Name of physical quantities. Basic physical quantities in mechanics, their measurement and units

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• Hydraulics 4th ed., trans. and additional Textbook and workshop for academic bachelor's degree, Eduard Mikhailovich Kartashov. The textbook outlines the basic physical and mechanical properties of liquids, issues of hydrostatics and hydrodynamics, provides the basics of the theory of hydrodynamic similarity and mathematical modeling...

1.2. Physical quantities

1.2.1. Physical quantities as an object of measurement

Magnitude- this is a property of something that can be distinguished from other properties and assessed in one way or another, including quantitatively. A quantity does not exist on its own; it exists only insofar as there is an object with properties expressed by a given quantity.

Values ​​can be divided into two types: real and ideal. Ideal values mainly relate to mathematics and are a generalization (model) of specific real concepts(see Fig. 1.1)

Real values are divided into physical and non-physical. Physical quantity in the general case, it can be defined as a quantity characteristic of material objects (processes, phenomena) studied in the natural and technical sciences. To non-physical should include quantities inherent in social (non-physical) sciences - philosophy, sociology, economics, etc.

Fig.1.1 Classification of quantities

Recommendations RMG 29-99 interpret a physical quantity as one of the properties of a physical object, in qualitatively common to many physical objects, and in quantitative terms – individual for each of them . Individuality in quantitative terms is understood in the sense that a property can be for a given object a certain number of times greater or less than that of another. Thus, physical quantities – these are the measured properties of physical objects and processes by which they can be studied.

Physical quantities are:

· measurable;

· evaluated.

The measured physical quantities can be expressed quantitatively in the form a certain number established units of measurement. Physical quantities for which, for one reason or another, a unit of measurement cannot be introduced, can only be estimated. Values ​​are assessed using scales .

Magnitude scale– an ordered sequence of its values, adopted by agreement based on the results of accurate measurements.

For a more detailed study of physical quantities, it is necessary to classify and identify their general metrological features separate groups.

According to the types of phenomena, physical quantities are divided into the following groups:

· real, i.e. describing physical and physicochemical characteristics substances, materials and products made from them. This group includes mass, density, electrical resistance, capacitance, inductance, etc. Sometimes these physical quantities are called passive. To measure them, it is necessary to use an additional energy source, with the help of which a signal of measurement information is generated. In this case, passive physical quantities are converted into active ones, which are measured;

· energy, i.e. quantities that describe the energy characteristics of the processes of transformation, transmission and use of energy. These include current, voltage, power, energy. These quantities are called active. They can be converted into measurement information signals without the use of auxiliary energy sources;

· characterizing the course of processes over time. This group includes various kinds of spectral characteristics, correlation functions, etc.

According to belonging to different groups of physical processes physical quantities are divided:

· spatiotemporal;

· mechanical;

· thermal;

· electrical;

· magnetic;

· acoustic;

· light;

· physical and chemical;

· ionizing radiation;

· atomic and nuclear physics.

According to the degree of conditional independence from other quantities

basic (conditionally independent),

· derivatives (conditionally dependent),

· additional.

Currently, the SI system uses seven physical quantities chosen as basic ones: length, time, mass, temperature, force electric current, luminous intensity and amount of matter. Additional physical quantities include plane and solid angles.

Unit of physical quantity is a physical quantity of a fixed size, which is conditionally assigned a numerical value equal to one. A unit of physical quantity is used to quantitatively express homogeneous physical quantities.

Physical quantity value is an estimate of its size in the form of a certain number of units accepted for it (Q).

Numeric value physical quantity (q) is an abstract number expressing the ratio of the value of a quantity to the corresponding unit of a given physical quantity.

The equation Q=q[Q] called basic measurement equation. The essence of the simplest measurement is to compare a physical quantity Q with the dimensions of the output value of an adjustable multivalued measure q[Q]. As a result of the comparison, it is established that q[Q] ‹ Q ‹ (q+1)[Q].

1.2.2. Systems of units of physical quantities

The set of basic and derived units is called a system of units of physical quantities.

The first system of units is considered metric system, where the meter was taken as the basic unit of length, and 1 cm3 was taken as the unit of weight chemically clean water at a temperature of about +40°C. In 1799, the first prototypes (standards) of the meter and kilogram were made. In addition to these two units, the metric system in its original version also included units of area (ap - the area of ​​a square with a side of 10 m), volume (ster - the volume of a cube with an edge of 10 m), capacity (liter, equal to the volume of a cube with an edge of 0.1 m). The metric system did not yet have a clear division of units into basic and derivative ones.

