Etymology.

According to the "Oxford English Dictionary", the first known use of the word "computer" was in 1613 in a book called "The Yong Mans Gleanings" by English writer Richard Braithwait: "I haue [sic] read the truest computer of Times, and the best Arithmetician that euer [sic] breathed, and he reduceth thy dayes into a short number." This usage of the term referred to a human computer, a person who carried out calculations or computations. The word continued with the same

History.

Pre-20th century.

Devices have been used to aid computation for thousands of years, mostly using one-to-one correspondence with fingers. The earliest counting device was probably a form of tally stick. Later record keeping aids throughout the Fertile Crescent included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in hollow unbaked clay containers. The use of counting rods is one example.  The abacus was initially used for arithmetic tasks. The Roman abacus was developed from devices used in Babylonia as early as 2400 BC. Since then, many other forms of reckoning boards or tables have been invented. In a medieval European counting house, a checkered

First computing device.

Charles Babbage, an English mechanical engineer and polymath, originated the concept of a programmable computer. Considered the "father of the computer", he conceptualized and invented the first mechanical computer in the early 19th century. After working on his revolutionary difference engine, designed to aid in navigational calculations, in 1833 he realized that a much more general design, an Analytical Engine, was possible. The input of programs and data was to be provided to the machine via punched cards, a method being used at the time to direct mechanical looms such as the Jacquard loom. For output, the machine would have a printer, a curve plotter and a bell. The machine would also be

Analog computers.

During the first half of the 20th century, many scientific computing needs were met by increasingly sophisticated analog computers, which used a direct mechanical or electrical model of the problem as a basis for computation. However, these were not programmable and generally lacked the versatility and accuracy of modern digital computers. The first modern analog computer was a tide-predicting machine, invented by Sir William Thomson in 1872. The differential analyser, a mechanical analog computer designed to solve differential

Digital computers.

Electromechanical.

By 1938, the United States Navy had developed an electromechanical analog computer small enough to use aboard a submarine. This was the Torpedo Data Computer, which used trigonometry to solve the problem of firing a torpedo at a moving target. During World War II similar devices were developed in other countries as well. Early digital computers were electromechanical; electric switches drove mechanical relays to perform the calculation. These devices had a low operating speed and were eventually superseded by much faster all-electric computers, originally using vacuum tubes. The Z2, created by German engineer

Vacuum tubes and digital electronic circuits.

Purely electronic circuit elements soon replaced their mechanical and electromechanical equivalents, at the same time that digital calculation replaced analog. The engineer Tommy Flowers, working at the Post Office Research Station in London in the 1930s, began to explore the possible use of electronics for the telephone exchange. Experimental equipment that he built in 1934 went into operation five years later, converting a portion of the telephone exchange network into an electronic data processing system, using thousands of vacuum tubes. In the US, John Vincent Atanasoff and Clifford E. Berry of Iowa State University developed and tested the Atanasoff–Berry Computer (ABC) in 1942, the first "automatic electronic digital computer". This design was also all-electronic and used about 300 vacuum tubes, with capacitors fixed in a mechanically rotating drum for memory. During World War II, the British at Bletchley Park achieved a number of successes at breaking encrypted German military communications. The German encryption machine, Enigma, was first attacked with the help of the electro-mechanical bombes which were often run by women. To crack the more sophisticated German Lorenz SZ 40/42 machine, used for high-level Army communications, Max Newman and his colleagues commissioned Flowers to build the Colossus. He spent eleven months from early February 1943 designing and building the first Colossus. After a functional test in December 1943, Colossus was shipped to

Modern computers.

Concept of modern computer.

The principle of the modern computer was proposed by Alan Turing in his seminal 1936 paper, "On Computable Numbers". Turing proposed a simple device that he called "Universal Computing machine" and that is now known as a universal Turing machine. He proved that such a machine is capable of computing anything that is computable by executing instructions (program) stored on

Stored programs.

Early computing machines had fixed programs. Changing its function required the re-wiring and re-structuring of the machine. With the proposal of the stored-program computer this changed. A stored-program computer includes by design an instruction set and can store in memory a set of instructions (a program) that details the computation. The theoretical basis for the stored-program computer was laid by Alan Turing in his 1936 paper. In 1945, Turing joined the National Physical Laboratory and began work on developing an electronic stored-program digital computer. His 1945 report "Proposed Electronic Calculator" was the first specification for such a device. John von Neumann at the University of Pennsylvania also circulated his "First Draft of a Report on the EDVAC" in 1945.  The Manchester Baby was the world's first stored-program computer. It was built at the Victoria University of Manchester by Frederic

Transistors.

The concept of a field-effect transistor was proposed by Julius Edgar Lilienfeld in 1925. John Bardeen and Walter Brattain, while working under William Shockley at Bell Labs, built the first working transistor, the point-contact transistor, in 1947, which was followed by Shockley's bipolar junction transistor in 1948. From 1955 onwards, transistors replaced vacuum tubes in computer designs, giving rise to the "second generation" of computers. Compared to vacuum tubes, transistors have many advantages: they are smaller, and require less power than vacuum tubes, so give off less heat. Junction transistors were much more reliable than vacuum tubes and had longer, indefinite, service life. Transistorized computers could contain tens of thousands of binary logic circuits in a relatively compact space. However, early junction transistors were relatively bulky devices that were difficult to manufacture on a mass-production basis, which limited them to a number of specialised applications.  At the University of Manchester, a team under the leadership of Tom

Integrated circuits.

The next great advance in computing power came with the advent of the integrated circuit (IC). The idea of the integrated circuit was first conceived by a radar scientist working for the Royal Radar Establishment of the Ministry of Defence, Geoffrey W.A. Dummer. Dummer presented the first public description of an integrated circuit at the Symposium on Progress in Quality Electronic Components in Washington, D.C. on 7 May 1952.  The first working ICs were invented by Jack Kilby at Texas Instruments and Robert Noyce at Fairchild Semiconductor. Kilby recorded his initial ideas concerning the integrated circuit in July 1958, successfully demonstrating the first working integrated example on 12 September 1958. In his patent application of 6 February 1959, Kilby described his new device as "a body of semiconductor material... wherein all the components of the electronic circuit are completely integrated". However, Kilby's invention was a hybrid integrated circuit (hybrid IC), rather than a monolithic integrated circuit (IC) chip. Kilby's IC had external wire connections, which made it difficult to mass-produce.  Noyce also came up with his own idea of an integrated circuit half a year later than Kilby. Noyce's invention was the first true monolithic IC chip. His chip solved many practical problems that Kilby's had not. Produced at Fairchild Semiconductor, it was made of silicon, whereas Kilby's chip was made of germanium. Noyce's monolithic IC was fabricated using the planar process, developed by his colleague Jean Hoerni in early 1959. In turn, the planar process was based on the silicon surface passivation and thermal oxidation processes developed by Mohamed Atalla at Bell

Mobile computers.

The first mobile computers were heavy and ran from mains power. The 50lb IBM 5100 was an early example. Later portables such as the Osborne 1 and Compaq Portable were considerably lighter but still needed to be plugged in. The first laptops, such as the Grid Compass, removed this requirement by incorporating batteries –

Types.

Computers can be classified

Hardware.

The term "hardware" covers all of those parts of a computer that are tangible physical objects. Circuits, computer chips, graphic cards, sound cards, memory (RAM), motherboard, displays, power supplies, cables, keyboards, printers and "mice" input devices are all hardware.

Other hardware topics.

A general purpose computer has four main components: the arithmetic logic unit (ALU), the control unit, the memory, and the input and output devices (collectively termed I/O). These parts are interconnected by buses, often made of groups of wires. Inside each of these parts are thousands to trillions of

Input devices.

When unprocessed data is sent to the computer with the help of input devices, the data is processed and

Output devices.

The means through which computer gives output

Control unit.

The control unit (often called a control system or central controller) manages the computer's various components; it reads and interprets (decodes) the program instructions, transforming them into control signals that activate other parts of the computer. Control systems in advanced computers may change the order of execution of some instructions to improve performance.  A key component common to all CPUs is the program counter, a special memory cell (a register) that keeps track of which location in memory the next instruction is to be read from.  The control system's function is as follows—note that this is a simplified description,

Central processing unit (CPU).

The control unit, ALU, and registers are collectively known as a central processing unit (CPU). Early

Arithmetic logic unit (ALU).

The ALU is capable of performing two classes of operations: arithmetic and logic. The set of arithmetic operations that a particular ALU supports may be limited to addition and subtraction, or might include multiplication, division, trigonometry functions such as sine, cosine, etc., and square roots. Some can only operate on whole numbers (integers) while others use floating point to represent real numbers, albeit with limited precision. However, any computer that is capable of performing just the simplest operations can be programmed to break down the

Memory.

A computer's memory can be viewed as a list of cells into which numbers can be placed or read. Each cell has a numbered "address" and can store a single number. The computer can be instructed to "put the number 123 into the cell numbered 1357" or to "add the number that is in cell 1357 to the number that is in cell 2468 and put the answer into cell 1595." The information stored in memory may represent practically anything. Letters, numbers, even computer instructions can be placed into memory with equal

Input/output (I/O).

