Stairs. Entry group. Materials. Doors. Locks. Design

• 1 General information
• 2 History
• 3 SI units
  • 3.1 Basic units
  • 3.2 Derived units
• 4 Non-SI units
• Consoles

General information

The SI system was adopted by the XI General Conference on Weights and Measures, and some subsequent conferences made a number of changes to the SI.

The SI system defines seven main And derivatives units of measurement, as well as a set of . Standard abbreviations for units of measurement and rules for recording derived units have been established.

In Russia, GOST 8.417-2002 is in force, which prescribes the mandatory use of SI. It lists the units of measurement, gives their Russian and international names and establishes the rules for their use. According to these rules, only international designations are allowed to be used in international documents and on instrument scales. In internal documents and publications, you can use either international or Russian designations (but not both at the same time).

Basic units: kilogram, meter, second, ampere, kelvin, mole and candela. Within the SI framework, these units are considered to have independent dimensions, that is, none of the basic units can be obtained from the others.

Derived units are obtained from the basic ones using algebraic operations such as multiplication and division. Some of the derived units in the SI System are given their own names.

Consoles can be used before names of units of measurement; they mean that a unit of measurement must be multiplied or divided by a certain integer, a power of 10. For example, the prefix “kilo” means multiplying by 1000 (kilometer = 1000 meters). SI prefixes are also called decimal prefixes.

Story

The SI system is based on the metric system of measures, which was created by French scientists and was first widely adopted after the French Revolution. Before the introduction of the metric system, units of measurement were chosen randomly and independently of each other. Therefore, conversion from one unit of measurement to another was difficult. In addition, different units of measurement were used in different places, sometimes with the same names. The metric system was supposed to become a convenient and uniform system of measures and weights.

In 1799, two standards were approved - for the unit of length (meter) and for the unit of weight (kilogram).

In 1874, the GHS system was introduced, based on three units of measurement - centimeter, gram and second. Decimal prefixes from micro to mega were also introduced.

In 1889, the 1st General Conference on Weights and Measures adopted a system of measures similar to the GHS, but based on the meter, kilogram and second, since these units were considered more convenient for practical use.

Subsequently, basic units were introduced for measuring physical quantities in the field of electricity and optics.

In 1960, the XI General Conference on Weights and Measures adopted a standard that was first called the International System of Units (SI).

In 1971, the IV General Conference on Weights and Measures amended the SI, adding, in particular, a unit for measuring the amount of a substance (mole).

SI is now accepted as the legal system of units of measurement by most countries in the world and is almost always used in the scientific field (even in countries that have not adopted SI).

SI units

There is no dot after the designations of SI units and their derivatives, unlike usual abbreviations.

Basic units

Magnitude	Unit		Designation
	Russian name	international name	Russian	international
Length	meter	meter (meter)	m	m
Weight	kilogram	kilogram	kg	kg
Time	second	second	With	s
Electric current strength	ampere	ampere	A	A
Thermodynamic temperature	kelvin	kelvin	TO	K
The power of light	candela	candela	cd	CD
Quantity of substance	mole	mole	mole	mol

Derived units

Derived units can be expressed in terms of base units using the mathematical operations of multiplication and division. Some of the derived units are given their own names for convenience; such units can also be used in mathematical expressions to form other derived units.

The mathematical expression for a derived unit of measurement follows from the physical law by which this unit of measurement is defined or the definition of the physical quantity for which it is introduced. For example, speed is the distance a body travels per unit time. Accordingly, the unit of measurement for speed is m/s (meter per second).

Often the same unit of measurement can be written in different ways, using a different set of base and derived units (see, for example, the last column in the table ). However, in practice, established (or simply generally accepted) expressions are used that best reflect the physical meaning of the quantity being measured. For example, to write the value of a moment of force, you should use N×m, and you should not use m×N or J.

Derived units with their own names

Magnitude	Unit		Designation		Expression
	Russian name	international name	Russian	international
Flat angle	radian	radian	glad	rad	m×m -1 = 1
Solid angle	steradian	steradian	Wed	sr	m 2 ×m -2 = 1
Temperature in Celsius	degrees Celsius	°C	degree Celsius	°C	K
Frequency	hertz	hertz	Hz	Hz	s -1
Force	newton	newton	N	N	kg×m/s 2
Energy	joule	joule	J	J	N×m = kg×m 2 /s 2
Power	watt	watt	W	W	J/s = kg × m 2 / s 3
Pressure	pascal	pascal	Pa	Pa	N/m 2 = kg? m -1 ? s 2
Light flow	lumen	lumen	lm	lm	kd×sr
Illumination	luxury	lux	OK	lx	lm/m 2 = cd×sr×m -2
Electric charge	pendant	coulomb	Cl	C	А×с
Potential difference	volt	volt	IN	V	J/C = kg×m 2 ×s -3 ×A -1
Resistance	ohm	ohm	Ohm	Ω	V/A = kg×m 2 ×s -3 ×A -2
Capacity	farad	farad	F	F	C/V = kg -1 ×m -2 ×s 4 ×A 2
Magnetic flux	weber	weber	Wb	Wb	kg×m 2 ×s -2 ×A -1
Magnetic induction	tesla	tesla	Tl	T	Wb/m 2 = kg × s -2 × A -1
Inductance	Henry	Henry	Gn	H	kg×m 2 ×s -2 ×A -2
Electrical conductivity	Siemens	siemens	Cm	S	Ohm -1 = kg -1 ×m -2 ×s 3 A 2
Radioactivity	becquerel	becquerel	Bk	Bq	s -1
Absorbed dose of ionizing radiation	Gray	gray	Gr	Gy	J/kg = m 2 / s 2
Effective dose of ionizing radiation	sievert	sievert	Sv	Sv	J/kg = m 2 / s 2
Catalyst activity	rolled	catal	cat	kat	mol×s -1

Units not included in the SI System

Some units of measurement not included in the SI System are, by decision of the General Conference on Weights and Measures, “allowed for use in conjunction with SI.”

