pictures which are now highly valued on account of their exquisite finish. Fearing the persecutions of Protestants, after his son was born he moved back North to The Hague in 1662, in this branch of his art was more successful. In 1668 he joined the Schutterij and Cosimo III de Medici and it is likely that Netscher knew the painters Frans van Mieris, Sr. He was patronized by William III, and his earnings soon enabled him to gratify his own taste by depicting musical and conversational pieces and it was in these that Netschers genius was fully displayed. The painter was gaining fame and wealth when he began to suffer from gout and took to his bed. His sons Constantyn, and Theodorus, were also painters after their fathers style and he was also the father of Anthonie who emigrated to Batavia. Spick, Jan Tilius and Aleida Wolfsen, attribution This article incorporates text from a publication now in the public domain, Chisholm, Hugh, ed. Netscher, Gaspar
Caspar Netscher
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Portrait of
Maria II Stuart, Queen of England
Caspar Netscher
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The Lace-Maker by Caspar Netscher (1662), oil on canvas, 33 x 27 cm. Wallace Collection, London
Caspar Netscher
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The Medaillon
Caspar Netscher
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Singing lesson
3.
Hofwijck
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Hofwijck is a mansion built for 17th-century politician Constantijn Huygens. After he became a widower, Huygens bought land on the Vliet in Voorburg with plans to build a home while the Vliet itself was still being dug in 1638. At the time it was fashionable to have a summer home on a river or canal. The building itself and the gardens were designed by Huygens himself in cooperation with the architect Jacob van Campen, the estate was to be a harmonious piece of paradise on earth, with a garden in God’s image and likeness. Huygens was very inspired by the works of classical Roman architect Vitruvius. Pieter Post was in charge of the building activities. The building was erected in unplastered brick and is in the Classicist style and it stands in the centre of a square swan pond. Hofwijck was inaugurated in 1642 in the company of friends and relatives, in the collection on display are various items from the Dutch Royal family that have to do with the work of either Constantijn or his son Christiaan. In the display room for Christiaan, various types of clockworks are shown, when Constantijn died, his son, the scientist Christiaan Huygens, came to live there. In 1750 the last Huygens to live there sold it, grossly neglected in later years, it was auctioned for demolition in 1849, which was avoided when it was acquired by politician Guillaume Groen van Prinsterer. The Hofwijck Association acquired it circa 1913, when demolition loomed again and it is now a museum, which opened its door for the first time on June 12,1928. Huygens had Hofwijck built so he would have a place to escape the tensions that life as a politician brought with it, however, it has more than one meaning, because hof can also mean garden and wijck can also mean place. The Latin name has a double meaning too, Vitaulium means garden of life as well as garden of Vitruvius, from 1950 to 1970 this house was on the Dutch 25 guilder note. Until 2006, the Dutch intercity trains stopped in Voorburg and this was the condition requested of the Dutch railway board by the city of Voorburg, when they gave a large piece of the garden to the building of the rails in the 19th century. K Wil Hofwijck, als het is, k wil Hofwijck, als t zal wezen, de vreemdeling doen zien, Constantijn Huygens Dutch Golden Age Official site of museum Hofwijck, poem on Hofwijck, a documentary Hofwijck, an explanation of the poem and the house
Hofwijck
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Hofwijck from the Southeast. Behind the main building, the elevated train station and highway A12 cross over the Vliet.
Hofwijck
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Hofwijck from the station.
Hofwijck
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Christiaan Huygens room, with pendulum from the church in
Scheveningen.
Hofwijck
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Hofwijck kitchen hearth.
4.
Voorburg
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Voorburg is a Dutch town and former municipality in the western part of the province of South Holland, the Netherlands. Together with Leidschendam and Stompwijk, it makes up the municipality Leidschendam-Voorburg and it has a population of approximately 39,000 people. It is considered to be the oldest city in The Netherlands, in 2002, the cities of Leidschendam and Voorburg were merged under the new municipality named Leidschendam-Voorburg. Situated adjacent to the city of The Hague, it is regarded as one of its suburbs. It was positioned along the Fossa Corbulonis, a canal connecting the Rhine and this waterway is now known as the Rijn-Schie canal and is still a dominant landmark of the present day borough. His son, the astronomer and mathematician Christiaan Huygens, spent several years in his fathers country house in Voorburg. The house, located next to the railway station, now functions as a museum. Philosopher Baruch Spinoza also lived in Voorburg from 1663 to 1670, in Voorburg, Spinoza continued work on the Ethics and corresponded with scientists, philosophers, and theologians throughout Europe. Until 2009 Voorburg hosted the major branch of the statistics institute, the CBS. The latter two are now part of the Randstad Rail network, Voorburg used to be an Intercity station, because there was an eternal agreement with the railways that every passing train should stop there. It lost that status, as the new station is elevated. Voorburg Cricket Club Sportpark Westvliet cricket ground was approved by the ICC as the Netherlands latest ODI venue and it joins the VRA ground in Amstelveen and the Hazelaarweg ground in Rotterdam in gaining ODI status. Bangladesh played one Twenty20 International match each against Scotland and Netherlands there in July 2012. org, Fossa Corbulonis
Voorburg
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The Herenstraat in the town centre
Voorburg
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The old church in Voorburg
Voorburg
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The old Town Hall 'Swaensteyn' from 1632
5.