I/O is the means by which a computer exchanges information with the outside world. Devices that provide input or output to the computer are called peripherals. On a typical personal computer, peripherals include input devices like the keyboard and mouse, and output devices such as the display and printer. Hard disk drives, floppy disk

Multitasking.

While a computer may be viewed as running one gigantic program stored in its main memory, in some systems it is necessary to give the appearance of running several programs simultaneously. This is achieved by multitasking i.e. having the computer switch rapidly between running each program in turn. One means by which this is done is with a special signal called an interrupt, which can periodically cause the computer to stop executing instructions where it was and do something else instead. By remembering where it was executing prior to the interrupt, the computer can return to that task later. If several programs are running "at the same time". then the interrupt generator might be causing several hundred interrupts per second, causing a

Multiprocessing.

Some computers are designed to distribute their work across several CPUs in a multiprocessing configuration, a technique once employed only in large and powerful machines such as supercomputers, mainframe computers and servers. Multiprocessor and multi-core (multiple CPUs on a single integrated circuit) personal and laptop computers are now widely available, and are being increasingly used in lower-end markets

Software.

"Software" refers to parts of the computer which do not have a material form, such as programs, data, protocols, etc. Software is that part of a computer system that consists of encoded information or computer instructions, in contrast to the physical hardware from which the system is built. Computer software includes computer programs, libraries and related non-executable data, such as online documentation or digital media. It is often divided into system software and application software Computer hardware and software require each other and neither can be realistically used on its own. When software is stored in hardware that cannot easily be modified, such as with BIOS ROM in an IBM PC compatible computer, it is sometimes called "firmware".

Languages.

There are thousands of different programming languages—some intended

Programs.

The defining feature of modern computers which distinguishes them from all other machines is that they can be programmed. That is to say that some type of instructions (the program) can be given to the computer, and it will process them. Modern computers based on the von Neumann architecture often have machine code in the form of an imperative programming language. In practical terms, a computer program may be just a few instructions or extend to many millions of instructions, as do the programs for word processors and web browsers for example. A typical modern computer can execute billions of instructions per second (gigaflops) and rarely makes a mistake over many years of operation. Large computer programs consisting of several million instructions may take teams of programmers years to write, and due to the complexity of the task almost certainly contain errors.

Stored program architecture.

This section applies to most common RAM machine–based computers.  In most cases, computer instructions are simple: add one number to another, move some data from one location to another, send a message to some external device, etc. These instructions are read from the computer's memory and are generally carried out (executed) in the order they were given. However, there are usually specialized instructions to tell the computer to jump ahead or backwards to some other place in the program and to carry on executing from there. These are called "jump" instructions (or branches). Furthermore, jump instructions may be made to happen conditionally so that different sequences of instructions may be used depending on the result of some previous calculation or some external event. Many computers directly support subroutines by providing a type of jump that "remembers" the location it jumped from and another instruction to return to

Machine code.

In most computers, individual instructions are stored as machine code with each instruction being given a unique number (its operation code or opcode for short). The command to add two numbers together would have one opcode; the command to multiply them would have a different opcode, and so on. The simplest computers are able to perform any of a handful of different instructions; the more complex computers have several hundred to choose from, each with a unique numerical code. Since the computer's memory is able to store numbers, it can also store the instruction codes. This leads to the important fact that entire programs (which are just lists of these instructions) can be represented as lists of numbers and can themselves be manipulated inside the computer in the same

Programming language.

Programming languages provide various ways of specifying programs for computers to run. Unlike natural languages, programming languages are designed to permit no ambiguity and to be concise. They are purely written languages and are often difficult to read aloud. They are generally either translated into machine code by a compiler or an assembler before being run, or translated directly at run time by an interpreter. Sometimes programs are executed by a hybrid method of the two techniques.

Program design.

Program design of small programs is relatively simple and involves the analysis of the problem, collection of inputs, using the programming constructs within languages, devising or using established procedures and algorithms, providing data for output devices and solutions to the problem as applicable. As problems become larger and more

Bugs.

Errors in computer programs are called "bugs". They may be benign and not affect the usefulness of the program, or have only subtle effects. But in some cases, they may cause the program or the entire system to "hang", becoming unresponsive to input such as mouse clicks or keystrokes, to completely fail, or to crash. Otherwise benign bugs may sometimes be harnessed for malicious intent by an unscrupulous user writing an exploit, code designed to take advantage of a bug and disrupt a computer's proper execution. Bugs are usually not the fault of the computer. Since computers merely execute the instructions they are given, bugs are nearly always the result of programmer error or an oversight made in the program's design. Admiral Grace Hopper, an American computer scientist and developer of the first compiler, is credited for having first used the term "bugs" in computing after a dead moth was found shorting a relay in the Harvard Mark II computer in September 1947.

Networking and the Internet.

Computers have been used to coordinate information between multiple locations since the 1950s. The U.S. military's SAGE system was the first large-scale example of such a system, which led to a number of special-purpose commercial systems such as Sabre. In the 1970s, computer engineers at research institutions throughout the United States began to link their computers together using telecommunications technology. The effort was funded by ARPA (now DARPA), and the computer network that resulted was called the ARPANET. The technologies that made the Arpanet possible spread and evolved.  In time, the network spread beyond academic and military institutions and became known

Unconventional computers.

A computer does not need to be electronic, nor even have a processor, nor RAM, nor even a hard disk. While popular usage of the word "computer" is synonymous with a personal electronic

Future.

There is active research to make computers out of many promising new types of technology, such as optical computers, DNA computers, neural computers, and quantum computers. Most computers are universal, and are able to calculate any computable function, and are limited only by their memory capacity and operating speed. However different designs of computers can give very different performance for particular problems; for example quantum computers can potentially break some modern encryption algorithms (by quantum factoring) very quickly.

Computer architecture paradigms.

There are many types of computer architectures:  Of all these abstract machines, a quantum computer holds the most promise for revolutionizing computing. Logic gates are a common abstraction which can apply to most of the above digital or analog paradigms. The ability to store and execute

Artificial intelligence.

A computer will solve problems in exactly the way it is programmed to, without regard to efficiency, alternative solutions, possible shortcuts, or possible errors in the code. Computer programs that learn and adapt are part of the emerging field of artificial intelligence and machine

Professions and organizations.

As the use of computers has spread throughout society, there are an increasing number of careers involving computers. The need for computers to work well together and to be able to exchange information has spawned the need for many standards organizations, clubs and societies of both a formal and informal nature.

A computer is a machine that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming. Modern computers have the ability to follow generalized sets of operations, called "programs." These programs enable computers to perform an extremely wide range of tasks. A "complete" computer including the hardware, the operating system (main software), and peripheral equipment required and used for "full" operation can be referred to as a computer system. This term may as well be used for a group of computers that are connected and work together, in particular a computer network or computer cluster.

Počítač je v informatice zařízení a výpočetní technika, která zpracovává data pomocí předem vytvořeného programu. Současný počítač je elektronický a skládá se z hardwaru, který představuje fyzické části počítače (mikroprocesor, klávesnice, monitor atd.) a ze softwaru (operační systém a programy). Počítač je zpravidla ovládán uživatelem, který poskytuje počítači data ke zpracování prostřednictvím jeho vstupních zařízení a počítač výsledky prezentuje pomocí výstupních zařízení. V současnosti jsou počítače využívány téměř ve všech oborech lidské činnosti.


Introduction.

Centrifugal force is an outward force apparent in a rotating reference frame. It does not exist when a system is described relative to an inertial frame of reference.  All measurements of position and velocity must be made relative to some frame of reference. For example, an analysis of the motion of an object in an airliner in flight could be made relative to the airliner, to the surface of the Earth, or even to the Sun. A reference frame that is at rest (or one that moves with no rotation and at constant velocity) relative to the "fixed stars" is generally taken to be an inertial frame. Any system can be analyzed in an inertial frame (and so with no centrifugal force). However, it is often more convenient to describe a rotating system by using a rotating frame—the calculations are simpler, and descriptions more intuitive. When this choice is made, fictitious forces, including the centrifugal force, arise.  In a reference frame rotating about an axis through its origin, all objects, regardless of their state of motion, appear to be under the influence of a radially (from the axis of rotation) outward force that is proportional to their mass, to the distance from the axis of rotation of the frame, and to the square of the angular velocity of the frame. This is the centrifugal force. As humans usually experience centrifugal force from within the rotating reference frame, e.g. on a merry-go-round or vehicle, this is much more well-known than centripetal force.  Motion relative to a rotating frame results in another fictitious force: the Coriolis force. If the rate of rotation of the frame changes, a third fictitious force (the Euler force) is required. These fictitious forces are necessary for the formulation of correct equations of motion in a rotating reference frame and allow Newton's laws to be used in their normal form in such a frame (with one exception: the fictitious forces do not obey Newton's third law: they have no equal and opposite counterparts).

Examples.

Vehicle driving round a curve.