Unit	International name	Designation		Value in SI units
		Russian	international
minute	minute	min	min	60 s
hour	hour	h	h	60 min = 3600 s
day	day	days	d	24 h = 86,400 s
degree	degree	°	°	(P/180) glad
arcminute	minute	′	′	(1/60)° = (P/10,800)
arcsecond	second	″	″	(1/60)′ = (P/648,000)
liter	liter (liter)	l	l, L	1 dm 3
ton	tons	T	t	1000 kg
neper	neper	Np	Np
white	bel	B	B
electron-volt	electronvolt	eV	eV	10 -19 J
atomic mass unit	unified atomic mass unit	A. eat.	u	=1.49597870691 -27 kg
astronomical unit	astronomical unit	A. e.	ua	10 11 m
nautical mile	nautical mile	mile		1852 m (exactly)
node	knot	bonds		1 nautical mile per hour = (1852/3600) m/s
ar	are	A	a	10 2 m 2
hectare	hectare	ha	ha	10 4 m 2
bar	bar	bar	bar	10 5 Pa
angstrom	ångström	Å	Å	10 -10 m
barn	barn	b	b	10 -28 m 2

System of units of physical quantities, a modern version of the metric system. SI is the most widely used system of units in the world, both in everyday life and in science and technology. SI is now accepted as the primary system of units by most countries in the world and is almost always used in engineering, even in countries where traditional units are used in everyday life. In these few countries (eg the US), the definitions of traditional units have been modified to relate them by fixed factors to the corresponding SI units.

The SI was adopted by the XI General Conference on Weights and Measures in 1960, and several subsequent conferences made a number of changes to the SI.

In 1971, the XIV General Conference on Weights and Measures amended the SI, adding, in particular, a unit of quantity of a substance (mole).

In 1979, the XVI General Conference on Weights and Measures adopted a new definition of the candela that is still in effect today.

In 1983, the XVII General Conference on Weights and Measures adopted a new definition of the meter that is still in effect today.

SI defines seven basic and derived units of physical quantities (hereinafter referred to as units), as well as a set of prefixes. Standard abbreviations for units and rules for recording derived units have been established.

Basic units: kilogram, meter, second, ampere, kelvin, mole and candela. Within the SI framework, these units are considered to have independent dimensions, that is, none of the basic units can be derived from the others.

Derived units are obtained from basic units using algebraic operations such as multiplication and division. Some of the SI derived units are given their own names, such as the radian.

Prefixes can be used before unit names; they mean that a unit must be multiplied or divided by a certain integer, a power of 10. For example, the prefix “kilo” means multiplied by 1000 (kilometer = 1000 meters). SI prefixes are also called decimal prefixes.

Many non-systemic units, such as, for example, ton, hour, liter and electron-volt are not included in the SI, but they are “allowed for use on a par with SI units.”

Seven basic units and the dependence of their definitions

Basic SI units

Unit	Designation	Magnitude	Definition	Historical Origins/Rationale
			A meter is the length of the path traveled by light in a vacuum in a time interval of 1/299,792,458 seconds. XVII General Conference on Weights and Measures (GCPM) (1983, Resolution 1)	1⁄10,000,000 of the distance from the Earth's equator to the north pole on the meridian of Paris.
Kilogram			The kilogram is a unit of mass equal to the mass of the international prototype of the kilogram. I GCPM (1899) and III GCPM (1901)	The mass of one cubic decimeter (liter) of pure water at a temperature of 4 C and standard atmospheric pressure at sea level.
			A second is a time equal to 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom. XIII CGPM (1967, Resolution 1) “At rest at 0 K in the absence of disturbance by external fields” (Added 1997)	The day is divided into 24 hours, each hour is divided into 60 minutes, each minute is divided into 60 seconds. A second is 1⁄(24 × 60 × 60) part of a day
		Electric current strength	An ampere is the force of an unchanging current which, when passing through two parallel straight conductors of infinite length and negligibly small circular cross-sectional area, located in a vacuum at a distance of 1 m from each other, would cause on each section of the conductor 1 m long an interaction force equal to 2 ·10 −7 newtons. International Committee of Weights and Measures (1946, Resolution 2, approved by the IX CGPM in 1948)
		Thermodynamic Temperature	Kelvin is a unit of thermodynamic temperature equal to 1/273.16 of the thermodynamic temperature of the triple point of water. XIII CGPM (1967, Resolution 4) In 2005, the International Committee of Weights and Measures established requirements for the isotopic composition of water when realizing the temperature of the triple point of water: 0.00015576 mol of 2H per mole of 1H, 0.0003799 mol of 17 O per mole of 16 O and 0.0020052 mol of 18 O per mole 16 O.	The Kelvin scale uses the same increments as the Celsius scale, but 0 Kelvin is the temperature of absolute zero, not the melting point of ice. According to the modern definition, the zero of the Celsius scale is set in such a way that the temperature of the triple point of water is equal to 0.01 C. As a result, the Celsius and Kelvin scales are shifted by 273.15 ° C = K - 273.15.
		Quantity of substance	A mole is the amount of substance in a system containing the same number of structural elements as there are atoms in carbon-12 weighing 0.012 kg. When using a mole, the structural elements must be specified and can be atoms, molecules, ions, electrons and other particles or specified groups of particles. XIV CGPM (1971, Resolution 3)
		The power of light	Candela is the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540·10 12 hertz, the energetic luminous intensity of which in this direction is (1/683) W/sr. XVI CGPM (1979, Resolution 3)

Magnitude		Unit
Name	Dimension	Name		Designation
		Russian	French/English	Russian	international
		kilogram	kilogramme/kilogram
Electric current strength
Thermodynamic temperature
Quantity of substance				mole
The power of light

Derived units with their own names

Magnitude	Unit		Designation		Expression
	Russian name	French/English title	Russian	international
Flat angle
Solid angle	steradian				m 2 m −2 = 1
Temperature in Celsius	degrees Celsius	degree Celsius/degree Celsius
					kg m s −2
					N m = kg m 2 s −2
Power					J/s = kg m 2 s −3
Pressure					N/m 2 = kg m −1 s −2
Light flow
Illumination					lm/m² = cd·sr/m²
Electric charge
Potential difference					J/C = kg m 2 s −3 A −1
Resistance					V/A = kg m 2 s −3 A −2
Electrical capacity					C/V = s 4 A 2 kg −1 m −2
Magnetic flux					kg m 2 s −2 A −1
Magnetic induction					Wb/m 2 = kg s −2 A −1
Inductance					kg m 2 s −2 A −2
Electrical conductivity					Ohm −1 = s 3 A 2 kg −1 m −2
Radioactive source activity	becquerel
Absorbed dose of ionizing radiation					J/kg = m²/s²
Effective dose of ionizing radiation					J/kg = m²/s²
Catalyst activity

Units not included in the SI, but by decision of the General Conference on Weights and Measures, are “allowed for use in conjunction with the SI.”