The Hague
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The Hague is a city on the western coast of the Netherlands, and the capital city of the province of South Holland. With a population of 520,704 inhabitants and more than one million including the suburbs, it is the third-largest city of the Netherlands. The Rotterdam The Hague Metropolitan Area, with a population of approximately 2.7 million, is the 12th-largest in the European Union and the most populous in the country. Located in the west of the Netherlands, The Hague is in the centre of the Haaglanden conurbation and lies at the southwest corner of the larger Randstad conurbation. The Hague is the seat of the Dutch government, parliament, the Supreme Court, and the Council of State, but the city is not the capital of the Netherlands, which constitutionally is Amsterdam. King Willem-Alexander of the Netherlands plans to live at Huis ten Bosch and works at Noordeinde Palace in The Hague, the Hague is also home to the world headquarters of Royal Dutch Shell and numerous other major Dutch companies. The Hague originated around 1230, when Count Floris IV of Holland purchased land alongside a pond, in 1248, his son and successor William II, King of the Romans, decided to extend the residence to a palace, which would later be called the Binnenhof. He died in 1256 before this palace was completed but parts of it were finished by his son Floris V, of which the Ridderzaal and it is still used for political events, such as the annual speech from the throne by the Dutch monarch. From the 13th century onwards, the counts of Holland used The Hague as their administrative centre, the village that originated around the Binnenhof was first mentioned as Haga in a charter dating from 1242. In the 15th century, the smarter des Graven hage came into use, literally The Counts Wood, with connotations like The Counts Hedge, s-Gravenhage was officially used for the city from the 17th century onwards. Today, this name is used in some official documents like birth. The city itself uses Den Haag in all its communication and their seat was located in The Hague. At the beginning of the Eighty Years War, the absence of city walls proved disastrous, in 1575, the States of Holland even considered demolishing the city but this proposal was abandoned, after mediation by William of Orange. From 1588, The Hague also became the seat of the government of the Dutch Republic, in order for the administration to maintain control over city matters, The Hague never received official city status, although it did have many of the privileges normally granted only to cities. In modern administrative law, city rights have no place anymore, only in 1806, when the Kingdom of Holland was a puppet state of the First French Empire, was the settlement granted city rights by Louis Bonaparte. After the Napoleonic Wars, modern-day Belgium and the Netherlands were combined in the United Kingdom of the Netherlands to form a buffer against France, as a compromise, Brussels and Amsterdam alternated as capital every two years, with the government remaining in The Hague. After the separation of Belgium in 1830, Amsterdam remained the capital of the Netherlands, when the government started to play a more prominent role in Dutch society after 1850, The Hague quickly expanded. The growing city annexed the rural municipality of Loosduinen partly in 1903, the city sustained heavy damage during World War II
The Hague
The Hague
The Hague
The Hague
6.
Dutch Republic
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It preceded the Batavian Republic, the Kingdom of Holland, the United Kingdom of the Netherlands, and ultimately the modern Kingdom of the Netherlands. Alternative names include the United Provinces, Seven Provinces, Federated Dutch Provinces, most of the Low Countries had come under the rule of the House of Burgundy and subsequently the House of Habsburg. In 1549 Holy Roman Emperor Charles V issued the Pragmatic Sanction, Charles was succeeded by his son, King Philip II of Spain. This was the start of the Eighty Years War, in 1579 a number of the northern provinces of the Low Countries signed the Union of Utrecht, in which they promised to support each other in their defence against the Spanish army. This was followed in 1581 by the Act of Abjuration, the declaration of independence of the provinces from Philip II. In 1582 the United Provinces invited Francis, Duke of Anjou to lead them, but after an attempt to take Antwerp in 1583. After the assassination of William of Orange, both Henry III of France and Elizabeth I of England declined the offer of sovereignty, however, the latter agreed to turn the United Provinces into a protectorate of England, and sent the Earl of Leicester as governor-general. This was unsuccessful and in 1588 the provinces became a confederacy, the Union of Utrecht is regarded as the foundation of the Republic of the Seven United Provinces, which was not recognized by the Spanish Empire until the Peace of Westphalia in 1648. During the Anglo-French war, the territory was divided into groups, the Patriots, who were pro-French and pro-American and the Orangists. The Republic of the United Provinces faced a series of revolutions in 1783–1787. During this period, republican forces occupied several major Dutch cities, initially on the defence, the Orangist forces received aid from Prussian troops and retook the Netherlands in 1787. After the French Republic became the French Empire under Napoleon, the Batavian Republic was replaced by the Napoleonic Kingdom of Holland, the Netherlands regained independence from France in 1813. In the Anglo-Dutch Treaty of 1814 the names United Provinces of the Netherlands, on 16 March 1815, the son of stadtholder William V crowned himself King William I of the Netherlands. Between 1815 and 1890 the King of the Netherlands was also in a union the Grand Duke of the sovereign Grand Duchy of Luxembourg. After Belgium gained its independence in 1830, the state became known as the Kingdom of the Netherlands. The County of Holland was the wealthiest and most urbanized region in the world, the free trade spirit of the time received a strong augmentation through the development of a modern, effective stock market in the Low Countries. The Netherlands has the oldest stock exchange in the world, founded in 1602 by the Dutch East India Company, while Rotterdam has the oldest bourse in the Netherlands, the worlds first stock exchange, that of the Dutch East-India Company, went public in six different cities. Later, a court ruled that the company had to reside legally in a city so Amsterdam is recognized as the oldest such institution based on modern trading principles
Dutch Republic
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Dutch East-India trading ship 1600
Dutch Republic
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Flag
Dutch Republic
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Onrust Island near
Batavia, 1699
Dutch Republic
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Courtyard of the Amsterdam Stock Exchange, 1653
7.
Leiden University
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Leiden University, located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, the Dutch Royal Family and Leiden University still have a close relationship, Queens Juliana and Beatrix and King Willem-Alexander are all former students. Leiden University has seven faculties, over 50 departments and enjoys an international reputation. Shanghai Jiao Tong Universitys 2011 Academic Ranking of World Universities ranked Leiden University as the 29th best university worldwide, the Times Higher Education World University Rankings consistently rank Leiden University as the best university in Continental Europe for Arts and Humanities. During this time Leiden was home to figures as René Descartes, Rembrandt, Christiaan Huygens, Hugo Grotius, Baruch Spinoza. The university is a member of the Coimbra Group, the Europaeum, Leiden University houses more than 40 national and international research institutes. In 1575, the emerging Dutch Republic did not have any universities in its northern heartland, the only other university in the Habsburg Netherlands was the University of Leuven in southern Leuven, firmly under Spanish control. It is said the choice fell on Leiden as a reward for the defence of Leiden against Spanish attacks in the previous year. Ironically, the name of Philip II of Spain, Williams adversary, appears on the foundation certificate. Philip II replied by forbidding any subject to study in Leiden, renowned philosopher Baruch Spinoza was based close to Leiden during this period and interacted with numerous scholars at the university. At the end of the century, Leiden University again became one of Europes leading universities. At the world’s first university low-temperature laboratory, professor Heike Kamerlingh Onnes achieved temperatures of one degree above absolute zero of −273 degrees Celsius. In 1908 he was also the first to succeed in liquifying helium, Kamerlingh Onnes was awarded the Nobel Prize for Physics in 1913. In 2005 the manuscript of Einstein on the theory of the monatomic ideal gas was discovered in one of Leidens libraries. Of the seventy-seven Spinozapremie, nineteen were granted to professors of the Universiteit Leiden, literary historian Frits van Oostrom was the first professor of Leiden to be granted the Spinoza award for his work on developing the NLCM centre into a top research centre. Among other leading professors are Wim Blockmans, professor of Medieval History, the portraits of many famous professors since the earliest days hang in the university aula, one of the most memorable places, as Niebuhr called it, in the history of science. The University Library, which has more than 5 and it houses the largest collections worldwide on Indonesia and the Caribbean. Scholars from all over the world visit Leiden University Library, the oldest in the Netherlands, the anatomical and pathological laboratories of the university are modern, and the museums of geology and mineralogy have been restored
Leiden University
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Leiden University
Leiden University
Leiden University
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The Leiden University Medical Centre
Leiden University
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Faculty of Law
8.