A common experience that gives rise to the idea of a centrifugal force is encountered by passengers riding in a vehicle, such as a car, that is changing direction. If a car is traveling at a constant speed along a straight road, then a passenger inside is not accelerating and, according to Newton's second law of motion, the net force acting on him is therefore zero (all forces acting on him cancel each other out). If the car enters a curve that bends to the left, the passenger experiences an apparent force that seems to be pulling him towards the right. This is the fictitious centrifugal force. It is needed within the passenger's local frame of reference to explain his sudden tendency to start accelerating to the right relative to the car—a tendency which he must resist by applying a rightward force to the car (for instance, a frictional force against the seat) in order to remain in a fixed position inside. Since he pushes the seat toward the right, Newton's third law says that the seat pushes him toward the left. The centrifugal force must be included in the passenger's reference frame (in which the passenger remains at rest): it counteracts the leftward force applied to the passenger by the seat, and explains why this otherwise unbalanced force does not cause him to accelerate. However, it would be apparent to a stationary observer watching from an overpass above that the frictional force exerted on the passenger by the seat is not being balanced; it constitutes a net force to the left, causing the passenger to accelerate toward the inside of the curve, as he must in order to keep moving with the car rather than proceeding in a straight line as he otherwise would. Thus the "centrifugal force" he feels is the result of a "centrifugal tendency" caused by inertia. Similar effects are encountered in aeroplanes and roller coasters where the magnitude of the apparent force is often reported in "G's".

Stone on a string.

If a stone is whirled round on a string, in a horizontal plane, the only real force acting on the stone in the horizontal plane is applied by the string (gravity acts vertically). There is a net force on the stone in the horizontal plane which acts toward the center.  In an inertial frame of reference, were it not for this net force acting on the stone, the stone would travel in a straight line, according to Newton's first law of motion. In order to keep the stone moving in a circular path, a centripetal force, in this case provided by the string, must be continuously applied to the stone. As soon as it is removed (for example if the string breaks) 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 Newton's laws of motion.  In a frame of reference rotating with the stone around the same axis as the stone, the stone is stationary. However, the force applied by the string is still acting on the stone. If one were to apply Newton's laws in their usual (inertial frame) form, one would conclude that the stone should accelerate in the direction of the net applied force—towards the axis of rotation—which it does not do. The centrifugal force and other fictitious forces must be included along with the real forces in order to apply Newton's laws of motion in the rotating frame.

Earth.

The Earth constitutes a rotating reference frame because it rotates once every 23 hours and 56 minutes around its axis. Because the rotation is slow, the fictitious forces it produces are often small, and in everyday situations can generally be neglected. Even in calculations requiring high precision, the centrifugal force is generally not explicitly included, but rather lumped in with the gravitational force: the strength and direction of the local "gravity" at any point on the Earth's surface is actually a combination of gravitational and centrifugal forces. However, the fictitious forces can be of arbitrary size. For example, in an Earth-bound reference system, the fictitious force (the net of Coriolis and centrifugal forces) is enormous and is responsible for the sun orbiting around the Earth (in the Earth-bound reference system). This is due to the large mass and velocity of the sun (relative to the Earth).

Weight of an object at the poles and on the equator.

If an object is weighed with a simple spring balance at one of the Earth's poles, there are two forces acting on the object: the Earth's gravity, which acts in a downward direction, and the equal and opposite restoring force in the spring, acting upward. Since the object is stationary and not accelerating, there is no net force acting on the object and the force from the spring is equal in magnitude to the force of gravity on the object. In this case, the balance shows the value of the force of gravity on the object.  When the same object is weighed on the equator, the same two real forces act upon the object. However, the object is moving in a circular path as the Earth rotates and therefore experiencing a centripetal acceleration. When considered in an inertial frame (that is to say, one that is not rotating with the Earth), the non-zero acceleration means that force of gravity will not balance with the force from the spring. In order to have a net centripetal force, the magnitude of the restoring force of the spring must be less than the magnitude of force of gravity. Less restoring force in the spring is reflected on the scale as less weight — about 0.3% less at the equator than at the poles. In the Earth reference frame (in which the object being weighed is at rest), the object does not appear to be accelerating, however the two real forces, gravity and the force from the spring, are the same magnitude and do not balance. The centrifugal force must be included to make the sum of the forces be zero to match the apparent lack of acceleration.

Equatorial railway.

This thought experiment is more complicated than the previous examples in that it requires the use of the Coriolis force as well as the centrifugal force.  If there were a railway line running round the Earth's equator, a train moving westward along it fast enough would remain stationary in a frame moving (but not rotating) with the Earth; it would stand still as the Earth spun beneath it. In this inertial frame the situation is easy to analyze. The only forces acting on the train (assuming no wind resistance or other horizontal forces) are its gravity (downward) and the equal and opposite (upward) force from the track. There is no net force on the train and it therefore remains stationary.  In a frame rotating with the Earth the train moves in a circular orbit as it travels round the Earth. In this frame, the upward reaction force from the track and the force of gravity on the train remain the same, as they are real forces. However, in the Earth's (rotating) frame, the train is traveling in a circular path and therefore requires a centripetal (downward) force to keep it on this path. Because this uses a rotating frame, the (fictitious) centrifugal force must be applied to the train. This is equal in value to the required centripetal force but acts in an upward direction — the opposite direction to that required. It would seem that there is a net upward force on the train and it should therefore accelerate upward.  The resolution to this paradox lies in the fact that the train is in motion with respect to the rotating frame and is subject to (in addition to the centrifugal force) the Coriolis force, which, in this example, acts in the downward direction and is twice as strong as the centrifugal force.

Derivation.

For the following formalism, the rotating frame of reference is regarded as a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame denoted the stationary frame.

Time derivatives in a rotating frame.

In a rotating frame of reference, the time derivatives of any vector function of time—such as the velocity and acceleration vectors of an object—will differ from its time derivatives in the stationary frame. If are the components of with respect to unit vectors directed along the axes of the rotating frame (i.e. ), then the first time derivative of with respect to the rotating frame is, by definition,. If the absolute angular velocity of the rotating frame is then the derivative of with respect to the stationary frame is related to by the equation:  where formula_1 denotes the vector cross product. In other words, the rate of change of in the stationary frame is the sum of its apparent rate of change in the rotating frame and a rate of rotation formula_2 attributable to the motion of the rotating frame. The vector has magnitude equal to the rate of rotation and is directed along the axis of rotation according to the right-hand rule.

Acceleration.

Newton's law of motion for a particle of mass "m" written in vector form is:  where is the vector sum of the physical forces applied to the particle and is the absolute acceleration (that is, acceleration in an inertial frame) of the particle, given by:  where is the position vector of the particle.  By applying the transformation above from the stationary to the rotating frame three times (twice to formula_5 and once to formula_6), the absolute acceleration of the particle can be written as:

Force.

The apparent acceleration in the rotating frame is. An observer unaware of the rotation would expect this to be zero in the absence of outside forces. However, Newton's laws of motion apply only in the inertial frame and describe dynamics in terms of the absolute acceleration. Therefore, the observer perceives the extra terms as contributions due to fictitious forces. These terms in the apparent acceleration are independent of mass; so it appears that each of these fictitious forces, like gravity, pulls on an object in proportion to its mass. When these forces are added, the equation of motion has the form:  From the perspective of the rotating frame, the additional force terms are experienced just like the real external forces and contribute to the apparent acceleration. The additional terms on the force side of the equation can be recognized as, reading from left to right, the Euler force formula_10, the Coriolis force formula_11, and the centrifugal force formula_12, respectively. Unlike the other two fictitious forces, the centrifugal force always points radially outward from the axis of rotation of the rotating frame, with magnitude, and unlike the Coriolis force in particular, it is independent of the motion of the particle in the rotating frame. As expected, for a non-rotating inertial frame of reference formula_13 the centrifugal force and all other fictitious forces disappear. Similarly, as the centrifugal force is proportional to the distance from object to the axis of rotation of the frame, the centrifugal force vanishes for objects that lie upon the axis.

Absolute rotation.

Three scenarios were suggested by Newton to answer the question of whether the absolute rotation of a local frame can be detected; that is, if an observer can decide whether an observed object is rotating or if the observer is rotating.  In these scenarios, the effects attributed to centrifugal force are only observed in the local frame (the frame in which the object is stationary) if the object is undergoing absolute rotation relative to an inertial frame. By contrast, in an inertial frame, the observed effects arise as a consequence of the inertia and the known forces without the need to introduce a centrifugal force. Based on this argument, the privileged frame, wherein the laws of physics take on the simplest form, is a stationary frame in which no fictitious forces need to be invoked.  Within this view of physics, any other phenomenon that is usually attributed to centrifugal force can be used to identify absolute rotation. For example, the oblateness of a sphere of freely flowing material is often explained in terms of centrifugal force. The oblate spheroid shape reflects, following Clairaut's theorem, the balance between containment by gravitational attraction and dispersal by centrifugal force. That the Earth is itself an oblate spheroid, bulging at the equator where the radial distance and hence the centrifugal force is larger, is taken as one of the evidences for its absolute rotation.

Applications.

The operations of numerous common rotating mechanical systems are most easily conceptualized in terms of centrifugal force. For example:  Nevertheless, all of these systems can also be described without requiring the concept of centrifugal force, in terms of motions and forces in a stationary frame, at the cost of taking somewhat more care in the consideration of forces and motions within the system.

