Informally, a physical quantity Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity. Being a fundamental term, quantity is used to refer to any type of quantitative properties or attributes of things is a physical property A physical property is any aspect of an object or substance that can be measured or perceived without changing its identity. Physical properties can be intensive or extensive. An intensive property does not depend on the size or amount of matter in the object, while an extensive property does. In addition to extensiveness, properties can also be that can be quantified A quantitative attribute is one that exists in a range of magnitudes, and can therefore be measured. Measurements of any particular quantitative property are expressed as a specific quantity, referred to as a unit, multiplied by a number. Examples of physical quantities are distance, mass, and time. Many attributes in the social sciences,. This means it can be measured and/or calculated and expressed in numbers. For example, "length Length is the long dimension of any object. Not to be confused with Depth which is the property of the object that appears to go away from the observer. The length of a thing is the distance between its ends, its linear extent as measured from end to end. This may be distinguished from height, which is vertical extent, and width or breadth, which" is a physical quantity that can be expressed by stating a number of some basic measurement unit such as metres The metre is the basic unit of length in the International System of Units (SI). Historically, the metre was defined by the French Academy of Sciences as the length between two marks on a platinum-iridium bar, which was designed to represent one ten-millionth of the distance from the Equator to the North Pole through Paris. In 1983, the metre was or inches An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. There are 36 inches in a yard and 12 inches in a foot. A corresponding unit of area is the square inch and a corresponding unit of volume is the cubic inch. The inch is usually the universal unit of measurement in, while "beauty Beauty is a characteristic of a person, animal, place, object, or idea that provides a perceptual experience of pleasure, meaning, or satisfaction.[citation needed] Beauty is studied as part of aesthetics, sociology, social psychology, and culture. An "ideal beauty" is an entity which is admired, or possesses features widely attributed" is a property that is difficult to describe with a number.
Formally, the International Vocabulary of Metrology', 3rd edition (VIM) defines quantity as:
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference[1]
Hence the value of a physical quantity Q is expressed as the product In the a mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied. The order in real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication. When matrices or members of various other associative algebras are multiplied the product of a numerical value A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels , {Q} and a unit of measurement The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Disparate systems of measurement used to be very common. Now there is a global standard, the International System of units, the modern form of the metric system. The SI has been or is in the process of [Q].
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- Q = {Q} x [Q]
The relationship between different physical quantities is described by quantity calculus Quantity calculus is the formal method for describing the mathematical relations between abstract physical quantities. Despite the name, it is more analogous to a system of algebra than calculus in the mathemtaical sense of the term. However, units refer to actual quantities, such as the cm, and are not algebraic symbols.
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Examples
If a person weighs 120 pounds The pound-force or simply pound is a unit of force, then "120" is the numerical value and "pound" is the unit. This physical quantity would be written as "120 lbs."
If the temperature outside is 30 degrees Celsius Celsius is a temperature scale that is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale two years before his death. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale as well as a unit to indicate a temperature interval (a difference between two temperatures, then "30" is the numerical value and "degree Celsius" is the unit. This quantity would be written as "30 °C".