Titan (moon)
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Titan is the largest moon of Saturn. It is the only known to have a dense atmosphere. Titan is the sixth ellipsoidal moon from Saturn, frequently described as a planet-like moon, Titan is 50% larger than Earths Moon, and it is 80% more massive. It is the second-largest moon in the Solar System, after Jupiters moon Ganymede, and is larger than the smallest planet, Mercury, discovered in 1655 by the Dutch astronomer Christiaan Huygens, Titan was the first known moon of Saturn, and the sixth known planetary satellite. Titan orbits Saturn at 20 Saturn radii, from Titans surface, Saturn subtends an arc of 5.09 degrees and would appear 11.4 times larger in the sky than the Moon from Earth. Titan is primarily composed of ice and rocky material. The geologically young surface is smooth, with few impact craters, although mountains. The atmosphere of Titan is largely nitrogen, minor components lead to the formation of methane and ethane clouds and nitrogen-rich organic smog. The climate—including wind and rain—creates surface features similar to those of Earth, such as dunes, rivers, lakes, seas, and deltas, Huygens was inspired by Galileos discovery of Jupiters four largest moons in 1610 and his improvements in telescope technology. Christiaan, with the help of his brother Constantijn Huygens, Jr. began building telescopes around 1650 and it was the sixth moon to be discovered. He named it Saturni Luna, publishing in the 1655 tract De Saturni Luna Observatio Nova, after Giovanni Domenico Cassini published his discoveries of four more moons of Saturn between 1673 and 1686, astronomers fell into the habit of referring to these and Titan as Saturn I through V. Other early epithets for Titan include Saturns ordinary satellite, Titan is officially numbered Saturn VI because after the 1789 discoveries the numbering scheme was frozen to avoid causing any more confusion. Numerous small moons have been discovered closer to Saturn since then and he suggested the names of the mythological Titans, brothers and sisters of Cronus, the Greek Saturn. In Greek mythology, the Titans were a race of powerful deities, descendants of Gaia and Uranus, Titan orbits Saturn once every 15 days and 22 hours. Because of this, there is a point on its surface. Longitudes on Titan are measured westward, starting from the passing through this point. Its orbital eccentricity is 0.0288, and the plane is inclined 0.348 degrees relative to the Saturnian equator. Viewed from Earth, Titan reaches a distance of about 20 Saturn radii from Saturn
Titan (moon)
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Titan in natural color. The thick atmosphere is orange due to a dense
organonitrogen haze.
Titan (moon)
Titan (moon)
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Christiaan Huygens discovered Titan in 1655.
Titan (moon)
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Size comparison: Titan (lower left) with the Moon and Earth (top and right)
9.
Centrifugal force
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In Newtonian mechanics, the centrifugal force is an inertial force directed away from the axis of rotation that appears to act on all objects when viewed in a rotating reference frame. When they are analyzed in a coordinate system. The term has also been used for the force that is a reaction to a centripetal force. The centrifugal force is an outward force apparent in a reference frame. All measurements of position and velocity must be relative to some frame of reference. An inertial frame of reference is one that is not accelerating, the use of an inertial frame of reference, which will be the case for all elementary calculations, is often not explicitly stated but may generally be assumed unless stated otherwise. In terms of a frame of reference, the centrifugal force does not exist. All calculations can be performed using only Newtons laws of motion, in its current usage the term centrifugal force has no meaning in an inertial frame. In an inertial frame, an object that has no acting on it travels in a straight line. When measurements are made with respect to a reference frame, however. If it is desired to apply Newtons laws in the frame, it is necessary to introduce new, fictitious. Consider a stone being whirled round on a string, in a horizontal plane, the only real force acting on the stone in the horizontal plane is the tension in the string. There are no forces acting on the stone so there is a net force on the stone in the horizontal plane. In an inertial frame of reference, were it not for this net force acting on the stone, in order to keep the stone moving in a circular path, this force, known as the centripetal force, must be continuously applied to the stone. As soon as it is removed the stone moves in a straight line, in this inertial frame, the concept of centrifugal force is not required as all motion can be properly described using only real forces and Newtons laws of motion. In a frame of reference rotating with the stone around the axis as the stone. However, the tension in the string is still acting on the stone, if Newtons laws were applied in their usual form, the stone would accelerate in the direction of the net applied force, towards the axis of rotation, which it does not do. With this new the net force on the stone is zero, with the addition of this extra inertial or fictitious force Newtons laws can be applied in the rotating frame as if it were an inertial frame
Centrifugal force
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The interface of two
immiscible liquids rotating around a vertical axis is an upward-opening circular paraboloid.
10.