Unit	French/English title	Designation		Value in SI units
		Russian	international
				60 min = 3600 s
				24 h = 86,400 s
arcminute				(1/60)° = (π/10,800)
arcsecond				(1/60)′ = (π/648,000)
				dimensionless
				dimensionless
electron-volt				≈1.602 177 33·10 −19 J
atomic mass unit, dalton	unité de masse atomique unifiée, dalton/unified atomic mass unit, dalton			≈1.660 540 2 10 −27 kg
astronomical unit	unité astronomique/astronomical unit			149 597 870 700 m (exactly)
nautical mile	mille marin/nautical mile			1852 m (exactly)
				1 nautical mile per hour = (1852/3600) m/s
angstrom

Rules for writing unit symbols

Unit designations are printed in straight font; a dot is not placed after the designation as an abbreviation sign.

Designations are placed after the numerical values ​​of quantities separated by a space; transfer to another line is not allowed. Exceptions are notations in the form of a sign above a line; they are not preceded by a space. Examples: 10 m/s, 15°.

If the numeric value is a fraction with a slash, it is enclosed in parentheses, for example: (1/60) s −1.

When indicating the values ​​of quantities with maximum deviations, they are enclosed in brackets or a unit designation is placed behind the numerical value of the quantity and its maximum deviation: (100.0 ± 0.1) kg, 50 g ± 1 g.

The designations of units included in the product are separated by dots on the center line (N·m, Pa·s); it is not allowed to use the symbol “×” for this purpose. In typewritten texts, it is allowed not to raise the period or to separate symbols with spaces if this does not cause misunderstandings.

You can use a horizontal bar or a slash (only one) as a division sign in notation. When using a slash, if the denominator contains a product of units, it is enclosed in parentheses. Correct: W/(m·K), incorrect: W/m/K, W/m·K.

It is allowed to use unit designations in the form of a product of unit designations raised to powers (positive and negative): W m −2 K −1 , A m². When using negative powers, you must not use a horizontal bar or a slash (divide sign).

It is allowed to use combinations of special characters with letter designations, for example: °/s (degrees per second).

It is not allowed to combine designations and full names of units. Incorrect: km/h, correct: km/h.

Unit designations derived from surnames are written with capital letters, including those with SI prefixes, for example: ampere - A, megapascal - MPa, kilonewton - kN, gigahertz - GHz.

Units of physical quantities- specific physical quantities, conventionally accepted as units of physical quantities.

A physical quantity is understood as a characteristic of a physical object that is common to many objects in a qualitative sense (for example, length, mass, power) and individual for each object in a quantitative sense (for example, the length of a nerve fiber, human body weight, absorbed dose rate of ionizing radiation). There is a natural connection between the physical quantities that characterize any object. The establishment of this connection through the measurement of physical quantities was of great scientific and practical significance. The measurement of a physical quantity means a set of experimental (using measures and standards) and, in some cases, computational operations to determine the quantity of a given quantity. In this case, a justified rational choice of its unit is important.

The history of the development of metrology indicates that most of the old units of length, area, volume, mass, time and other quantities were chosen arbitrarily, without taking into account any internal connection between them. This led to the emergence in different countries of the world of many different units for measuring the same physical quantities. Thus, length was measured in arshins, elbows, feet, inches, mass - in ounces, pounds, spools, etc. In a number of cases, units were chosen based on the convenience of measurement technology or practical application. This is how, for example, a millimeter of mercury and horsepower appeared. The intensive and initially independent development of individual fields of science and technology in various countries at the beginning of the 19th century, the formation of new branches of knowledge contributed to the emergence of new physical quantities and, accordingly, many new units. The multiplicity of units of measurement was a serious obstacle to the further development of science and the growth of material production; The lack of unity in the understanding, definition and designation of physical quantities complicated international trade relations and hampered scientific and technological progress in general. All this caused the need for strict unification of units and the development of systems of units of physical quantities convenient for widespread use. The construction of such a system was based on the principle of selecting a small number of basic units, independent of each other, on the basis of which, with the help of mathematical relationships expressing natural connections between physical quantities, the remaining units of the system were established.

Attempts to create a unified system of units have been made repeatedly. The Metric system of measures, the ISS, ICSA, MKGSS, GHS, etc. systems were created. However, each of these systems individually did not provide the possibility of using it in all areas of scientific and practical human activity, and the parallel use of various systems created, among other inconveniences, certain difficulties in mutual recalculations. Various international scientific and technical organizations working in the field of metrology during the second half of the 19th century. and in the first half of the 20th century. prepared the way for the creation of a unified international system of units, and on October 7, 1958, the International Committee of Legal Metrology announced the establishment of this system.

By decision of the General Conference on Weights and Measures in 1960, a universal system of units of physical quantities was adopted. called "Systeme internationale d"unites" (International System of Units) or abbreviated SI (in Russian transcription SI). The CMEA Standing Commission on Standardization approved the fundamental standard "Metrology. Units of physical quantities. ST CMEA 1052-78", the author and developer of which is the USSR. The standard established mandatory application starting from 1979-1980 in the member countries of the CMEA International System of Units. By the Decree of the USSR State Committee on Standards of March 19, 1981, the CMEA standard was replaced by the State Standard GOST 8.417-81 (ST CMEA 1052- 78) “Units of physical quantities”, put into effect on January 1, 1982, GOST established a list of E. physical units for use in the USSR, their name and designation, as well as the procedure for using non-system units and excluding a number of non-system units subject to withdrawal The use of SI has become mandatory in all areas of science and technology, as well as in the national economy.