History of conceptions of centrifugal and centripetal forces.

The conception of centrifugal force has evolved since the time of Huygens, Newton, Leibniz, and Hooke who expressed early conceptions of it. Its modern conception as a fictitious force arising in a rotating reference frame evolved in the eighteenth and nineteenth centuries.  Centrifugal force has also played a role in debates in classical mechanics about detection of absolute motion. Newton suggested two arguments to answer the question of whether absolute rotation can be detected: the rotating bucket argument, and the rotating spheres argument. According to Newton, in each scenario the centrifugal force would be observed in the object's local frame (the frame where the object is stationary) only if the frame were rotating with respect to absolute space. Nearly two centuries later, Mach's principle was proposed where, instead of absolute rotation, the motion of the distant stars relative to the local inertial frame gives rise through some (hypothetical) physical law to the centrifugal force and other inertia effects. Today's view is based upon the idea of an inertial frame of reference, which privileges observers for which the laws of physics take on their simplest form, and in particular, frames that do not use centrifugal forces in their equations of motion in order to describe motions correctly.  The analogy between centrifugal force (sometimes used to create artificial gravity) and gravitational forces led to the equivalence principle of general relativity.

Other uses of the term.

While the majority of the scientific literature uses the term "centrifugal force" to refer to the particular fictitious force that arises in rotating frames, there are a few limited instances in the literature of the term applied to other distinct physical concepts. One of these instances occurs in Lagrangian mechanics. Lagrangian mechanics formulates mechanics in terms of generalized coordinates {"q"}, which can be as simple as the usual polar coordinates formula_14 or a much more extensive list of variables. Within this formulation the motion is described in terms of "generalized forces", using in place of Newton's laws the Euler–Lagrange equations. Among the generalized forces, those involving the square of the time derivatives {(d"q" ⁄ "dt" )} are sometimes called centrifugal forces. In the case of motion in a central potential the Lagrangian centrifugal force has the same form as the fictitious centrifugal force derived in a co-rotating frame. However, the Lagrangian use of "centrifugal force" in other, more general cases has only a limited connection to the Newtonian definition.  In another instance the term refers to the reaction force to a centripetal force, or reactive centrifugal force. A body undergoing curved motion, such as circular motion, is accelerating toward a center at any particular point in time. This centripetal acceleration is provided by a centripetal force, which is exerted on the body in curved motion by some other body. In accordance with Newton's third law of motion, the body in curved motion exerts an equal and opposite force on the other body. This reactive force is exerted "by" the body in curved motion "on" the other body that provides the centripetal force and its direction is from that other body toward the body in curved motion. This reaction force is sometimes described as a "centrifugal inertial reaction", that is, a force that is centrifugally directed, which is a reactive force equal and opposite to the centripetal force that is curving the path of the mass.  The concept of the reactive centrifugal force is sometimes used in mechanics and engineering. It is sometimes referred to as just "centrifugal force" rather than as "reactive" centrifugal force although this usage is deprecated in elementary mechanics.

In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is parallel to the axis of rotation and passing through the coordinate system's origin. If the axis of rotation passes through the coordinate system's origin, the centrifugal force is directed radially outwards from that axis. The magnitude of centrifugal force "F" on an object of mass "m" at the distance "r" from the origin of a frame of reference rotating with angular velocity "ω" is: The concept of centrifugal force can be applied in rotating devices, such as centrifuges, centrifugal pumps, centrifugal governors, and centrifugal clutches, and in centrifugal railways, planetary orbits and banked curves, when they are analyzed in a rotating coordinate system. The term has sometimes also been used for the reactive centrifugal force that may be viewed as a reaction to a centripetal force in some circumstances.

Odstředivá síla (nebo také "centrifugální") je síla působící na těleso resp. hmotný bod směrem od středu křivosti trajektorie. V případě pohybu po kružnici jde o střed této kružnice. V obecnějším případě pohybu po hladké křivce jde o střed oskulační kružnice. Existují dva odlišné typy sil, které mají odstředivý směr. Prvním je reakce na dostředivou sílu v inerciální vztažné soustavě, což je síla "skutečná". Druhým typem je setrvačná odstředivá síla, kterou zavádíme v otáčející se vztažné soustavě, má charakter zdánlivé síly, a proto k ní neexistuje žádná reakce. Zaměňování těchto dvou druhů sil je běžné, ale nesprávné a často zavádějící.


History.

In a well-known but probably apocryphal tale, Archimedes was given the task of determining whether King Hiero's goldsmith was embezzling gold during the manufacture of a golden wreath dedicated to the gods and replacing it with another, cheaper alloy. Archimedes knew that the irregularly shaped wreath could be crushed into a cube whose volume could be calculated easily and compared with the mass; but the king did not approve of this. Baffled, Archimedes is said to have taken an immersion bath and observed from the rise of the water upon entering that he could calculate the volume of the gold wreath through the displacement of the water. Upon this discovery, he leapt from his bath and ran naked through the streets shouting, "Eureka! Eureka!" (Εύρηκα! Greek "I have found it"). As a result, the term "eureka" entered common parlance and is used today to indicate a moment of enlightenment.  The story first appeared in written form in Vitruvius' "books of architecture", two centuries after it supposedly took place. Some scholars have doubted the accuracy of this tale, saying among other things that the method would have required precise measurements that would have been difficult to make at the time.  From the equation for density ("ρ" = "m"/"V"), mass density has units of mass divided by volume. As there are many units of mass and volume covering many different magnitudes there are a large number of units for mass density in use. The SI unit of kilogram per cubic metre (kg/m) and the cgs unit of gram per cubic centimetre (g/cm) are probably the most commonly used units for density. One g/cm is equal to 1000 kg/m. One cubic centimetre (abbreviation cc) is equal to one millilitre. In industry, other larger or smaller units of mass and or volume are often more practical and US customary units may be used. See below for a list of some of the most common units of density.

Measurement of density.

A number of techniques as well as standards exist for the measurement of density of materials. Such techniques include the use of a hydrometer (a buoyancy method for liquids), Hydrostatic balance (a buoyancy method for liquids and solids), immersed body method (a buoyancy method for liquids), pycnometer (liquids and solids), air comparison pycnometer (solids), oscillating densitometer (liquids), as well as pour and tap (solids). However, each individual method or technique measures different types of density (e.g. bulk density, skeletal density, etc.), and therefore it is necessary to have an understanding of the type of density being measured as well as the type of material in question.

Homogeneous materials.

The density at all points of a homogeneous object equals its total mass divided by its total volume. The mass is normally measured with a scale or balance; the volume may be measured directly (from the geometry of the object) or by the displacement of a fluid. To determine the density of a liquid or a gas, a hydrometer, a dasymeter or a Coriolis flow meter may be used, respectively. Similarly, hydrostatic weighing uses the displacement of water due to a submerged object to determine the density of the object.

Heterogeneous materials.

If the body is not homogeneous, then its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: formula_2, where formula_3 is an elementary volume at position formula_4. The mass of the body then can be expressed as

Non-compact materials.

In practice, bulk materials such as sugar, sand, or snow contain voids. Many materials exist in nature as flakes, pellets, or granules.  Voids are regions which contain something other than the considered material. Commonly the void is air, but it could also be vacuum, liquid, solid, or a different gas or gaseous mixture.  The bulk volume of a material—inclusive of the void fraction—is often obtained by a simple measurement (e.g. with a calibrated measuring cup) or geometrically from known dimensions.  Mass divided by "bulk" volume determines bulk density. This is not the same thing as volumetric mass density.  To determine volumetric mass density, one must first discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For the close-packing of equal spheres the non-void fraction can be at most about 74%. It can also be determined empirically. Some bulk materials, however, such as sand, have a "variable" void fraction which depends on how the material is agitated or poured. It might be loose or compact, with more or less air space depending on handling.  In practice, the void fraction is not necessarily air, or even gaseous. In the case of sand, it could be water, which can be advantageous for measurement as the void fraction for sand saturated in water—once any air bubbles are thoroughly driven out—is potentially more consistent than dry sand measured with an air void.  In the case of non-compact materials, one must also take care in determining the mass of the material sample. If the material is under pressure (commonly ambient air pressure at the earth's surface) the determination of mass from a measured sample weight might need to account for buoyancy effects due to the density of the void constituent, depending on how the measurement was conducted. In the case of dry sand, sand is so much denser than air that the buoyancy effect is commonly neglected (less than one part in one thousand).  Mass change upon displacing one void material with another while maintaining constant volume can be used to estimate the void fraction, if the difference in density of the two voids materials is reliably known.

Changes of density.

In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures.  The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10 bar (1 bar = 0.1 MPa) and a typical thermal expansivity is 10 K. This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires a temperature increase on the order of thousands of degrees Celsius.  In contrast, the density of gases is strongly affected by pressure. The density of an ideal gas is  where is the molar mass, is the pressure, is the universal gas constant, and is the absolute temperature. This means that the density of an ideal gas can be doubled by doubling the pressure, or by halving the absolute temperature.  In the case of volumic thermal expansion at constant pressure and small intervals of temperature the temperature dependence of density is :  where formula_8 is the density at a reference temperature, formula_9 is the thermal expansion coefficient of the material at temperatures close to formula_10.