Collision
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A collision or crash is an event in which two or more bodies exert forces on each other for a relatively short time. Some examples of interactions that scientists would consider collisions, An insect touches its antenna to the leaf of a plant. The antenna is said to collide with leaf, a cat walks delicately through the grass. Each contact that its paws make with the ground is a collision, each brush of its fur against a blade of grass is a collision. When a boxer throws a punch, his fist is said to collide with the opponents face, the magnitude of the velocity difference just before impact is called the closing speed. What distinguishes different types of collisions is whether they also conserve kinetic energy, the Line of impact is the line which is collinear to the common normal of the surfaces that are closest or in contact during impact. This is the line along which internal force of collision acts during impact, specifically, collisions can either be elastic, meaning they conserve both momentum and kinetic energy, or inelastic, meaning they conserve momentum but not kinetic energy. An inelastic collision is sometimes called a plastic collision. A “perfectly inelastic” collision is a case of inelastic collision in which the two bodies stick together after impact. The degree to which a collision is elastic or inelastic is quantified by the coefficient of restitution, a perfectly elastic collision has a coefficient of restitution of one, a perfectly inelastic collision has a coefficient of restitution of zero. In reality, any macroscopic collision between objects will convert some kinetic energy to internal energy and other forms of energy, so no large-scale impacts are perfectly elastic, however, some problems are sufficiently close to perfectly elastic that they can be approximated as such. In this case, the coefficient of restitution equals one, an inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Momentum is conserved in collisions, but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. In this case, coefficient of restitution does not equal one, collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic, collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the velocities in two-body collisions. In maritime law, it is desirable to distinguish between the situation of a vessel striking a moving object, and that of it striking a stationary object. The word allision is then used to mean the striking of a stationary object, relatively few problems involving collisions can be solved analytically, the remainder require numerical methods
Collision
11.
Pendulum clock
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A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is an oscillator, it swings back and forth in a precise time interval dependent on its length. From its invention in 1656 by Christiaan Huygens until the 1930s, Pendulum clocks must be stationary to operate, any motion or accelerations will affect the motion of the pendulum, causing inaccuracies, so other mechanisms must be used in portable timepieces. They are now mostly for their decorative and antique value. The pendulum clock was invented in 1656 by Dutch scientist and inventor Christiaan Huygens, Huygens contracted the construction of his clock designs to clockmaker Salomon Coster, who actually built the clock. Huygens was inspired by investigations of pendulums by Galileo Galilei beginning around 1602, Galileo discovered the key property that makes pendulums useful timekeepers, isochronism, which means that the period of swing of a pendulum is approximately the same for different sized swings. Galileo had the idea for a clock in 1637, which was partly constructed by his son in 1649. These early clocks, due to their verge escapements, had wide pendulum swings of up to 100°, clockmakers realization that only pendulums with small swings of a few degrees are isochronous motivated the invention of the anchor escapement around 1670, which reduced the pendulums swing to 4–6°. The anchor became the standard escapement used in pendulum clocks, in addition to increased accuracy, the anchors narrow pendulum swing allowed the clocks case to accommodate longer, slower pendulums, which needed less power and caused less wear on the movement. The seconds pendulum,0.994 m long, in which each swing takes one second, the long narrow clocks built around these pendulums, first made by William Clement around 1680, became known as grandfather clocks. The increased accuracy resulting from these developments caused the hand, previously rare. The 18th and 19th century wave of innovation that followed the invention of the pendulum brought many improvements to pendulum clocks. Observation that pendulum clocks slowed down in summer brought the realization that thermal expansion and contraction of the rod with changes in temperature was a source of error. This was solved by the invention of temperature-compensated pendulums, the pendulum by George Graham in 1721. With these improvements, by the mid-18th century precision pendulum clocks achieved accuracies of a few seconds per week, until the 19th century, clocks were handmade by individual craftsmen and were very expensive. The rich ornamentation of pendulum clocks of this period indicates their value as symbols of the wealthy. The clockmakers of each country and region in Europe developed their own distinctive styles, by the 19th century, factory production of clock parts gradually made pendulum clocks affordable by middle-class families. During the Industrial Revolution, daily life was organized around the pendulum clock
Pendulum clock
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Pendulum clock conceived by
Galileo Galilei around 1637. The earliest known pendulum clock design, it was never completed.
Pendulum clock
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Vienna regulator style pendulum wall clock
Pendulum clock
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A
lantern clock that has been converted to use a pendulum. To accommodate the wide pendulum swings caused by the
verge escapement, "wings" have been added on the sides
Pendulum clock
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Mantel clock (around 1800) by Julien Béliard,
Paris, maître horloger recorded on the rue Saint-Benôit and rue Pavée in 1777, still active in 1817, or Julien-Antoine Béliard, maître horloger in 1786, recorded on the rue de Hurepoix, 1787–1806.
12.
Wave theory
–
In physics, a wave is an oscillation accompanied by a transfer of energy that travels through a medium. Frequency refers to the addition of time, wave motion transfers energy from one point to another, which displace particles of the transmission medium–that is, with little or no associated mass transport. Waves consist, instead, of oscillations or vibrations, around almost fixed locations, there are two main types of waves. Mechanical waves propagate through a medium, and the substance of this medium is deformed, restoring forces then reverse the deformation. For example, sound waves propagate via air molecules colliding with their neighbors, when the molecules collide, they also bounce away from each other. This keeps the molecules from continuing to travel in the direction of the wave, the second main type, electromagnetic waves, do not require a medium. Instead, they consist of periodic oscillations of electrical and magnetic fields generated by charged particles. These types vary in wavelength, and include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, waves are described by a wave equation which sets out how the disturbance proceeds over time. The mathematical form of this varies depending on the type of wave. Further, the behavior of particles in quantum mechanics are described by waves, in addition, gravitational waves also travel through space, which are a result of a vibration or movement in gravitational fields. While mechanical waves can be transverse and longitudinal, all electromagnetic waves are transverse in free space. A single, all-encompassing definition for the wave is not straightforward. A vibration can be defined as a back-and-forth motion around a reference value, however, a vibration is not necessarily a wave. An attempt to define the necessary and sufficient characteristics that qualify a phenomenon as a results in a blurred line. The term wave is often understood as referring to a transport of spatial disturbances that are generally not accompanied by a motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium and it may appear that the description of waves is closely related to their physical origin for each specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a rather than an electromagnetic wave transfer caused by vibration. Concepts such as mass, momentum, inertia, or elasticity and this difference in origin introduces certain wave characteristics particular to the properties of the medium involved
Wave theory
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Surface waves in
water
Wave theory
–
Wavelength λ, can be measured between any two corresponding points on a waveform
Wave theory
–
Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism
13.