Structure of the International System of Units (SI). The International System of Units is a set of basic and derived units covering all areas of measurement of mechanical, thermal, electrical, magnetic and other quantities. An important advantage of this system is also that its constituent basic and derived units are convenient for practical purposes. The main advantage of SI is its coherence (consistency), i.e. all derived units in it are obtained using defining formulas (the so-called dimension formulas) by multiplying or dividing the basic units without introducing numerical coefficients showing how many times the value of the derived unit increases or decreases when the values ​​of the basic units change. for example, for a unit of speed it has the following form: v = kL×T-1~; Where k- proportionality coefficient equal to 1 , L- path length, T- time. If instead L And T Substitute the names of the units of measurement of length and time in the SI system, and we obtain the formula for the dimension of the unit of speed in this system: V = m/s, or v = m×s-1 . If a physical quantity is a ratio of two dimensional quantities of the same nature, then it has no dimension. Such dimensionless quantities are, for example, the refractive index, mass or volume fraction of a substance.

Units of physical quantities that are established independently of others and on which the system of units is based are called the basic units of the system. Units defined using formulas and equations that relate physical quantities to each other are called derived units of the system. Basic or derived units included in a system of units are called system units.

The International System of Units includes 7 main ones ( table 1 ), 2 additional ( table 2 ), as well as derived units formed from basic and additional units ( table 3 and 4 ). Additional units (radians and steradians) are independent of the basic units and have zero dimension. They are not used for direct measurements due to the lack of measuring instruments calibrated in radians and steradians. These units are used for theoretical research and calculations.

Table 1.

Basic SI units and the quantities they measure

Unit name	Designation		Measured quantity
	international
Kilogram
			Electric current strength
			Thermodynamic temperature*
		mole	Quantity of substance
			The power of light

* The name “Kelvin temperature” is also acceptable. In addition to the Kelvin temperature ( T) you can use Celsius temperature ( t), determined from the expression: t = T – T 0 Where T- thermodynamic temperature, T 0= 273.15 K. For a temperature difference of 1°C = 1 K.

Table 2.

Additional SI units and quantities they measure

Chapter 1

BASIC CONCEPTS AND DEFINITIONS

A Brief History of Metrology

In the course of human history, certain ideas about the sizes, shapes, and properties of objects and processes were developed, and in connection with this, various methods and means of measurement arose and developed.

Any object (object, process, phenomenon) can be characterized by its properties or qualities, which are manifested to a greater or lesser extent and, therefore, are subject to quantitative assessment. Currently, F. Engels’ statement “Every quality has infinitely many quantitative gradations” is well known. How is a quantitative assessment of these properties or qualities of an object made? Of course, by measurements.

In Russia in ancient times, the units of measurement of length were the span and the cubit. The cubit as a unit of measurement was used in many states (Babylon, Egypt). Naturally, the elbow size was different.

For a long time, one of the main measures of length in Russia was the sazhen (mentioned in the chronicles of the early 10th century). Its size was not constant: a simple fathom, an oblique fathom, a government fathom, etc. were known. By decree of Peter I, Russian length measures were agreed upon with English ones (~ 1725).

In 1835, Nicholas I, in his “Decree to the Government Senate,” approved the fathom as the main measure of length in Russia, and the standard pound was adopted as the basic unit of mass - a cubic inch of water at a temperature of 13.3 degrees according to Reaumur in airless space (a pound was equal to 409 ,51241 g). Also in Russia, arshin (0.7112 m) and verst were also used (at different times its size was different, 500 fathoms - 1.0668 km).

To maintain the unity of the established measures, there were reference (exemplary) measures that were located in temples and churches.

In 1841, in accordance with the decree “On the System of Russian Weights and Measures”, which legalized a number of measures of length, volume and weight, the Depot of Model Weights and Measures was organized at the St. Petersburg Mint - the first state verification institution. The main tasks of the Depot were storing standards, compiling tables of Russian and foreign measures, producing model measures and distributing the latter to the regions of the country. Verification of weights and measures was made the responsibility of city councils, councils and treasury chambers. In 1892, the great Russian scientist D.I. was appointed scientific keeper of the Depot of Exemplary Weights and Measures. Mendeleev. At his suggestion, the Depot was transformed in 1893 into the Main Chamber of Weights and Measures, which quickly became an outstanding scientific and methodological center. For comparison, we can say that in Germany the metrological center was founded in 1887, in England - in 1900, in the USA - in 1901.

“Science begins... from the moment they begin to measure,” in this scientific credo of D.I. Mendeleev expressed, in essence, the most important principle of the development of science, which has not lost its relevance in modern conditions.

DI. Mendeleev made a great practical and scientific contribution to the development of the science of measurements. In 1860, he developed a device for determining the density of liquids, called the Mendeleev pycnometer. In 1865 he created an original method of weighing at a constant load, eliminating temperature errors and is still used today. In 1875, he refined Euler's formula for calculating precision laboratory balances with maximum sensitivity. In 1873-1874 proposed, independently of Kelvin, a new temperature scale with “one experimentally realizable point.” In 1889, the “Regulations on Weights and Measures” were approved, in which the Russian standards of the arshin and pound were legalized and their exact correlations with metric measures were introduced. This Regulation allowed for the optional use in Russia of a progressive metrological system of measures, the implementation of which Mendeleev devoted a lot of effort.

Mendeleev was the first to speak from the rostrum of the congress of Russian natural scientists with a call to promote the preparation of the metric reform by using the metric system in scientific research, in lectures and lessons. Mendeleev said then; “Let us also facilitate in our humble field the possibility of universal dissemination of the metric system and through this we contribute to the common benefit and the future desired rapprochement of peoples. Not soon, little by little, but it will come. Let's go meet him."

Mendeleev's work laid a solid foundation for both the optional and subsequent mandatory implementation of the metric system of measures in our country. Russia officially switched to the metric system in September 1918.