Density of solutions.

The density of a solution is the sum of mass (massic) concentrations of the components of that solution.  Mass (massic) concentration of each given component ρ in a solution sums to density of the solution.  Expressed as a function of the densities of pure components of the mixture and their volume participation, it allows the determination of excess molar volumes: provided that there is no interaction between the components.  Knowing the relation between excess volumes and activity coefficients of the components, one can determine the activity coefficients.

Common units.

The SI unit for density is:  The litre and metric tons are not part of the SI, but are acceptable for use with it, leading to the following units:  Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m). Liquid water has a density of about 1 kg/dm, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm.  In US customary units density can be stated in:  Imperial units differing from the above (as the Imperial gallon and bushel differ from the US units) in practice are rarely used, though found in older documents. The Imperial gallon was based on the concept that an Imperial fluid ounce of water would have a mass of one Avoirdupois ounce, and indeed 1 g/cm ≈ 1.00224129 ounces per Imperial fluid ounce = 10.0224129 pounds per Imperial gallon. The density of precious metals could conceivably be based on Troy ounces and pounds, a possible cause of confusion.

The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its mass per unit volume. The symbol most often used for density is "ρ" (the lower case Greek letter rho), although the Latin letter "D" can also be used. Mathematically, density is defined as mass divided by volume:

Hustota představuje hodnotu dané veličiny vztažené k jednotkovému objemu (bývá také označována jako objemová hustota), jednotkovému obsahu plochy (pak se hovoří o plošné hustotě) nebo jednotkové délce (pak se hovoří o lineární hustotě). Hustota se také mění v závislosti na teplotě, tlaku a látkovém množství (viz stavová rovnice).


Early life.

Baghy was born into a theatrical family — his father was an actor, and his mother a stage prompter. He began learning Esperanto in 1911. He started work as an actor and theatre manager, but the First World War intervened and took him out of his home country for six years.  He was captured and made a prisoner of war in Siberia. It was during this time that he began to work for the Esperanto movement, writing poetry and teaching the language to his fellow inmates.

Literary works.

Books.

Baghy wrote two books on the subject of captivity in Siberia: "Viktimoj" (Victims, 1925), and "Sur Sanga Tero" (On Bloody Soil, 1933), republished together as a single volume in 1971. His satirical novel "Hura!" (Hooray!, 1930) was somewhat less of a success. Its sequel "Insulo de Espero" (Island of Hope) was lost during the war.  His most famous novel "Printempo en Aŭtuno" (Spring in Autumn) was written in 1931.

Poetry.

It is however for his poetry that Baghy is best known. His first poems were written during his time of captivity in Siberia. Hitherto those poets, such as Zamenhof, who had written in Esperanto were limited by the still young language, and apart from Antoni Grabowski, no poet had managed to make a mark on the language.  Baghy's most significant collections of poems was his first: "Preter la Vivo" (Beyond Life, published in 1922). Among his more notable collection of poems are "Pilgrimo" (Pilgrim, 1926) and "Vagabondo Kantas" (The Vagabond Sings, 1933).  In 1966 he produced "Ĉielarko" (Rainbow), retelling in verse folk tales from twelve different nations. His last collection of poems, "Aŭtunaj folioj" (Autumn leaves), was published posthumously in 1970.

Esperanto movement.

Returning to Hungary after the war, he became one of the principal teachers of the Esperanto movement, organising newsgroups and literary evenings. In addition to working in his native Hungary, he organised courses in countries such as Estonia, Latvia, the Netherlands and France.  He was one of the principal writers for the Esperanto literary review "Literatura Mondo" until 1933.  His works reflect a slogan of his: "Amo kreas pacon, Paco konservas homecon, Homeco estas plej alta idealismo." (Love creates peace, Peace preserves humanity, Humanity is the highest ideal.)  Several of his works were granted awards by the Academy of Esperanto and a number of his novels have been translated into several languages.

Julio Baghy (13 January 1891, Szeged – 18 March 1967, Budapest; in Hungarian Baghy Gyula) was a Hungarian actor and one of the leading authors of the Esperanto movement. He is the author of several famous novels but it is particularly in the field of poetry that he proved his mastery of Esperanto.

Julio Baghy (13. ledna 1891, Segedín – 18. března 1967, Budapešť) byl maďarský herec, režisér a jeden z předních autorů esperantského hnutí. Je autorem několika novel, ale své mistrné zvládnutí esperanta dokázal především na poli poezie. Jeho verše jsou plné lyriky, humanismu a veselé nálady. Jeho první velkou básnickou sbírkou je "Preter la Vivo", z níž bylo mnoho básní zhudebněno.


Introduction.

The International System of Units, the SI, is a decimal and metric system of units established in 1960 and periodically updated since then. The SI has an official status in most countries, including the United States and the United Kingdom, with these two countries being amongst a handful of nations that, to various degrees, continue to resist widespread internal adoption of the SI system. As a consequence, the SI system “has been used around the world as the preferred system of units, the basic language for science, technology, industry and trade.”  The only other types of measurement system that still have widespread use across the world are the Imperial and US customary measurement systems, and they are legally defined in terms of the SI system. There are other, less widespread systems of measurement that are occasionally used in particular regions of the world. In addition, there are many individual non-SI units that don't belong to any comprehensive system of units, but that are nevertheless still regularly used in particular fields and regions. Both of these categories of unit are also typically defined legally in terms of SI units.

Controlling body.

The SI was established and is maintained by the General Conference on Weights and Measures (CGPM). In practice, the CGPM follows the recommendations of the Consultative Committee for Units (CCU), which is the actual body conducting technical deliberations concerning new scientific and technological developments related

Overview of the units.

SI base units.

The SI selects seven units to serve as base units, corresponding to seven base physical quantities. They are the second, with the symbol, which is the SI unit of the physical quantity of time; the metre, symbol, the SI unit of length; kilogram (, the unit

SI derived units.

The system allows for an unlimited number of additional units, called "derived units", which can always be represented as products of powers of the base units, possibly with a nontrivial numeric multiplier. When that multiplier is one, the unit is called a "coherent" derived unit.

SI metric prefixes and the decimal nature of the SI system.

Like all metric systems, the SI uses metric prefixes to systematically construct, for one and the same physical quantity, a whole set of units of widely different sizes that are decimal multiples of each other.  For example, while the coherent unit of length is the metre, the SI provides a full range of smaller and larger units of length, any of which may be more convenient for any given application – for example, driving distances are normally given in kilometres (symbol ) rather than in metres. Here the metric prefix ‘kilo-’ (symbol ‘k’) stands for a factor of 1000; thus, =.  The current version of the SI provides twenty metric prefixes that signify decimal powers ranging from

Coherent and non-coherent SI units.

When prefixes are used with the coherent SI units, the resulting units are no longer coherent, because the prefix introduces a numerical factor other than one. The one exception is the kilogram, the only coherent SI unit whose name and symbol, for historical reasons, include a prefix.  The complete set of SI units consists of both the coherent set and the multiples and sub-multiples of coherent units formed by using the SI prefixes. For example, the metre, kilometre, centimetre, nanometre, etc. are all SI units of length, though only the metre is a "coherent" SI unit. A similar statement holds for derived units: for example,,,, /, etc. are

Non-SI units accepted for use with SI.

There is a special group of units that are called ‘non-SI units that are accepted for use with the SI’ (see below for a complete list). Most of these, in order to be converted to the

New units.

Defining magnitudes of units.

Since 2019, the magnitudes of all SI units have been defined in an abstract way, which is conceptually separated from any practical realisation of them. Namely, the SI units are defined by declaring that seven "defining constants" have certain exact numerical values when expressed in terms of their SI units. Probably the most widely known of these constants is the speed of light in vacuum,, which in the SI by definition has the exact value of =. The other six constants are formula_1, the hyperfine transition frequency of caesium;, the Planck constant;, the elementary charge;, the Boltzmann constant;, the Avogadro constant; and, the luminous efficacy of monochromatic radiation of frequency.<br> </math>.}}}} The nature of the defining constants ranges from fundamental constants of nature such as to the purely technical constant.. Prior

Specifying fundamental constants vs. other methods of definition.

The current way of defining the SI system is the result of a decades-long move towards increasingly abstract and idealised formulation in which the realisations of the units are separated conceptually from the definitions.  The great advantage of doing it this way is that as science and technologies develop, new and superior realisations may be introduced without the need to redefine the units. Units can now be realised with ‘an accuracy that is ultimately limited only by the quantum structure of nature and our technical abilities but not by the definitions themselves. Any valid equation of physics relating the defining constants to a unit can be used to realise the unit, thus creating opportunities for innovation... with increasing accuracy as technology proceeds.’ In practice, the CIPM Consultative Committees provide so-called ""mises en pratique" (practical techniques), which are the descriptions of what are currently believed to be best experimental realisations of the units.  This system lacks the conceptual simplicity of using artefacts (referred to as "prototypes") as realisations of units to define those units: with prototypes, the definition and the

History.