Birefringence
–
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent, the birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress and this effect was first described by the Danish scientist Rasmus Bartholin in 1669, who observed it in calcite, a crystal having one of the strongest birefringences. A mathematical description of wave propagation in a birefringent medium is presented below, following is a qualitative explanation of the phenomenon. Thus rotating the material around this axis does not change its optical behavior and this special direction is known as the optic axis of the material. Light whose polarization is perpendicular to the axis is governed by a refractive index no. Light whose polarization is in the direction of the optic axis sees an optical index ne, for any ray direction there is a linear polarization direction perpendicular to the optic axis, and this is called an ordinary ray. The magnitude of the difference is quantified by the birefringence, Δ n = n e − n o, the propagation of the ordinary ray is simply described by no as if there were no birefringence involved. However the extraordinary ray, as its name suggests, propagates unlike any wave in an optical material. Its refraction at a surface can be using the effective refractive index. However it is in fact an inhomogeneous wave whose power flow is not exactly in the direction of the wave vector and this causes an additional shift in that beam, even when launched at normal incidence, as is popularly observed using a crystal of calcite as photographed above. Rotating the calcite crystal will cause one of the two images, that of the ray, to rotate slightly around that of the ordinary ray. When the light propagates either along or orthogonal to the optic axis, in the first case, both polarizations see the same effective refractive index, so there is no extraordinary ray. In the second case the extraordinary ray propagates at a different phase velocity but is not an inhomogeneous wave, for instance, a quarter-wave plate is commonly used to create circular polarization from a linearly polarized source. The case of so-called biaxial crystals is substantially more complex and these are characterized by three refractive indices corresponding to three principal axes of the crystal. For most ray directions, both polarizations would be classified as extraordinary rays but with different effective refractive indices, being extraordinary waves, however, the direction of power flow is not identical to the direction of the wave vector in either case. The two refractive indices can be determined using the index ellipsoids for given directions of the polarization, note that for biaxial crystals the index ellipsoid will not be an ellipsoid of revolution but is described by three unequal principle refractive indices nα, nβ and nγ. Thus there is no axis around which a rotation leaves the optical properties invariant, for this reason, birefringent materials with three distinct refractive indices are called biaxial
Birefringence
–
A
calcite crystal laid upon a graph paper with blue lines showing the double refraction
Birefringence
–
Incoming light in the parallel (s) polarization sees a different effective
index of refraction than light in the perpendicular (p) polarization, and is thus
refracted at a different angle.
Birefringence
–
Urate crystals, with the crystals with their long axis seen as horizontal in this view being parallel to that of a red compensator filter. These appear as yellow, and are thereby of negative birefringence.
Birefringence
–
Color pattern of a plastic box with "frozen in"
mechanical stress placed between two crossed
polarizers.
14.
Huygenian eyepiece
–
An eyepiece, or ocular lens, is a type of lens that is attached to a variety of optical devices such as telescopes and microscopes. It is so named because it is usually the lens that is closest to the eye when someone looks through the device, the objective lens or mirror collects light and brings it to focus creating an image. The eyepiece is placed near the point of the objective to magnify this image. The amount of magnification depends on the length of the eyepiece. An eyepiece consists of several elements in a housing, with a barrel on one end. The barrel is shaped to fit in an opening of the instrument to which it is attached. The image can be focused by moving the eyepiece nearer and further from the objective, most instruments have a focusing mechanism to allow movement of the shaft in which the eyepiece is mounted, without needing to manipulate the eyepiece directly. The eyepieces of binoculars are usually mounted in the binoculars, causing them to have a pre-determined magnification. With telescopes and microscopes, however, eyepieces are usually interchangeable, by switching the eyepiece, the user can adjust what is viewed. For instance, eyepieces will often be interchanged to increase or decrease the magnification of a telescope, eyepieces also offer varying fields of view, and differing degrees of eye relief for the person who looks through them. Several properties of an eyepiece are likely to be of interest to a user of an optical instrument, eyepieces are optical systems where the entrance pupil is invariably located outside of the system. They must be designed for optimal performance for a distance to this entrance pupil. In a refracting astronomical telescope the entrance pupil is identical with the objective and this may be several feet distant from the eyepiece, whereas with a microscope eyepiece the entrance pupil is close to the back focal plane of the objective, mere inches from the eyepiece. Microscope eyepieces may be corrected differently from telescope eyepieces, however, elements are the individual lenses, which may come as simple lenses or singlets and cemented doublets or triplets. When lenses are cemented together in pairs or triples, the elements are called groups. The first eyepieces had only a lens element, which delivered highly distorted images. Two and three-element designs were invented soon after, and quickly became standard due to the image quality. Today, engineers assisted by computer-aided drafting software have designed eyepieces with seven or eight elements that deliver exceptionally large, internal reflections, sometimes called scatter, cause the light passing through an eyepiece to disperse and reduce the contrast of the image projected by the eyepiece
Huygenian eyepiece
–
A collection of different types of eyepieces.
Huygenian eyepiece
–
A 25 mm Kellner eyepiece
Huygenian eyepiece
–
Simulation of views through a telescope using different eyepieces. The center image uses an eyepiece of the same focal length as the one on the left, but has a wider apparent field of view giving a larger image that shows more area. The image on the right also has a shorter focal length, giving the same true field of view as the left image but at higher magnification.
Huygenian eyepiece
–
The Plössl, an eyepiece with a large apparent field of view
15.
31 equal temperament
–
In music,31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO, also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equal-sized steps. Play Each step represents a ratio of 31√2, or 38.71 cents. 31-ET is a good approximation of quarter-comma meantone temperament. More generally, it is a diatonic tuning in which the tempered perfect fifth is equal to 696.77 cents. In 1666, Lemme Rossi first proposed an equal temperament of this order, shortly thereafter, having discovered it independently, scientist Christiaan Huygens wrote about it also. Huygens not only realized this, he went farther and noted that 31-ET provides an excellent approximation of septimal, the composer Joel Mandelbaum used this tuning system specifically because of its good matches to the 7th and 11th partials in the harmonic series. The tuning has poor matches to both the 9,8 and 10,9 intervals, however, it has a match for the average of the two. Practically it is close to quarter-comma meantone. This tuning can be considered a meantone temperament, many chords of 31-ET are discussed in the article on septimal meantone temperament. Chords not discussed there include the neutral thirds triad, which might be written C–E–G, C–D–G or C–F–G, and the Orwell tetrad, usual chords like the major chord is rendered nicely in 31-ET because the third and the fifth are very well approximated. Also, it is possible to play chords and supermajor chords. It is also possible to render nicely the harmonic seventh chord, for example on C with C–E–G–A♯. The seventh here is different from stacking a fifth and a minor third and this difference cannot be made in 12-ET
31 equal temperament
–
Figure 1: 31-ET on the syntonic temperament’s tuning continuum at P5= 696.77 cents, from (Milne et al. 2007).