Fig.1.2. Classification of physical quantities

The concept of a system of units, as a set of basic and derivatives, was first proposed by the German scientist Gauss in 1832. The basic ones in this system were: the unit of length - millimeter, the unit of mass - milligram, the unit of time - second. This system was called absolute.

In 1881 it was adopted GHS system(centimeter-gram-second), at the beginning of the twentieth century there was also a system of the Italian scientist Giorgi - MCSA (meter, kilogram, second, ampere). There were other systems of units. Even today, some countries have not moved away from historically established units of measurement. In the UK, USA, Canada, the unit of mass is the pound, and its size varies.

The most widely used in the world International system of unitsSI –SystemeInternational.

The General Conference on Weights and Measures (GCPM) in 1954 defined six basic units of physical quantities for their use in international relations: meter, kilogram, second, ampere, Kelvin, candle. Subsequently, the system was supplemented by one main, additional and derived units. In addition, definitions of basic units have been developed.

Unit of length - meter– the length of the path that light travels in a vacuum in 1/2 of a second.

Unit of mass – kilogram– mass equal to the mass of the international prototype of the kilogram.

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

The unit of electric current is ampere.- the strength of an unchanging current, which, when passing through two parallel conductors of infinite length and negligible round section, located at a distance of 1 m from each other in a vacuum, would create a force between these conductors equal to 2·10-7 N per meter of length.

The unit of thermodynamic temperature is kelvin.– 1/273.16 part of the thermodynamic temperature of the triple point of water. The use of the Celsius scale is also permitted.

Unit of amount of substance – mole– the amount of substance in a system containing the same amount structural elements, how many atoms are contained in a carbon-12 nuclide weighing 0.012 kg.

The unit of luminous intensity is the candela.– the intensity of light in a given direction of a source emitting monochromatic radiation with a frequency of 540·1012 Hz, the energy intensity of which in this direction is 1/683 W/sr2.

The given definitions are quite complex and require a sufficient level of knowledge, primarily in physics. But they give an idea of ​​the natural, natural origin accepted units.

The international SI system is the most advanced and universal compared to its predecessors. In addition to the basic units, the SI system has additional units for measuring plane and solid angles - radians and steradians, respectively, as well as a large number of derived units of space and time, mechanical quantities, electrical and magnetic quantities, thermal, light and acoustic quantities, as well as ionizing radiation (Table 1.2.) The Unified International System of Units was adopted by the XI General Conference on Weights and Measures in 1960. On the territory of our country, the SI system of units has been in effect since January 1, 1982 in accordance with GOST 8.417-81. The SI system is logical development the GHS and MKGSS systems that preceded it. The advantages and benefits of the SI system include:

· universality, i.e. coverage of all areas of science and technology;

· unification of all areas and types of measurements;

· coherence of quantities;

· the ability to reproduce units with high accuracy in accordance with their definition;

· simplification of writing formulas due to the lack of conversion factors;

· reduction in the number of allowed units;

· a unified system of multiple and submultiple units;

Table 1.1

Basic and additional units of physical quantities

Derived unit is a unit of a derivative of a physical quantity of a system of units, formed in accordance with equations connecting it with the basic units or with the basic and already defined derivatives. Derived SI units that have proper name, are given in table 1.2.

To establish derived units:

· select physical quantities whose units are accepted as basic ones;

· set the size of these units;

· select a defining equation that connects quantities measured by basic units with the quantity for which a derived unit is established. In this case, the symbols of all quantities included in the defining equation should be considered not as the quantities themselves, but as their named ones numeric values;

· equate to unity (or another constant number) the proportionality coefficient k included in the defining equation. This equation should be written in the form of an explicit functional dependence of the derivative quantity on the basic quantities.

Derived units established in this way can be used to introduce new derived units.

Units of physical quantities are divided into systemic and non-systemic. System unit– a unit of physical quantity included in one of the accepted systems. All basic, derivative, multiple and submultiple units are systemic. Non-systemic unit is a unit of physical quantity that is not included in any of the accepted systems of units. Non-system units in relation to SI system units are divided into four types:

Table 1.2.

Derived units of the systemSI having a special name

· accepted on a par with SI units, for example, mass units - ton; flat angle – degree, minute, second; volume - liter, etc. Non-system units allowed for use along with SI units are given in Table 1.3;

· allowed for use in special areas, for example, the astronomical unit - parsec, light year - units of length in astronomy; diopter – a unit of optical power in optics; electron-volt is a unit of energy in physics, etc.;

· temporarily accepted for use along with SI units, for example, nautical mile - in maritime navigation; carat – a unit of mass in jewelry, etc. These units should be withdrawn from use in accordance with international agreements;

· withdrawn from use, for example, millimeter of mercury - a unit of pressure; horsepower is a unit of power and some others.