The original motivation for the development of the SI was the diversity of units that had sprung up within the centimetre–gram–second (CGS) systems (specifically the inconsistency between the systems of electrostatic units and electromagnetic units) and the lack of coordination between the various disciplines that used them. The General Conference

Controlling authority.

The SI is regulated and continually developed by three international organisations that were established in 1875 under the terms of the Metre Convention. They are the General Conference on Weights and Measures (CGPM), the International Committee for Weights and Measures (CIPM), and the International Bureau of Weights and Measures (BIPM). The ultimate authority rests with the CGPM, which is a plenary body through which its Member States act together on matters related to measurement science and measurement standards; it usually convenes every four years. The CGPM elects the CIPM, which is an 18-person committee of eminent scientists. The CIPM operates based on the advice of a number of its Consultative Committees, which bring together the world's experts in their specified fields as advisers

Units and prefixes.

The International System of Units consists of a set of base units, derived units, and a set of decimal-based multipliers that are used as prefixes. The units, excluding prefixed units, form a coherent system of units, which is based on a system of quantities in such a way that the equations between the numerical values expressed in coherent units have exactly the same form, including numerical factors, as the corresponding equations between the quantities. For example, 1 N = 1 kg × 1 m/s says that "one" newton is the force required to accelerate a mass of "one" kilogram at "one" metre per second squared, as related through the principle of coherence to the equation relating the corresponding quantities:.  Derived units apply to derived quantities, which may by definition be expressed in terms of base quantities, and thus are not independent; for example, electrical conductance is the inverse of electrical resistance, with the consequence that the siemens is the inverse of the ohm, and similarly, the ohm and siemens can be replaced with a ratio of an ampere and a volt, because those quantities bear a defined relationship to each other. Other useful derived quantities can be specified in terms of the SI base and derived units that have no named units in the SI system, such as acceleration, which is defined in SI units as m/s.

Base units.

The SI base units are the building blocks

Derived units.

The derived units in the SI are formed by powers, products, or quotients of the base units and are potentially unlimited in number. Derived units are associated with derived quantities; for example, velocity is a quantity that is derived from the base quantities of time and length, and thus

Prefixes.

Prefixes are added to unit names to produce multiples and submultiples of the original unit. All of these are integer powers of ten, and above a hundred or below a hundredth all are integer powers of a thousand. For example, "kilo-" denotes a multiple of a thousand and "milli-" denotes a multiple of a thousandth, so there are one thousand

Non-SI units accepted for use with SI.

Many non-SI units continue to be used in the scientific, technical, and commercial literature. Some units are deeply embedded in history and culture, and their use has not been entirely replaced by their SI alternatives. The CIPM recognised and acknowledged such traditions by compiling a list of non-SI units accepted for use with SI:  Some units of time, angle, and legacy non-SI units have a long history of use. Most societies have used the

Common notions of the metric units.

The basic units of the metric system, as originally defined, represented common quantities or relationships in nature. They still do – the modern precisely

Lexicographic conventions.

Unit names.

The symbols for the SI units are intended to be identical, regardless of the language used, but names are ordinary nouns and use the character set and follow the grammatical rules of the language concerned. Names of units follow the grammatical rules associated with common nouns: in English and in French they start

Unit symbols and the values of quantities.

Although the writing of unit names is language-specific, the writing of unit symbols and the values of quantities is consistent across all languages and therefore the SI Brochure has specific rules in respect of writing them. The guideline produced by the National Institute of Standards and Technology (NIST) clarifies language-specific areas in respect of American English that were left open by the SI Brochure, but is otherwise identical to the SI Brochure.

General rules.

General rules for writing SI units and quantities

Printing SI symbols.

The rules covering printing of quantities and units are part of ISO 80000-1:2009.  Further rules are specified in respect of production of text using printing presses, word processors, typewriters, and the like.

International System of Quantities.

The quantities and equations that provide the context in which the SI units are defined are now referred to as the "International System of Quantities" (ISQ). The ISQ is based on the quantities underlying each of the seven base units of the SI. Other

Realisation of units.

Metrologists carefully distinguish between the definition of a unit and its realisation. The definition of each base unit of the SI is drawn up so that it is unique and provides a sound theoretical basis on which the most accurate and reproducible measurements can be made. The realisation of the definition of a unit is the procedure by which the definition may be used to establish the value and associated uncertainty of a

Evolution of the SI.

Changes to the SI.

The International Bureau of Weights and Measures (BIPM) has described SI as "the modern form of metric system". Changing technology has led to an evolution of the definitions and standards that has followed two principal strands – changes to SI itself, and clarification of how to use units of measure that are not part of SI but are still nevertheless used on a worldwide basis.  Since 1960 the CGPM has made a number of changes to the SI to meet the needs of specific fields, notably chemistry and radiometry. These are mostly additions to the list of named derived units, and include the "mole" (symbol mol) for an amount

2019 redefinitions.

After the metre was redefined in 1960, the International Prototype of the Kilogram (IPK) was the only physical artefact upon which base units (directly the kilogram and indirectly the ampere, mole and candela) depended for their definition, making these units subject to periodic comparisons of national standard kilograms with the IPK. During the 2nd and 3rd Periodic Verification of National Prototypes of the Kilogram, a significant divergence had occurred between the mass of the

History.

The improvisation of units.

The units and unit magnitudes of the metric system which became the SI were improvised piecemeal from everyday physical quantities starting in the mid-18th century. Only later were they moulded into an orthogonal coherent decimal system of measurement.  The degree centigrade as a unit of temperature resulted from the scale devised by Swedish astronomer Anders Celsius in 1742. His scale counter-intuitively designated 100 as the freezing point of water and 0 as the boiling point. Independently, in 1743, the French physicist Jean-Pierre Christin described a scale with 0 as the freezing point of water and 100 the boiling

Metre Convention.

A French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention, also called Treaty of the Metre, by 17 nations. Initially the convention only covered standards for the metre and the kilogram. In 1921, the Metre Convention was extended to include all physical units, including the ampere and others thereby enabling the CGPM to address inconsistencies in the way that the metric system had been

The CGS and MKS systems.

In the 1860s, James Clerk Maxwell, William Thomson (later Lord Kelvin) and others working under the auspices of the British Association for the Advancement of Science, built on Gauss's work and formalised the concept of a coherent system of units with base units and derived units christened the centimetre–gram–second system of units in 1874. The principle of coherence was successfully used to define a number of units of measure based on the CGS, including the erg for energy, the dyne for force, the barye for pressure, the poise for dynamic viscosity and the stokes for kinematic viscosity.  In 1879, the CIPM published recommendations for writing the symbols for length, area, volume and mass, but it was outside its domain to publish recommendations for other quantities. Beginning in about 1900, physicists who had been using the symbol "μ" (mu) for "micrometre" or "micron", "λ" (lambda) for "microlitre", and "γ" (gamma) for "microgram" started to use the symbols "μm", "μL" and "μg".  At the close of the 19th century three different systems of units

The "Practical system of units".

In 1948, the 9th CGPM commissioned a study to assess the measurement needs of the scientific, technical, and educational communities and "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention". This working document was "Practical system of units of measurement". Based on this study, the 10th CGPM in 1954 defined an international system derived from six

Birth of the SI.

In 1960, the 11th CGPM synthesised the results of the 12-year study into a

Historical definitions.

When Maxwell first introduced the concept of a coherent system, he identified three quantities that could be used as base units: mass, length, and time. Giorgi later identified the need for an electrical base unit, for which the unit of electric current was chosen for SI. Another three base units (for temperature, amount of substance, and luminous intensity) were added later.  The early metric systems defined a unit of weight as a base unit, while the SI defines an analogous unit of mass. In everyday use, these are mostly interchangeable, but in scientific contexts the difference matters. Mass, strictly the inertial mass, represents a quantity of matter.

Metric units that are not recognised by the SI.