In 1849, the first scientific and educational book by F.I. Petrushevsky “General metrology” (in two parts), according to which the first generations of Russian metrologists studied.

An important stage in the development of Russian metrology was the signing by Russia of the metric convention on May 20, 1875. In the same year, the International Organization of Weights and Measures (IOMV) was created, which was located in Sevres (near Paris, France). Russian scientists actively took part in the work of this organization.

Measurement objects

The usual objects of measurement are physical quantities, that is, any properties of a physical object (object, process), for example length, mass, time, temperature, etc. However, in the last decade, in addition to physical quantities, so-called non-physical disciplines have begun to be used in applied metrology. This is due to the use of the term “measurement” in economics, computer science, and quality management.

The infinite number of physical quantities that surround us has an infinite number of different qualities and properties. From this huge number, a person identifies a certain limited number of properties that are qualitatively common to a number of homogeneous objects and sufficient to describe them. In each such quality, in turn, many gradations can be distinguished. If we are able to establish the size of the gradation, that is, the magnitude of a given property, and physically implement it in the form of a measure or scale, then by comparing the size of the property of an object that interests us with such a measure or scale, we will obtain its quantitative assessment. Properties for which gradations of a certain size can be established and reproduced are called physical quantities.

In other words, physical quantity– one of the properties of a physical object (physical system, phenomenon or process) that is qualitatively common for many physical objects, but quantitatively individual for each of them.

The qualitative side of the concept “physical quantity” determines the type of quantity (length as a characteristic of extension in general, electrical resistance as a general property of electrical conductors, etc.), and the quantitative side – its size (the length of a specific object, the resistance of a specific conductor). The size of a physical quantity exists objectively, regardless of whether we know it or not.

Analysis of existing values ​​shows that they can be divided into two types: real and ideal (Fig. 2).

Unit name	Designation		Measured quantity
	international
	In the 50–60s of the XX century. Increasingly, the desire of many countries to create a single universal system of units that could become international was manifested. Among the general requirements for basic and derived units, the requirement of coherence of such a system of units was put forward. In 1954 The X General Conference on Weights and Measures established six basic units for international relations: meter, kilogram, second, ampere, Kelvin, candle. IN 1960 The XI General Conference on Weights and Measures approved International system of units, abbreviated S.I.(initial letters of the French name Systeme International d Unites), in Russian transcription - SI. As a result of some modifications adopted by the General Conferences on Weights and Measures in 1967, 1971, 1979, the system currently includes seven main units (Table 3.3.1). Table 3.3.1 Basic and additional units of physical quantities of the SI system Magnitude Unit Designation Name Dimension Recommended designation Name Russian international Length Basic L meter m m Weight M m kilogram kg kg Time T t second With s Electric current strength I I ampere A A Thermodynamic temperature Q T kelvin TO TO Quantity of substance N n, v mole mole mol The power of light J J candella cd CD Flat angle Additional - - radian glad rad Solid angle - - steradian Wed sr The SI system of units operates on the territory of our country. from January 1, 1982. in accordance with GOST 8.417–81. The SI system is a logical development of the previous systems of units GHS and MKGSS, etc. Definition and content of SI basic units. In accordance with the decisions of the General Conference on Weights and Measures (GCPM), adopted in different years, the following definitions of the basic SI units are currently in effect. Unit of length– meter– the length of the path traveled by light in a vacuum in 1/299,792,458 fractions of a second (decision of the XVII CGPM in 1983). Unit of mass– kilogram– mass equal to the mass of the international prototype of the kilogram (decision of the 1st CGPM in 1889). Unit of time– second– duration of 9192631770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom, not perturbed by external fields (decision of the XIII CGPM in 1967). Unit of electric current– ampere- the strength of a constant current, which, when passing through two parallel conductors of infinite length and negligible circular cross-section, located at a distance of 1 m from each other in a vacuum, would create between these conductors a force equal to 2 10 -7 N per meter of length (approved IX GCPM in 1948). Thermodynamic temperature unit– kelvin(until 1967 it was called degrees Kelvin) – 1/273.16 part of the thermodynamic temperature of the triple point of water. Expression of thermodynamic temperature in degrees Celsius is allowed (resolution XIII CGPM in 1967). Unit of quantity of substance– mole– the amount of substance of a system containing the same number of structural elements as there are atoms contained in a carbon-12 nuclide weighing 0.012 kg (resolution XIV GCPM in 1971). Luminous intensity unit– candela– the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540 10 12 Hz, the energetic luminous intensity of which in this direction is 1/683 W/sr (resolution XVI GCPM in 1979). Lecture 4. Ensuring uniformity of measurements Unity of measurements When carrying out measurements, it is necessary to ensure their unity. Under uniformity of measurements is understood characteristic of the quality of measurements, which consists in the fact that their results are expressed in legal units, the sizes of which, within established limits, are equal to the sizes of the reproduced quantities, and the errors of the measurement results are known with a given probability and do not go beyond the established limits. The concept of “unity of measurements” is quite capacious. It covers the most important tasks of metrology: unification of PV units, development of systems for reproducing quantities and transferring their sizes to working measuring instruments with established accuracy and a number of other questions. The uniformity of measurements must be ensured with any accuracy required by science and technology. The activities of state and departmental metrological services, carried out in accordance with established rules, requirements and standards, are aimed at achieving and maintaining the uniformity of measurements at the proper level. At the state level, activities to ensure the uniformity of measurements are regulated by the standards of the State System for Ensuring the Uniformity of Measurements (GSI) or regulatory documents of metrological service bodies. The State System for Ensuring the Uniformity of Measurements (GSI) is a set of interconnected rules, regulations, requirements and norms established by standards that determine the organization and methodology of carrying out work to assess and ensure measurement accuracy. Legal basis To ensure the uniformity of measurements, legal metrology is used, which is a set of state laws (the Law of the Russian Federation “On Ensuring the Uniformity of Measurements”), acts and regulatory and technical documents of various levels regulating metrological rules, requirements and norms. Technical basis GSI are: 1. The system (set) of state standards of units and scales of physical quantities is the country’s reference base. 2. A system for transferring the sizes of units and scales of physical quantities from standards to all SI using standards and other means of verification. 3. A system for the development, launch into production and release into circulation of working measuring instruments, providing research, development, determination with the required accuracy of the characteristics of products, technological processes and other objects. 4. System of state testing of measuring instruments (approval of measuring instruments type), intended for serial or mass production and import from abroad in batches. 5. System of state and departmental metrological certification, verification and calibration of measuring instruments. 6. System of reference materials for the composition and properties of substances and materials, System of standard reference data on physical constants and properties of substances and materials.