16.
Physics
–
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
–
Sir Isaac Newton (1643–1727), whose
laws of motion and
universal gravitation were major milestones in classical physics
Physics
–
Albert Einstein (1879–1955), whose work on the
photoelectric effect and the
theory of relativity led to a revolution in 20th century physics
17.
Mathematics
–
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
–
Euclid (holding
calipers), Greek mathematician, 3rd century BC, as imagined by
Raphael in this detail from
The School of Athens.
Mathematics
–
Greek mathematician
Pythagoras (c. 570 – c. 495 BC), commonly credited with discovering the
Pythagorean theorem
Mathematics
–
Leonardo Fibonacci, the
Italian mathematician who established the Hindu–Arabic numeral system to the Western World
Mathematics
–
Carl Friedrich Gauss, known as the prince of mathematicians
18.
Astronomy
–
Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics, physics, and chemistry, in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, moons, stars, galaxies, and comets, while the phenomena include supernovae explosions, gamma ray bursts, more generally, all astronomical phenomena that originate outside Earths atmosphere are within the purview of astronomy. A related but distinct subject, physical cosmology, is concerned with the study of the Universe as a whole, Astronomy is the oldest of the natural sciences. The early civilizations in recorded history, such as the Babylonians, Greeks, Indians, Egyptians, Nubians, Iranians, Chinese, during the 20th century, the field of professional astronomy split into observational and theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain the results and observations being used to confirm theoretical results. Astronomy is one of the few sciences where amateurs can play an active role, especially in the discovery. Amateur astronomers have made and contributed to many important astronomical discoveries, Astronomy means law of the stars. Astronomy should not be confused with astrology, the system which claims that human affairs are correlated with the positions of celestial objects. Although the two share a common origin, they are now entirely distinct. Generally, either the term astronomy or astrophysics may be used to refer to this subject, however, since most modern astronomical research deals with subjects related to physics, modern astronomy could actually be called astrophysics. Few fields, such as astrometry, are purely astronomy rather than also astrophysics, some titles of the leading scientific journals in this field includeThe Astronomical Journal, The Astrophysical Journal and Astronomy and Astrophysics. In early times, astronomy only comprised the observation and predictions of the motions of objects visible to the naked eye, in some locations, early cultures assembled massive artifacts that possibly had some astronomical purpose. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye, most of early astronomy actually consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, and the nature of the Sun, Moon, the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the model of the Universe, or the Ptolemaic system. The Babylonians discovered that lunar eclipses recurred in a cycle known as a saros
Astronomy
–
A
star -forming region in the
Large Magellanic Cloud, an
irregular galaxy.
Astronomy
–
A giant
Hubble mosaic of the
Crab Nebula, a
supernova remnant
Astronomy
–
19th century
Sydney Observatory,
Australia (1873)
Astronomy
–
19th century
Quito Astronomical Observatory is located 12 minutes south of the
Equator in
Quito,
Ecuador.
19.
Horology
–
Horology is the art and/or science of measuring time. Ancient Sanskrit language has a similar word hora meaning hour and this word is also used as a measurement of time. Clocks, watches, clockwork, sundials, hourglasses, clepsydras, timers, time recorders, marine chronometers, people interested in horology are called horologists. That term is used both by people who deal professionally with timekeeping apparatus, as well as aficionados and scholars of horology, horology and horologists have numerous organizations, both professional associations and more scholarly societies. There are many museums and several specialized libraries devoted to the subject. One example is the Royal Greenwich Observatory, which is also the source of the Prime Meridian, one of the more comprehensive museums dedicated to horology is the Musée international dhorlogerie in La Chaux-de-Fonds. The Musée dHorlogerie du Locle is smaller but located nearby, one of the better horological museums in Germany is the Deutsches Uhrenmuseum in Furtwangen im Schwarzwald, in the Black Forest. The two leading specialised horological museums in North America are the National Watch and Clock Museum in Columbia, Pennsylvania, the eastern French city of Besançon has the Musée du Temps in the historic Palais Grenvelle. An example of a devoted to one particular type of clock is the Cuckooland Museum in the UK. One of the most comprehensive horological libraries open to the public is the National Watch, other good horological libraries providing public access are at the Musée international dhorlogerie in Switzerland, at the Deutsches Uhrenmuseum in Germany, and at the Guildhall Library in London. Another museum dedicated to clocks is the Willard House and Clock Museum in Grafton, Massachusetts. A
Horology
–
"Universal Clock" at the Clock Museum in
Zacatlán,
Puebla, Mexico
Horology
–
Key concepts
20.
Royal Society of London
–
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 of London
–
The entrance to the Royal Society in Carlton House Terrace, London
Royal Society of London
–
The President, Council, and Fellows of the Royal Society of London for Improving Natural Knowledge
Royal Society of London
–
John Evelyn, who helped to found the Royal Society
Royal Society of London
–
Mace granted by Charles II
21.