Although the term "metric system" is often used as an informal alternative name for the International System of Units, other metric systems exist, some of which were in widespread use in the past or are even still used in particular areas. There are also individual metric units such as the sverdrup that exist outside of any system of units. Most of the units of the other metric systems are not recognised by the SI. Here are some examples. The centimetre–gram–second (CGS) system was the dominant metric system in the physical sciences and electrical engineering from the 1860s until at least the 1960s, and is still in use in some fields. It includes such SI-unrecognised units as the gal, dyne, erg, barye, etc. in its mechanical sector, as well as the poise and stokes in fluid dynamics. When it comes to the units for quantities in electricity and magnetism, there are several versions of the CGS system. Two of these are obsolete: the CGS electrostatic ('CGS-ESU', with the SI-unrecognised units of statcoulomb, statvolt, statampere, etc.) and the CGS electromagnetic system ('CGS-EMU', with abampere, abcoulomb, oersted, maxwell, abhenry, gilbert, etc.). A 'blend' of these two systems is still popular and is known as the Gaussian system (which includes the gauss as a special name for the CGS-EMU unit maxwell per square centimetre). In engineering (other than electrical engineering), there was formerly a long tradition of using the gravitational metric system, whose SI-unrecognised units include the kilogram-force (kilopond), technical atmosphere, metric horsepower, etc. The metre–tonne–second (mts) system, used in the Soviet Union from 1933 to 1955, had such SI-unrecognised units as the sthène, pièze, etc. Other groups of SI-unrecognised metric units are the various legacy and CGS units related to ionising radiation (rutherford, curie, roentgen, rad, rem, etc.), radiometry (langley, jansky), photometry (phot, nox, stilb, nit, metre-candle, lambert, apostilb, skot, brill, troland, talbot, candlepower, candle), thermodynamics (calorie), and spectroscopy (reciprocal centimetre). The angstrom is still used in various fields. Some other SI-unrecognised metric units that don't fit into any of the already mentioned categories include the are, bar, barn, fermi,<ref name="IEEE/ASTM SI 10-2016></ref> gradian (gon, grad, or grade), metric carat, micron, millimetre of mercury, torr, millimetre (or centimetre, or metre) of water, millimicron, mho, stere, x unit, (unit of mass), (unit of magnetic flux density), and (unit of volume). In some cases, the SI-unrecognised metric units have equivalent SI units formed by combining a metric prefix with a coherent SI unit. For example,,,, etc. (a related group are the correspondences such as ≘, ≘, etc.). Sometimes it is not even a matter of a metric prefix: the SI-nonrecognised unit may be exactly the same as an SI coherent unit, except for the fact that the SI does not recognise the special name and symbol. For example, the nit is just an SI-unrecognised name for the SI unit candela per square metre and the talbot is an SI-unrecognised name for the SI unit lumen second. Frequently, a non-SI metric unit is related to an SI unit through a power of ten factor, but not one that has a metric prefix, e.g. =, =, etc. (and correspondences like ≘ ). Finally, there are metric units whose conversion factors to SI units are not powers of ten, e.g. and. Some SI-unrecognised metric units are still frequently used, e.g. the calorie (in nutrition), the rem (in the U.S.), the jansky (in radio astronomy), the reciprocal centimetre (in spectroscopy), the gauss (in industry) and the CGS-Gaussian units more generally (in some subfields of physics), the metric horsepower (for engine power, in Europe), the kilogram-force (for rocket engine thrust, in China and sometimes in Europe), etc. Others are now rarely used, such as the sthène and the rutherford.

The International System of Units (SI, abbreviated from the French "") is the modern form of the metric system. It is the only system of measurement with an official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units, which are the second (the unit of time with the symbol s), metre (length, m), kilogram (mass, kg), ampere (electric current, A), kelvin (thermodynamic temperature, K), mole (amount of substance, mol), and candela (luminous intensity, cd). The system allows for an unlimited number of additional units, called derived units, which can always be represented as products of powers of the base units. Twenty-two derived units have been provided with special names and symbols. The seven base units and the 22 derived units with special names and symbols may be used in combination to express other derived units, which are adopted to facilitate measurement of diverse quantities. The SI system also provides twenty prefixes to the unit names and unit symbols that may be used when specifying power-of-ten (i.e. decimal) multiples and sub-multiples of SI units. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves.

Soustava SI (zkratka z francouzského "„Le Système International d'Unités“" – česky "„Mezinárodní systém jednotek“") je mezinárodně domluvená soustava jednotek fyzikálních veličin, která se skládá ze sedmi základních jednotek, na nich aritmeticky závisejících odvozených jednotek a dekadickými předponami tvořených násobků a dílů jednotek. Definice těchto jednotek a uchovávání případných etalonů garantuje Mezinárodní úřad pro míry a váhy v Sèvres (Francie).


History of atomic theory.

Atoms in philosophy.

The idea that matter is made up of discrete units is a very old idea, appearing in many ancient cultures such as

First evidence-based theory.

In the early 1800s, John Dalton compiled experimental data gathered by himself and other scientists and observed that chemical elements seemed to combine by mass in ratios of small whole numbers; he called this pattern the "law of multiple proportions". For instance, there are two types of tin oxide: one is 88.1% tin and 11.9% oxygen, and the other is 78.7% tin and 21.3% oxygen. This means that 100 g of tin will combine either with 13.5 g or 27 g of oxygen. 13.5 and 27 form a ratio of 1:2, a ratio of small whole numbers. Similarly, there are two common

Brownian motion.

In 1827, botanist Robert Brown used a microscope to look at dust grains floating in water and discovered that they moved about erratically, a phenomenon that became known as "Brownian motion". This was thought to be

Discovery of the electron.

In 1897, J.J. Thomson discovered that cathode rays are not electromagnetic waves but made of particles that are 1,800 times lighter than hydrogen (the lightest atom). Therefore, they were not atoms, but a new particle, the first "subatomic" particle to be discovered. He originally called these new

Discovery of the nucleus.

J.J. Thomson postulated that the negatively-charged electrons were distributed throughout the atom in a uniform sea of positive charge. This was known as the plum pudding model. In 1909, Hans Geiger and Ernest Marsden, working under the direction of Ernest Rutherford, bombarded metal foil with alpha particles to observe how they scattered. They expected all the alpha particles to pass straight

Discovery of isotopes.

While experimenting with the products of radioactive decay, in 1913 radiochemist Frederick Soddy discovered that there appeared to be more than one type of atom at each position on the

Bohr model.

In 1913 the physicist Niels Bohr proposed a model in which the electrons of an atom were assumed to orbit the nucleus but could only do so in a finite set of orbits, and could jump between these orbits only in discrete changes of energy corresponding to absorption or radiation of a photon. This quantization was used to explain why the electrons' orbits are stable (given that normally, charges in acceleration, including circular

Chemical bonding explained.

Chemical bonds between atoms were now explained, by Gilbert Newton Lewis in 1916, as the interactions between their constituent electrons. As the chemical properties of the elements were known to largely repeat

Further developments in quantum physics.

The Stern–Gerlach experiment of 1922 provided further evidence of the quantum nature of atomic properties. When a beam of silver atoms was passed through a specially shaped magnetic field, the beam was split in a way correlated with the direction of an atom's angular momentum, or spin. As this spin direction is initially random, the beam would be expected to deflect in a random direction. Instead, the beam was split into two directional components, corresponding to the atomic spin being oriented up or down with respect to the magnetic field.  In 1925 Werner Heisenberg published the first consistent mathematical formulation of quantum mechanics (matrix mechanics). One year earlier, Louis de Broglie had proposed the de

Discovery of the neutron.

The development of the mass spectrometer allowed the mass of atoms to be measured with increased accuracy. The device uses a magnet to bend the trajectory of a beam of ions, and the amount of deflection is determined by the ratio of an atom's mass to its charge. The chemist Francis

Fission, high-energy physics and condensed matter.

In 1938, the German chemist Otto Hahn, a student of Rutherford, directed neutrons onto uranium atoms expecting to get transuranium elements. Instead, his chemical experiments showed barium as a product. A year later, Lise Meitner and her nephew Otto Frisch verified that Hahn's result were the first experimental "nuclear fission". In 1944, Hahn received the Nobel prize

Structure.

Subatomic particles.

Though the word "atom" originally denoted a particle that cannot be cut into smaller particles, in modern scientific usage the atom is composed of various subatomic particles. The constituent particles of an atom are the electron, the proton and the neutron.  The electron is by far the least massive of these particles at, with a negative electrical charge and a size that is too small to be measured using available techniques. It was the lightest particle with a positive rest mass measured, until the discovery of neutrino mass. Under ordinary conditions, electrons are bound to the positively charged nucleus by the attraction created from opposite electric charges. If an atom has more or fewer electrons than its atomic number, then it becomes respectively negatively or positively charged as a whole; a charged atom is called an ion. Electrons have been known since the late 19th century, mostly thanks to J.J. Thomson; see history of subatomic physics for details.  Protons have a positive charge and a mass 1,836 times that of the electron, at. The number of protons in an atom is called

Nucleus.

All the bound protons and neutrons in an atom make up a tiny atomic nucleus, and are collectively called nucleons. The radius of a nucleus is approximately equal to 1.07 fm, where "A" is the total number of nucleons. This is much smaller than the radius of the atom, which is on the order of 10 fm. The nucleons are bound together by a short-ranged attractive potential called the residual strong force. At distances smaller than 2.5 fm this force is much more powerful than the electrostatic force that causes positively charged protons to repel each other.  Atoms of the same element have

Electron cloud.

The electrons in an atom are attracted to the protons in the nucleus by the electromagnetic force. This force binds the electrons inside an electrostatic potential well surrounding the smaller nucleus, which means that an external source of energy is needed for the electron to escape. The closer an electron is to the nucleus, the greater the attractive force. Hence electrons bound near the center of the potential well require more energy to escape than those at greater separations.  Electrons, like other particles, have properties of both a particle and a wave. The electron cloud is a region inside the potential well where each electron forms a type of three-dimensional standing wave—a wave form that does not move relative to the nucleus. This behavior is defined by an atomic orbital, a mathematical function that characterises the probability that an electron appears to be at a particular location when its position is measured. Only a discrete (or quantized) set of

Properties.

Nuclear properties.