In equation form, a measurement of power In physics, power is the rate at which work is performed or energy is converted. It is an energy per unit of time. As a rate of change of work done or the energy of a subsystem, power is, employing SI The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science units and scientific notation Scientific notation, also known as standard form or as exponential notation, is a way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is often favored by scientists, mathematicians and engineers, who work with such for the number, might be written as
- P = 42.3 x 103 W,
Here, P represents the physical quantity 'power', 42.3 x 103 is the numerical value {P}, and W is the symbol for the unit The International System of Units specifies a set of seven base units from which all other units of measurement are formed. These units are called SI derived units and are also considered part of the standard of power [P], the watt The watt is a derived unit of power in the International System of Units (SI). It measures rate of energy conversion. One watt is equivalent to 1 joule (J) of energy per second
Symbols for physical quantities
Usually, the symbols A symbol is something such as an object, picture, written word, sound, or particular mark that represents something else by association, resemblance, or convention. For example, a red octagon may be a symbol for "STOP". On maps, crossed sabres may indicate a battlefield. Numerals are symbols for numbers. All language consists of symbols for physical quantities are chosen to be a single letter of the Latin The Latin alphabet, also called the Roman alphabet, is the most widely used alphabetic writing system in the world today. It evolved from the western variety of the Greek alphabet called the Cumaean alphabet, which was borrowed and modified by the Etruscans who ruled early Rome, which alphabet was then adapted and further modified by the ancient or Greek alphabet The Greek alphabet is a set of twenty-four letters that has been used to write the Greek language since the late 9th or early 8th century BCE. It is the first and oldest alphabet in the narrow sense that it notes each vowel and consonant with a separate symbol. It is as such in continuous use to this day. The letters were also used to represent written in italic type. Often, the symbols are modified by subscripts A subscript or superscript is a number, figure, symbol, or indicator that appears smaller than the normal line of type and is set slightly below or above it – subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are perhaps best known for their use in formulas, mathematical expressions, and and superscripts A subscript or superscript is a number, figure, symbol, or indicator that appears smaller than the normal line of type and is set slightly below or above it – subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are perhaps best known for their use in formulas, mathematical expressions, and, in order to specify what they pertain to — for instance Ek is usually used to denote kinetic energy The kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Negative work of the same magnitude and cp heat capacity Thermal mass is the capacity of a body to store heat. It is typically measured in units of J/°C or J/K (which are equivalent). If the body consists of a homogeneous material with sufficiently known physical properties, the thermal mass is simply the amount of material present times the specific heat capacity of that material. For bodies made of at constant pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
Symbols for quantities should be chosen according to the international recommendations from ISO 31 International Standard ISO 31 is the most widely respected style guide for the use of physical quantities and units of measurement, and formulas involving them, in scientific and educational documents worldwide[citation needed]. In most countries, the notations used in mathematics and science textbooks at schools and universities follow closely, the IUPAP red book The International Union of Pure and Applied Physics is an international non-governmental organization devoted to the advancement of physics. It was established in 1922 and the first General Assembly was held in 1923 in Paris and the IUPAC green book. For example, the recommended symbol for the physical quantity 'mass' is m, and the recommended symbol for the quantity 'charge' is Q.
Units of physical quantities
Most physical quantities Q include a unit A unit of measurement is a definite amount of a physical quantity, defined and adopted by convention, that is used as a standard for measurement of the same physical quantity of any amount. A unit is given a universally recognised symbol that represents the definite amount of the physical quantity. For measurement, a pure number is written before [Q] (where [Q] means "unit of Q"). Neither the name of a physical quantity, nor the symbol used to denote it, implies a particular choice of unit. For example, a quantity of mass might be represented by the symbol m, and could be expressed in the units kilograms The kilogram is the base unit of mass in the International System of Units (SI, from the French Le Système International d’Unités).[Note 2] The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK),[Note 3] which is almost exactly equal to the mass of one liter of water. It is the only SI base unit with (kg), pounds The pound or pound-mass is a unit of mass used in the imperial, United States customary and other systems of measurement. A number of different definitions have been used, the most common today being the international avoirdupois pound of exactly 0.45359237 kilogram (lb), or Daltons The unified atomic mass unit or atomic mass unit , or dalton (Da) or, sometimes, universal mass unit (u), is a unit of mass used to express atomic and molecular masses. It is the approximate mass of a hydrogen atom, a proton, or a neutron (Da). SI The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science units A unit of measurement is a definite amount of a physical quantity, defined and adopted by convention, that is used as a standard for measurement of the same physical quantity of any amount. A unit is given a universally recognised symbol that represents the definite amount of the physical quantity. For measurement, a pure number is written before are usually preferred today.