French Academy of Sciences
–
The French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the forefront of developments in Europe in the 17th and 18th centuries. Currently headed by Sébastien Candel, it is one of the five Academies of the Institut de France, the Academy of Sciences makes its origin to Colberts plan to create a general academy. He chose a group of scholars who met on 22 December 1666 in the Kings library. The first 30 years of the Academys existence were relatively informal, in contrast to its British counterpart, the Academy was founded as an organ of government. The Academy was expected to remain apolitical, and to avoid discussion of religious, on 20 January 1699, Louis XIV gave the Company its first rules. The Academy received the name of Royal Academy of Sciences and was installed in the Louvre in Paris, following this reform, the Academy began publishing a volume each year with information on all the work done by its members and obituaries for members who had died. This reform also codified the method by which members of the Academy could receive pensions for their work, on 8 August 1793, the National Convention abolished all the academies. Almost all the old members of the previously abolished Académie were formally re-elected, among the exceptions was Dominique, comte de Cassini, who refused to take his seat. In 1816, the again renamed Royal Academy of Sciences became autonomous, while forming part of the Institute of France, in the Second Republic, the name returned to Académie des sciences. During this period, the Academy was funded by and accountable to the Ministry of Public Instruction, the Academy came to control French patent laws in the course of the eighteenth century, acting as the liaison of artisans knowledge to the public domain. As a result, academicians dominated technological activities in France, the Academy proceedings were published under the name Comptes rendus de lAcadémie des sciences. The Comptes rendus is now a series with seven titles. The publications can be found on site of the French National Library, in 1818 the French Academy of Sciences launched a competition to explain the properties of light. The civil engineer Augustin-Jean Fresnel entered this competition by submitting a new theory of light. Siméon Denis Poisson, one of the members of the judging committee, being a supporter of the particle-theory of light, he looked for a way to disprove it. The Poisson spot is not easily observed in every-day situations, so it was natural for Poisson to interpret it as an absurd result. However, the head of the committee, Dominique-François-Jean Arago, and he molded a 2-mm metallic disk to a glass plate with wax
French Academy of Sciences
–
A heroic depiction of the activities of the Academy from 1698
French Academy of Sciences
–
Colbert Presenting the Members of the Royal Academy of Sciences to Louis XIV in 1667
French Academy of Sciences
–
The
Institut de France in Paris where the Academy is housed
22.
Galileo Galilei
–
Galileo Galilei was an Italian polymath, astronomer, physicist, engineer, philosopher, and mathematician. He played a role in the scientific revolution of the seventeenth century. Galileo also worked in applied science and technology, inventing an improved military compass, Galileos championing of heliocentrism and Copernicanism was controversial during his lifetime, when most subscribed to either geocentrism or the Tychonic system. He met with opposition from astronomers, who doubted heliocentrism because of the absence of a stellar parallax. He was tried by the Inquisition, found vehemently suspect of heresy and he spent the rest of his life under house arrest. He has been called the father of observational astronomy, the father of modern physics, the father of scientific method, and the father of science. Galileo was born in Pisa, Italy, on 15 February 1564, the first of six children of Vincenzo Galilei, a famous lutenist, composer, and music theorist, and Giulia, three of Galileos five siblings survived infancy. The youngest, Michelangelo, also became a noted lutenist and composer although he contributed to financial burdens during Galileos young adulthood, Michelangelo was unable to contribute his fair share of their fathers promised dowries to their brothers-in-law, who would later attempt to seek legal remedies for payments due. Michelangelo would also occasionally have to borrow funds from Galileo to support his musical endeavours and these financial burdens may have contributed to Galileos early fire to develop inventions that would bring him additional income. When Galileo Galilei was eight, his family moved to Florence and he then was educated in the Vallombrosa Abbey, about 30 km southeast of Florence. Galileo Bonaiuti was buried in the church, the Basilica of Santa Croce in Florence. It was common for mid-sixteenth century Tuscan families to name the eldest son after the parents surname, hence, Galileo Galilei was not necessarily named after his ancestor Galileo Bonaiuti. The Italian male given name Galileo derives from the Latin Galilaeus, meaning of Galilee, the biblical roots of Galileos name and surname were to become the subject of a famous pun. In 1614, during the Galileo affair, one of Galileos opponents, in it he made a point of quoting Acts 1,11, Ye men of Galilee, why stand ye gazing up into heaven. Despite being a genuinely pious Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba and they had two daughters, Virginia and Livia, and a son, Vincenzo. Their only worthy alternative was the religious life, both girls were accepted by the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia took the name Maria Celeste upon entering the convent and she died on 2 April 1634, and is buried with Galileo at the Basilica of Santa Croce, Florence. Livia took the name Sister Arcangela and was ill for most of her life, Vincenzo was later legitimised as the legal heir of Galileo and married Sestilia Bocchineri
Galileo Galilei
–
Portrait of Galileo Galilei by
Giusto Sustermans
Galileo Galilei
–
Galileo's beloved elder daughter, Virginia (
Sister Maria Celeste), was particularly devoted to her father. She is buried with him in his tomb in the
Basilica of Santa Croce, Florence.
Galileo Galilei
–
Galileo Galilei. Portrait by
Leoni
Galileo Galilei
–
Cristiano Banti 's 1857 painting Galileo facing the
Roman Inquisition
23.
Frans van Schooten
–
Franciscus van Schooten was a Dutch mathematician who is most known for popularizing the analytic geometry of René Descartes. Van Schootens father was a professor of mathematics at the University of Leiden, having Christiaan Huygens, Johann van Waveren Hudde, Van Schooten met Descartes in 1632 and read his Géométrie while it was still unpublished. Finding it hard to understand, he went to France to study the works of important mathematicians of his time, such as François Viète. When Frans van Schooten returned to his home in Leiden in 1646, he inherited his fathers position and one of his most important pupils, Huygens. Over the next decade he enlisted the aid of other mathematicians of the time, de Beaune, Hudde, Heuraet, de Witt and this edition and its extensive commentaries was far more influential than the 1649 edition. It was this edition that Gottfried Leibniz and Isaac Newton knew, Van Schooten was one of the first to suggest, in exercises published in 1657, that these ideas be extended to three-dimensional space. Van Schootens efforts also made Leiden the centre of the community for a short period in the middle of the seventeenth century. Some Contemporaries of Descartes, Fermat, Pascal and Huygens, Van Schooten, robertson, Edmund F. Frans van Schooten, MacTutor History of Mathematics archive, University of St Andrews. An e-textbook developed from Frans van Schooten 1646 by dbook
Frans van Schooten
–
Frans van Schooten
Frans van Schooten
–
Exercitationum mathematicarum libri, 1656-1657
24.