By definition, any two atoms with an identical number of "protons" in their nuclei belong to the same chemical element. Atoms with equal numbers of protons but a different number of "neutrons" are different isotopes of the same element. For example, all hydrogen atoms admit exactly one proton, but isotopes exist with no neutrons (hydrogen-1, by far the most common form, also called protium), one neutron (deuterium), two neutrons (tritium) and more than two neutrons. The known elements form a set of atomic numbers, from the single proton element hydrogen up to the 118-proton element oganesson. All known isotopes of elements with atomic numbers greater than 82 are radioactive, although the radioactivity of element 83 (bismuth) is so slight as to be practically negligible.  About 339 nuclides occur naturally on Earth, of which 252 (about 74%) have not been observed to decay, and are referred to as "stable isotopes". Only 90 nuclides are stable theoretically, while another 162 (bringing the total to 252) have not been observed to decay, even though in theory it is energetically possible. These are also formally classified as "stable". An additional 34 radioactive nuclides have half-lives

Mass.

The large majority of an atom's mass comes from the protons and neutrons that make it up. The total number of these particles (called "nucleons") in a given atom is called the mass number. It is a positive integer and dimensionless (instead of having dimension of mass), because it expresses a count. An example of use of a mass number is "carbon-12," which has 12 nucleons (six protons and six neutrons).  The actual mass of an atom at rest is often expressed in daltons (Da), also called the unified atomic mass unit (u). This unit is defined as a twelfth of the mass of a free neutral atom of carbon-12, which is approximately. Hydrogen-1 (the lightest isotope of hydrogen which

Shape and size.

Atoms lack a well-defined outer boundary, so their dimensions are usually described in terms of an atomic radius. This is a measure of the distance out to which the electron cloud extends from the nucleus. This assumes the atom to exhibit a spherical shape, which is only obeyed for atoms in vacuum or free space. Atomic radii may be derived from the distances between two nuclei when the two atoms are joined in a chemical bond. The radius varies with the location of an atom on the atomic chart, the type of chemical bond, the number of neighboring atoms (coordination number) and a quantum mechanical property known as spin. On the periodic table of the elements, atom size tends to increase when moving down columns, but decrease when moving across rows (left to right). Consequently, the smallest atom is helium

Radioactive decay.

Every element has one or more isotopes that have unstable nuclei that are subject to radioactive decay, causing the nucleus to emit particles or electromagnetic radiation. Radioactivity can occur when the radius of a nucleus is large compared with the radius of the strong force, which only acts over distances on the order of 1 fm.  The most common forms of radioactive decay are:  Other more rare types of radioactive decay include ejection of neutrons or protons or clusters of nucleons from a nucleus, or

Magnetic moment.

Elementary particles possess an intrinsic quantum mechanical property known as spin. This is analogous to the angular momentum of an object that is spinning around its center of mass, although strictly speaking these particles are believed to be point-like and cannot be said to be rotating. Spin is measured in units of the reduced Planck constant (ħ), with electrons, protons and neutrons all having spin 1⁄2 ħ, or "spin-1⁄2". In an atom, electrons in motion around the nucleus possess orbital angular momentum in addition to their spin, while the nucleus itself possesses angular momentum due to its nuclear spin.  The magnetic field produced by an atom—its magnetic moment—is determined by these various forms of angular momentum, just as a rotating charged object classically produces a magnetic field, but the most dominant contribution comes from electron spin. Due to the nature of electrons to obey the Pauli exclusion principle, in which no two electrons may be found in the same quantum state, bound electrons

Energy levels.

The potential energy of an electron in an atom is negative, its dependence of its position reaches the minimum (the most absolute value) inside the nucleus, and vanishes when the distance from the nucleus goes to infinity, roughly in an inverse proportion to the distance. In the quantum-mechanical model, a bound electron can only occupy a set of states centered on the nucleus, and each state corresponds to a specific energy level; see time-independent Schrödinger equation for theoretical explanation. An energy level can be measured by the amount of energy needed to unbind the electron from the atom, and is usually given in units of electronvolts (eV). The lowest energy

Valence and bonding behavior.

Valency is the combining power of an element. It is equal to number of hydrogen atoms that atom can combine or displace in forming compounds. The outermost electron shell of an atom in its uncombined state is known as the valence shell, and the electrons in that shell are called valence electrons. The number of valence electrons determines the bonding behavior with other atoms. Atoms tend to chemically react with each other in a manner that fills (or empties) their outer valence shells. For example, a transfer of a single electron between atoms is a useful approximation for bonds that form between atoms with

States.

Quantities of atoms are found in different states of matter that depend on the physical conditions, such as temperature and pressure. By varying the conditions, materials can transition between solids, liquids, gases and plasmas. Within a state, a material can also exist in different allotropes. An example of this is

Identification.

The scanning tunneling microscope is a device for viewing surfaces at the atomic level. It uses the quantum tunneling phenomenon, which allows particles to pass through a barrier that would be insurmountable in the classical perspective. Electrons tunnel through the vacuum between two planar metal electrodes, on each of which is an adsorbed atom, providing a tunneling-current density that can be measured. Scanning one atom (taken as the tip) as it moves past the other (the sample) permits plotting of tip displacement versus lateral separation for a constant current. The calculation shows the extent to which scanning-tunneling-microscope images of an individual atom are visible. It confirms that for low bias, the microscope images the space-averaged dimensions of the electron orbitals across closely packed energy levels—the Fermi level local density of states.  An atom can be ionized by removing one of its electrons. The electric charge causes the trajectory of an atom

Origin and current state.

Baryonic matter forms about 4% of the total energy density of the observable Universe, with an average density of about 0.25 particles/m (mostly protons and electrons). Within a galaxy such as the Milky Way, particles have a much higher concentration, with the density of matter in the interstellar medium (ISM) ranging from 10 to 10 atoms/m. The Sun is believed to be inside the Local Bubble, so the density in the solar neighborhood is only about 10 atoms/m. Stars form from dense clouds in the ISM, and the evolutionary processes of stars result in the steady enrichment of the ISM with elements more massive than hydrogen and helium.  Up to 95% of the Milky Way's baryonic matter are concentrated inside stars, where conditions are unfavorable for atomic matter. The total baryonic mass is about 10% of the mass of the galaxy; the remainder of the mass is an unknown dark matter. High temperature inside stars makes most "atoms" fully ionized, that is, separates "all" electrons from the nuclei. In stellar remnants—with exception of their surface layers—an immense pressure make electron shells impossible.

Formation.

Electrons are thought to exist in the Universe since early stages of the Big Bang. Atomic nuclei forms in nucleosynthesis reactions. In about three minutes Big Bang nucleosynthesis produced most of the helium, lithium, and deuterium in the Universe, and perhaps some of the beryllium and boron.  Ubiquitousness and stability of atoms relies on their binding energy, which means that an atom has a lower energy than an unbound system of the nucleus and electrons. Where the temperature is much higher than ionization potential, the matter exists in the form of plasma—a gas of positively charged ions (possibly, bare nuclei) and electrons. When the temperature drops below the ionization potential, atoms become statistically

Earth.

Most of the atoms that make up the Earth and its inhabitants were present in their current form in the nebula that collapsed out of a molecular cloud to form the Solar System. The rest are the result of radioactive decay, and their relative proportion can be used to determine the age of the Earth through radiometric dating. Most of the helium in the crust of the Earth (about 99% of the helium from gas wells, as shown by its lower abundance of helium-3) is a product of alpha decay.  There are a few trace atoms on Earth that were not present at the beginning (i.e., not "primordial"), nor are results of radioactive decay. Carbon-14 is continuously generated by cosmic rays in the atmosphere.

Rare and theoretical forms.

Superheavy elements.

All nuclides with atomic numbers higher than 82 (lead) are known to be radioactive. No nuclide with an atomic number exceeding 92 (uranium) exists on Earth as a primordial nuclide, and heavier elements generally have shorter half-lives. Nevertheless, an "island of stability" encompassing relatively

Exotic matter.

Each particle of matter has a corresponding antimatter particle with the opposite electrical charge. Thus, the positron is a positively charged antielectron and the antiproton is a negatively charged equivalent of a proton. When a matter and corresponding antimatter particle meet, they annihilate each other. Because of this, along with an imbalance between the number of matter and antimatter particles, the latter are rare in the universe. The first causes of this imbalance are not yet fully understood, although theories of baryogenesis may offer an explanation. As a result, no antimatter atoms have been discovered in nature. In 1996 the antimatter counterpart of the hydrogen atom (antihydrogen) was synthesized at the CERN laboratory in Geneva.  Other exotic atoms have been created by replacing one of the protons, neutrons or electrons with other particles that have the same charge. For example, an electron can be replaced by a more massive muon, forming a muonic atom. These types of atoms can be used to test the fundamental predictions of physics.

An atom is the smallest constituent unit of ordinary matter that constitutes a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small, typically around 100 picometers across. They are so small that accurately predicting their behavior using classical physics – as if they were billiard balls, for example – is not possible due to quantum effects. Current atomic models use quantum principles to better explain and predict this behavior.

Atom (z řeckého ἄτομος, "átomos" – "nedělitelný") je nejmenší částice běžné hmoty, částice, kterou už chemickými prostředky dále nelze dělit (ovšem fyzikálními ano – viz např. jaderná reakce) a která definuje vlastnosti daného chemického prvku. Atom se skládá z atomového jádra obsahujícího protony a neutrony a obalu obsahujícího elektrony.