Rice. 2. Classification of quantities

Non-physical quantities include those that are operated by non-physical sciences (philosophy, sociology, economics of quality management, etc.).

Non-physical quantity– the value of an intangible size, estimated by non-instrumental methods, as well as the value of the size of an intangible object. Non-physical quantities are used to evaluate intelligence, knowledge, safety, attractiveness, etc.

In order for each object to be able to establish differences in the quantitative content of the property reflected by the physical quantity, the concepts of its size and value have been introduced in metrology.

Size of physical quantity – quantitative determination of a physical quantity inherent in a specific material object, system, phenomenon or process.

Value of a quantity – expression of the size of a physical quantity in the form of a certain number of units accepted for it.

Unit of measurement– a physical quantity of a fixed size, which is conventionally assigned a numerical value equal to one, and is used for the quantitative expression of physical quantities similar to it.

In general, according to the classification (Fig. 2), all physical quantities are divided into measured and estimated. Measured physical quantities can be expressed quantitatively in the form of a certain number of established units of measurement of a physical quantity, and estimated ones are the result of the evaluation operation. Evaluation is carried out when it is impossible to make a measurement: the quantity is not identified as physical and the unit of measurement of this quantity, for example, color intensity, is not defined.

By identifying the general metrological features of individual groups of physical quantities, we can propose their classification according to the following criteria (Fig. 3):

1) by type of phenomena(I group): on material, energy and characterizing the course of processes in time;

2) by belonging to various groups of physical processes(II group): on spatiotemporal, mechanical, thermal, electrical, acoustic, light, physicochemical, ionizing radiation, atomic and nuclear physics;

3) according to the degree of conditional independence from other quantities(III group): into basic (conditionally independent), derivatives (conditionally dependent) and additional;

4) by the presence (dimension) of physical quantities(IV group): into those having dimension (dimensional) and dimensionless.

The purpose of measurement and its final result is to find the value of a physical quantity. To achieve this goal, metrology uses the concepts of true and actual value of a physical quantity.

Finding the true value of a measured quantity is the central problem of metrology.

PHYSICAL QUANTITIES

By type of phenomena		By belonging to different groups of physical processes		According to the degree of conditions of independence from other quantities		Based on the presence of dimensions of physical quantities
1. Real (passive)		1. Spatio-temporal		1. Basic		1. Dimensions
2. Energy (active)		2. Mechanical		2. Derivatives		2. Dimensionless
3. Characterizing processes		3. Thermal		3. Additional
		4. Electric and magnetic
		5. Acoustic
		6. Light
		7. Ionizing radiation
		8. Physico-chemical
		9. Atomic and nuclear physics

Rice. 3. Classification of physical quantities

True value of a quantity – This is the value of a physical quantity that ideally characterizes the corresponding physical quantity in qualitative and quantitative terms. This value of a physical quantity is considered unknown and is used in theoretical studies. The value of a physical quantity obtained experimentally and so close to the true value that it can be used instead of it in the given measurement task is called conventional true value.

As is known, there are basic and derived physical quantities. The main ones are the quantities that characterize the fundamental properties of the material world. Mechanics is based on three basic quantities, heat engineering – on four, all physics – on seven: length, mass, time, thermodynamic temperature, amount of matter, light intensity, electric current, with the help of which the whole variety of derived physical quantities is created and a description of any properties of physical objects and phenomena.

Base quantity– a physical quantity included in a system of quantities and conventionally accepted as independent of other quantities of this system.

Derived quantity– a physical quantity included in a system of quantities and determined through the basic quantities of this system.

A formalized reflection of the qualitative difference between measured quantities is their dimension. According to the international ISO standard, the dimensions of the main quantities - length, mass and time - are indicated by the corresponding letters:

dim l = L; dim m = M; dim t = T.

Dimension of a quantity– an expression in the form of a power monomial, composed of products of symbols of basic physical quantities in various powers and reflecting the relationship of a given physical quantity with physical quantities accepted in a given system of units as basic:

Where L, M, T – dimensions of quantities: length, mass and time, respectively;

a, b, g – indicators of the dimension of physical quantities (indicators of the power to which the dimensions of basic quantities are raised).

Each dimension can be positive or negative, integer, fractional, or zero. If all dimension indicators are equal to zero, then the quantity is called dimensionless.

The result of the measurement is to obtain information about the size of the physical quantity being measured.

The operations of multiplication, division, exponentiation and root extraction can be carried out on dimensions, and it should be emphasized that the same dimension can be inherent in quantities that have different qualitative natures and differ from each other in the form of the equations that define them. For example, the distance traveled by a car and the circumference are qualitatively lengths, but are determined by completely different equations.

International system of units of physical quantities

The currently used International System of Units SI (Systeme International d`Unitas - SI) was approved in 1960 by the XI General Conference on Weights and Measures (GCPM). On the territory of our country, the system of SI units has been in effect since January 1, 1982 in accordance with GOST 8.417-2000 GSI. Units of quantities. This system provides seven main units and two additional ones (Table 1).