Gottfried Wilhelm Leibniz
–
Leibnizs notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and he became one of the most prolific inventors in the field of mechanical calculators. He also refined the number system, which is the foundation of virtually all digital computers. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th-century advocates of rationalism and he wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibnizs contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters and he wrote in several languages, but primarily in Latin, French, and German. There is no complete gathering of the writings of Leibniz in English, Gottfried Leibniz was born on July 1,1646, toward the end of the Thirty Years War, in Leipzig, Saxony, to Friedrich Leibniz and Catharina Schmuck. Friedrich noted in his journal,21. Juny am Sontag 1646 Ist mein Sohn Gottfried Wilhelm, post sextam vespertinam 1/4 uff 7 uhr abents zur welt gebohren, in English, On Sunday 21 June 1646, my son Gottfried Wilhelm is born into the world a quarter after six in the evening, in Aquarius. Leibniz was baptized on July 3 of that year at St. Nicholas Church, Leipzig and his father died when he was six and a half years old, and from that point on he was raised by his mother. Her teachings influenced Leibnizs philosophical thoughts in his later life, Leibnizs father had been a Professor of Moral Philosophy at the University of Leipzig, and the boy later inherited his fathers personal library. He was given access to it from the age of seven. Access to his fathers library, largely written in Latin, also led to his proficiency in the Latin language and he also composed 300 hexameters of Latin verse, in a single morning, for a special event at school at the age of 13. In April 1661 he enrolled in his fathers former university at age 15 and he defended his Disputatio Metaphysica de Principio Individui, which addressed the principle of individuation, on June 9,1663. Leibniz earned his masters degree in Philosophy on February 7,1664, after one year of legal studies, he was awarded his bachelors degree in Law on September 28,1665. His dissertation was titled De conditionibus, in early 1666, at age 19, Leibniz wrote his first book, De Arte Combinatoria, the first part of which was also his habilitation thesis in Philosophy, which he defended in March 1666. His next goal was to earn his license and Doctorate in Law, in 1666, the University of Leipzig turned down Leibnizs doctoral application and refused to grant him a Doctorate in Law, most likely due to his relative youth. Leibniz then enrolled in the University of Altdorf and quickly submitted a thesis, the title of his thesis was Disputatio Inauguralis de Casibus Perplexis in Jure. Leibniz earned his license to practice law and his Doctorate in Law in November 1666 and he next declined the offer of an academic appointment at Altdorf, saying that my thoughts were turned in an entirely different direction
Gottfried Wilhelm Leibniz
–
Portrait by
Christoph Bernhard Francke
Gottfried Wilhelm Leibniz
–
Engraving of Gottfried Wilhelm Leibniz
Gottfried Wilhelm Leibniz
–
Stepped Reckoner
Gottfried Wilhelm Leibniz
–
Leibniz's correspondence, papers and notes from 1669-1704,
National Library of Poland.
25.
Isaac Newton
–
His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. Newtons Principia formulated the laws of motion and universal gravitation that dominated scientists view of the universe for the next three centuries. Newtons work on light was collected in his influential book Opticks. He also formulated a law of cooling, made the first theoretical calculation of the speed of sound. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, politically and personally tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02. He was knighted by Queen Anne in 1705 and he spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint and his father, also named Isaac Newton, had died three months before. Born prematurely, he was a child, his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Newtons mother had three children from her second marriage. From the age of twelve until he was seventeen, Newton was educated at The Kings School, Grantham which taught Latin and Greek. He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, Henry Stokes, master at the Kings School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a bully, he became the top-ranked student. In June 1661, he was admitted to Trinity College, Cambridge and he started as a subsizar—paying his way by performing valets duties—until he was awarded a scholarship in 1664, which guaranteed him four more years until he would get his M. A. He set down in his notebook a series of Quaestiones about mechanical philosophy as he found it, in 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton had obtained his B. A. degree in August 1665, in April 1667, he returned to Cambridge and in October was elected as a fellow of Trinity. Fellows were required to become ordained priests, although this was not enforced in the restoration years, however, by 1675 the issue could not be avoided and by then his unconventional views stood in the way. Nevertheless, Newton managed to avoid it by means of a special permission from Charles II. A and he was elected a Fellow of the Royal Society in 1672. Newtons work has been said to distinctly advance every branch of mathematics then studied and his work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newtons mathematical papers
Isaac Newton
–
Portrait of Isaac Newton in 1689 (age 46) by
Godfrey Kneller
Isaac Newton
–
Newton in a 1702 portrait by
Godfrey Kneller
Isaac Newton
–
Isaac Newton (Bolton, Sarah K. Famous Men of Science. NY: Thomas Y. Crowell & Co., 1889)
Isaac Newton
–
Replica of Newton's second
Reflecting telescope that he presented to the
Royal Society in 1672
26.
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.
27.
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
28.
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
29.
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
30.
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.
31.
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
32.
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
33.
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.
34.
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
35.
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
36.
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.
37.
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
38.
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.
39.
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.
40.
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)
41.
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
42.
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.
43.
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
44.
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
45.
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.
46.
Momentum
–
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
–
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.
47.
Space
–
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
–
Gottfried Leibniz
Space
–
A right-handed three-dimensional
Cartesian coordinate system used to indicate positions in space.
Space
–
Isaac Newton
Space
–
Immanuel Kant
48.
Speed
–
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.
49.
Time
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Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is often referred to as the dimension, along with the three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems. Two contrasting viewpoints on time divide prominent philosophers, one view is that time is part of the fundamental structure of the universe—a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is referred to as Newtonian time. This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, Time in physics is unambiguously operationally defined as what a clock reads. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities, Time is used to define other quantities—such as velocity—so defining time in terms of such quantities would result in circularity of definition. The operational definition leaves aside the question there is something called time, apart from the counting activity just mentioned, that flows. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Furthermore, it may be there is a subjective component to time. Temporal measurement has occupied scientists and technologists, and was a motivation in navigation. Periodic events and periodic motion have long served as standards for units of time, examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is also of significant social importance, having economic value as well as value, due to an awareness of the limited time in each day. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day, increasingly, personal electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of an event as to hour or date is obtained by counting from a fiducial epoch—a central reference point. Artifacts from the Paleolithic suggest that the moon was used to time as early as 6,000 years ago. Lunar calendars were among the first to appear, either 12 or 13 lunar months, without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months
Time
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The flow of
sand in an
hourglass can be used to keep track of elapsed time. It also concretely represents the
present as being between the
past and the
future.
Time
Time
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Horizontal
sundial in
Taganrog
Time
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A contemporary
quartz watch