Base quantities, derived quantities and dimensions
The notion of physical dimension In mathematics and science, dimensional analysis is a tool to understand the properties of physical quantities independent of the units used to measure them. Every physical quantity is some combination of mass, length, time, electric charge, and temperature, . For example, velocity, which may be measured in meters per second (m/s), miles per hour ( of a physical quantity was introduced by Fourier Jean Baptiste Joseph Fourier was a French mathematician and physicist best known for initiating the investigation of Fourier series and their application to problems of heat transfer. The Fourier transform and Fourier's Law are also named in his honour. Fourier is also generally credited with the discovery of the greenhouse effect in 1822.[2] By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension. The seven base quantities of the International System of Quantities The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science (ISQ) and their corresponding SI The International System of Units is the modern form of the metric system and is generally a system devised around the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science units are listed in the following table. Other conventions may have a different number of fundamental units A set of fundamental units is a set of units for physical quantities from which every other unit can be generated (e.g. the CGS The centimetre-gram-second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways of extending the CGS system to cover electromagnetism and MKS A physical system of units that expresses any given measurement using fundamental units of the metre, kilogram, and/or second systems of units).
All other quantities are derived quantities since their dimensions are derived from those of base quantities by multiplication and division. For example, the physical quantity velocity is derived from base quantities length and time and has dimension L/T. Some derived physical quantities have dimension 1 and are said to be dimensionless quantities.
Further information: dimensional analysisExtensive and intensive quantities
A quantity is called:
- extensive when its magnitude is additive for subsystems (volume, mass, etc.)
- intensive when the magnitude is independent of the extent of the system (temperature, pressure, etc.)
Some physical quantities are prefixed in order to further qualify their meaning:
- specific is added to refer to a quantity which is expressed per unit mass (such as specific heat capacity)
- molar is added to refer to a quantity which is expressed per unit amount of substance (such as molar volume)
There are also physical quantities that can be classified as neither extensive nor intensive, for example angular momentum, area, force, length, and time.
Physical quantities as coordinates over spaces of physical qualities
The meaning of the term physical quantity is generally well understood (everyone understands what is meant by the frequency of a periodic phenomenon, or the resistance of an electric wire). It is clear that behind a set of quantities like temperature − inverse temperature − logarithmic temperature, there is a qualitative notion: the cold−hot quality. Over this one-dimensional quality space, we may choose different coordinates: the temperature, the inverse temperature, etc. Other quality spaces are multidimensional. For instance, to represent the properties of an ideal elastic medium we need 21 coefficients, that can be the 21 components of the elastic stiffness tensor cijkl , or the 21 components of the elastic compliance tensor (inverse of the stiffness tensor), or the proper elements (six eigenvalues and 15 angles) of any of the two tensors, etc. Again, we are selecting coordinates over a 21-dimensional quality space. On this space, each point represents a particular elastic medium.
It is always possible to define the distance between two points of any quality space, and this distance is —inside a given theoretical context— uniquely defined. For instance, two periodic phenomena can be characterized by their periods, T1 and T2, or by their frequencies, ν1 and ν2 . The only definition of distance that respects some clearly defined invariances is D = | log(T2 / T1) | = | log(ν2 / ν1) | .
These notions have implications in physics. As soon as we accept that behind the usual physical quantities there are quality spaces, that usual quantities are only special coordinates over these quality spaces, and that there is a metric in each space, the following question arises: Can we do physics intrinsically, i.e., can we develop physics using directly the notion of physical quality, and of metric, and without using particular coordinates (i.e., without any particular choice of physical quantities)? In fact, physics can (and must?) be developed independently of any particular choice of coordinates over the quality spaces, i.e., independently of any particular choice of physical quantities to represent the measurable physical qualities.[3]
See also
Notes
- ^ Joint Committee for Guides in Metrology (JCGM), International Vocabulary of Metrology, Basic and General Concepts and Associated Terms (VIM), III ed., Pavillon de Breteuil : JCGM 200:2008, 1.1 (on-line)
- ^ Fourier, Joseph. Théorie analytique de la chaleur, Firmin Didot, Paris, 1822. (In this book, Fourier introduces the concept of physical dimensions for the physical quantities.)
- ^ Tarantola, Albert. Elements for physics - Quantities, qualities and intrinsic theories, Springer, 2006. ISBN 3-540-25302-5. [1]
References
- Cook, Alan H. The observational foundations of physics, Cambridge, 1994. ISBN 0-521-45597-
Categories: Physical quantities | Introductory physics
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