-L - length. Unit - meter- the path length that light travels in a vacuum in 1/299,792,458 seconds;

- M - mass. Unit – kilogram– mass equal to the mass of the international prototype kilogram;

- T–time. Unit – second – the duration of 9192631770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom in the absence of disturbances from external fields;

- I–electric current strength.Unit – ampere – force, an unchanging current, which, when passing through two parallel conductors of infinite length and a negligibly small circular cross-sectional area, located in a vacuum at a distance of 1 m from each other, creates on each section of a conductor 1 m long an interaction force equal to 2 × 10 -7 N ;

-q–thermodynamic temperature. Unit - kelvin(degree Kelvin before 1967) – 1/273.16 part of the thermodynamic temperature of the triple point of water;

- N–amount of substance. Unit – moth– the amount of substance of the system containing the same number of structural elements as there are atoms in carbon ~ 12 with a mass of 0.012 kg (when applying the concept of a mole, the structural elements must be specified and can be atoms, molecules, ions and other particles);

- J–the power of light. Unit - candela– luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540×10 12 Hz, the luminous energy intensity of which in this direction is 1/683 W/sr (W/sr 2).

Table 1

SI Basic and Additional Units

Magnitude	Unit
Name	Dimension	Name	Designation
Russian	international
Basic
Length	L	meter	m	m
Weight	M	kilogram	kg	kg
Time	T	second	With	s
Electric current strength	I	ampere	A	F
Thermodynamic temperature	q	kelvin	TO	R
Quantity of substance	N	mole	mole	mol
The power of light	J	candela	cd	CD
Additional
Flat angle	-	radian	glad	rad
Solid angle	-	steradian	Wed	cr

The complexity of the above formulations reflects the development of modern science, which makes it possible to present the basic units, on the one hand, as reliable and accurate, and on the other, as explainable and understandable for all countries of the world. This is what makes the system in question truly international.

In 1960, the SI system introduced two additional units for measuring plane and solid angles - radians and steradians, respectively.

Flat angle. Unit - radian– the angle between two radii of a circle, the length of the arc between which is equal to the radius.

Solid angle.Unit - steradian- a solid angle with a vertex at the center of the sphere, cutting out an area on the surface of the sphere equal to the area of ​​a square with a side equal to the radius of the sphere.

All other physical quantities can be obtained as derivatives of the basic ones. For example, the unit of force - newton - is a derived unit formed by the basic units - kilogram, meter and second. Using Newton's second law: (), we find the dimension of the force unit:

.

Derived SI units, which have special names, can also be used to form other derived units. For example, pascal - this derived unit is formed by derived units - newton and square meter.

Units not included in the accepted system are called non-systemic and are divided into four types:

Accepted on a par with SI units (ton, minute, degree, second, liter, etc.);

Allowed for use in special fields (in astronomy - parsec, light year; in optics - dioptre; in physics - electron-volt, etc.);

Temporarily accepted for use on a par with SI units (mile, carat, etc.), but subject to withdrawal from circulation;

Discontinued (millimeter of mercury, horsepower, etc.).

The use of the first group of non-systemic units is allowed due to their convenience and prevalence in specific life situations (that have stood the test of time), for example: ton, atomic mass unit, hour, degree, etc. The second and third groups are made up of specific, traditional units for a specific area of ​​application (Table 2).

table 2

Non-system units of physical quantities

Name of quantity	Unit
Name	Designation	Relation to SI unit
Weight	ton	T	10 3 kg
atomic mass unit	a.e.m.	1.66057×10 -27 kg (approx.)
Time	minute	min	60 s
hour	h	3600 s
day	days	86400 s
Flat angle	degree	… O	(π/180) rad =1.745329….10 -2 rad
minute	…¢	(π/10800)rad = 2.908882...10 -4 rad
second	…²	(π/648000) rad = 4.8848137….10 -6 rad
hail	hail	(π/200) rad
Volume	liter	l	10 -3 m 3
Length	Astronomical unit	a.e.	1.45598·10 -11 m (approx.)
light year	holy year	9.4605·10 -15 m (approx.)
parsec	PC	3.0857·10 -16 m (approx.)
Optical power	diopter	diopter	1 m -1
Square	hectare	ha	10 4 m 3
Energy	electron-volt	eV	1.60219·10 -19 J (approx.)
Full power	volt-ampere	В×А	-
Reactive power	var	var	-

For the convenience of using SI units of physical quantities, prefixes have been adopted to form decimal multiples and submultiples (smaller) units, the factors and prefixes of which are given in Table. 3.

Table 3

Factors and prefixes for forming decimals

multiples and submultiples and their names

Multiple unit is a unit of physical quantity that is an integer number of times greater than lobular– reducing a systemic or non-systemic unit by an integer number of times.

Scales

In measurement theory, it is generally accepted to distinguish between four types of scales: names, order, intervals and ratios (Fig. 4).

Physical quantity scale - an ordered set of values ​​of a physical quantity that serves as the initial basis for measuring a given quantity. It can be represented in the general case by a set of conventional signs arranged in a certain way; in this case, certain signs indicate the beginning and end of the scale, and the intervals between the signs characterize the accepted gradation of the scale (division value, spectrum width) and can have color and digital design.

Name scale - This is a kind of qualitative, not quantitative scale; it does not contain zero or units of measurement. An example is a color atlas (color scale). The measurement process involves visually comparing a painted item with color swatches (reference color swatches).

ASSESSMENT Measurement Rice. 4. Types of scales

Since each color has many variations, such a comparison can be done by an experienced expert who has not only practical experience, but also the corresponding special characteristics of visual capabilities. When rated on a naming scale, a number or sign is assigned to an object only for the purpose of identifying it or for class numbering. This assignment of numbers performs in practice the same function as a name.

Order scale characterizes the ordering of objects relative to a specific property, that is, the arrangement of objects in descending or ascending order of a given property. For example, the earthquake scale, the hardness scale of physical bodies, etc. The resulting ordered series is called a ranked series, and the procedure itself is called ranking.

The order scale compares homogeneous objects for which the values ​​of the properties of interest are unknown. Therefore, a ranked series can answer questions like: “What is more (less)?” or, “Which is better (worse)?” The order scale cannot provide more detailed information (how much more or less, how many times worse or better). Obviously, calling the procedure for assessing the properties of an object on an order scale a measurement is only a stretch. Results obtained from the order scale cannot be subject to any arithmetic operations.

Interval scale. The difference in values ​​of a physical quantity is plotted on the interval scale. Examples of interval scales are temperature scales. On the Celsius temperature scale, the temperature at which the ice melts is taken as the starting point for the temperature difference. All other temperatures are compared with it. For ease of use of the scale, the interval between the melting temperature of ice and the boiling temperature of water is divided into 100 equal intervals - degrees. The Celsius scale extends towards both positive and negative intervals. When they say that the air temperature is 25 ° C, this means that it is 25 ° C higher than the temperature taken as the zero mark of the scale (above zero). On the Fahrenheit temperature scale, the same interval is divided into 180 degrees. Therefore, a Fahrenheit degree is smaller in size than a Celsius degree. In addition, the Fahrenheit scale is shifted 32 degrees toward colder temperatures, with the Fahrenheit melting temperature of 32°F.

Dividing the interval scale into equal parts-gradations establishes a unit of physical quantity, which allows not only to express the measurement result in a numerical measure, but also to estimate the measurement error.

The results of measurements on an interval scale can be added to and subtracted from each other, that is, to determine how much one value of a physical quantity is greater or less than another. It is impossible to determine on an interval scale how many times one value of a quantity is greater or less than another, since the origin of the physical quantity is not defined on the scale. But at the same time, this can be done in relation to intervals (differences). So, a temperature difference of 25 degrees is 5 times greater than a temperature difference of 5 degrees.

Relationship scale is an interval scale with a natural zero origin, such as the Kelvin temperature scale, length scale, or mass scale. The relationship scale is the most advanced and most informative. The results of measurements on a ratio scale can be added, subtracted, multiplied and divided.

The naming and order scales are called non-metric (conceptual), and interval and ratio scales metric (material).

In practice, measurement scales are implemented through standardization of both the measurement unit scales themselves and, if necessary, the methods and conditions for their unambiguous reproduction.

Chapter 2

MEASUREMENTS

Postulates of measurement theory

Metrology, like any other science, is built on a number of fundamental postulates that describe its basic axioms. Currently, we can talk about building a theoretical foundation for metrology based on several common properties for the entire variety of any physical objects in the form of the formulation of the following postulates:

1) postulate α . Within the framework of the accepted model of the object of study, there is a certain measurable physical quantity and its true value;

2) postulate β. The true value of the measured quantity is constant;

3) postulate γ. There is a discrepancy between the measured quantity and the property of the object under study.

When taking measurements, the distance between two points located between the fixed elements of the measuring instrument is physically determined. Each variant of joining the measured part and the measuring tool will correspond to a specific measurement result. Based on this, it can be argued that the measured value exists only within the framework of the accepted model, that is, it makes sense only as long as the model is recognized as adequate to the object.

A specific procedure for performing measurements is considered as a sequence of complex and heterogeneous actions, consisting of a number of stages, which can vary significantly in the number, type and labor intensity of the operations performed. In each specific case, the ratio and significance of each of the stages may change noticeably, but a clear identification of the stages and the conscious implementation of the necessary and sufficient number of measurement actions leads to optimization of the measurement implementation process and the elimination of corresponding methodological errors. The main stages include the following:

¨ setting the measurement task;

¨ measurement planning;

¨ carrying out a measuring experiment;

¨ processing of experimental data.

Table 4

Stage	Contents of the stage
1. Statement of the measurement problem	1.1. Collection of data on measurement conditions and the physical quantity being studied. 1.2. The choice of specific quantities by which the value of the measured quantity will be found. 1.3. Formulation of the measurement equation
2. Measurement planning	2.1. Selection of measurement methods and possible types of measuring instruments. 2.2. A priori estimate of measurement error 2.3. Determination of requirements for metrological characteristics of measuring instruments and measurement conditions. 2.4. Preparation of measuring instruments. 2.5. Providing the required measurement conditions and creating the possibility of their control.
3. Conducting a measuring experiment	3.1. Interaction of means of measurement objects. 3.2. Registration of result
4. Processing of experimental data	4.1. Preliminary analysis of information obtained at previous stages of measurement. 4.2. Calculation and introduction of possible corrections for systematic errors. 4.3. Formulation and analysis of a mathematical data processing problem. 4.4. Carrying out calculations that result in the values ​​of the measured quantity and measurement errors. 4.5. Analysis and interpretation of the results obtained. 4.6. Recording measurement results and error indicators in accordance with the established presentation form

The quality of measurement preparation always depends on the extent to which the necessary a priori information has been obtained and used. Errors made during the preparation of measurements are difficult to detect and correct at subsequent stages.

Types and methods of measurements

To carry out a measuring experiment, special technical means are required - measuring instruments. The result of the measurement is an assessment of the physical quantity in the form of a certain number of units accepted for it.

Measurement of a physical quantity– a set of operations for the use of a technical means that stores a unit of physical quantity, ensuring that the relationship (explicitly or implicitly) of the measured quantity with its unit is found and the value of this quantity is obtained.

Despite the fact that measurements are continuously evolving and becoming more complex, the metrological essence remains unchanged and boils down to the basic measurement equation:

Q = X[Q]

Where Q– measured quantity;

X– numerical value of the measured quantity in the accepted unit of measurement;

[Q]– unit selected for measurement.

Depending on what intervals the scale is divided into, the same size is presented differently. Let's say the length of a straight line segment of 10 cm is measured using a ruler with divisions in centimeters and millimeters.

For the first case Q 1 = 10 cm at X 1 = 10 and = 1 cm.

For the second case Q 2 = 100 mmat X 2 = 100 and = 1 mm.

Wherein Q 1 = Q 2 , since 10 cm = 100 mm .

The use of different units in the measurement process only leads to a change in the numerical value of the measurement result.

The purpose of measurement is to obtain a certain physical quantity in the form most convenient for use. Any measurement consists of comparing a given quantity with a certain value taken as a unit of comparison. This approach has been developed through hundreds of years of measurement practice. Even the great mathematician L. Euler argued: “It is impossible to define or measure one quantity except by taking as known another quantity of the same kind and indicating the relationship in which they exist.”

Measurements as experimental procedures are very diverse and are classified according to different criteria (Fig. 5).