Table 1.3

Non-system units allowed for use

on par with unitsS.I.

There are multiple and submultiple units of physical quantities .

Multiple unit is a unit of physical quantity that is an integer number of times greater than a systemic or non-systemic unit. submultiple unit is a unit of physical quantity, the value of which is an integer number of times less than a systemic or non-systemic unit. Prefixes for the formation of multiples and submultiples are given in Table 1.4.

Table 1.4

Prefixes for forming decimal multiples

and submultiple units and their names

The concept of a physical quantity is common in physics and metrology and is used to describe material systems of objects.

Physical quantity, as mentioned above, this is a characteristic that is common in a qualitative sense for many objects, processes, phenomena, and in a quantitative sense - individual for each of them. For example, all bodies have their own mass and temperature, but the numerical values ​​of these parameters are different for different bodies. The quantitative content of this property in an object is the size of the physical quantity, numerical estimate of its size called the value of a physical quantity.

A physical quantity that expresses the same quality in a qualitative sense is called homogeneous (of the same name ).

Main task of measurements - obtaining information about the values ​​of a physical quantity in the form of a certain number of units accepted for it.

The values ​​of physical quantities are divided into true and real.

True meaning - this is a value that ideally reflects the qualitatively and quantitatively corresponding properties of an object.

Real value - this is a value found experimentally and so close to the true one that it can be taken instead.

Physical quantities are classified according to a number of characteristics. The following are distinguished: classifications:

1) in relation to measurement information signals, physical quantities are: active - quantities that can be converted into a measurement information signal without the use of auxiliary energy sources; passive new - quantities that require the use of auxiliary energy sources, through which a measurement information signal is created;

2) on the basis of additivity, physical quantities are divided into: additive , or extensive, which can be measured in parts, and also accurately reproduced using a multi-valued measure based on the summation of the sizes of individual measures; Not additive, or intensive, which are not directly measured, but are converted into a measurement of magnitude or measurement by indirect measurements. (Additivity (Latin additivus - added) is a property of quantities, consisting in the fact that the value of a quantity corresponding to the whole object is equal to the sum of the values ​​of quantities corresponding to its parts).

Evolution of development systems of physical units.

Metric system- the first system of units of physical quantities

was adopted in 1791 by the French National Assembly. It included units of length, area, volume, capacity and weight , which were based on two units - meter and kilogram . It was different from the system of units used now, and was not yet a system of units in the modern sense.

Absolute systemunits of physical quantities.

The method for constructing a system of units as a set of basic and derived units was developed and proposed in 1832 by the German mathematician K. Gauss, calling it an absolute system. He took as a basis three quantities independent of each other - mass, length, time .

For the main units he accepted these quantities milligram, millimeter, second , assuming that the remaining units can be determined using them.

Later, a number of systems of units of physical quantities appeared, built on the principle proposed by Gauss, and based on the metric system of measures, but differing in basic units.

In accordance with the proposed Gauss principle, the main systems of units of physical quantities are:

GHS system, in which the basic units are the centimeter as a unit of length, the gram as a unit of mass and the second as a unit of time; was installed in 1881;

MKGSS system. The use of the kilogram as a unit of weight, and later as a unit of force in general, led at the end of the 19th century. to the formation of a system of units of physical quantities with three basic units: meter - a unit of length, kilogram - force - a unit of force, second - a unit of time;

5. MKSA system- The basic units are meter, kilogram, second and ampere. The foundations of this system were proposed in 1901 by the Italian scientist G. Giorgi.

International relations in the field of science and economics required the unification of units of measurement, the creation unified system units of physical quantities, covering various branches of the measurement area and preserving the principle of coherence, i.e. equality of the coefficient of proportionality to unity in the equations of connection between physical quantities.

SystemSI. In 1954, the commission to develop a unified International

system of units proposed a draft system of units, which was approved in 1960. XI General Conference on Weights and Measures. The International System of Units (abbreviated SI) takes its name from the initial letters of the French name System International.

The International System of Units (SI) includes seven main ones (Table 1), two additional ones and a number of non-systemic units of measurement.

Table 1 - International system of units

Source: Tyurin N.I. Introduction to metrology. M.: Standards Publishing House, 1985.

Basic units measurements physical quantities in accordance with the decisions of the General Conference on Weights and Measures are defined as follows:

meter - the length of the path that light travels in a vacuum in 1/299,792,458 of a second;

a kilogram is equal to the mass of the international prototype of the kilogram;

a second is equal to 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the Cs 133 atom;

An ampere is equal to the strength of a constant current, which, when passing through two parallel straight conductors of infinite length and negligibly small circular cross-sectional area, located at a distance of 1 m from each other in a vacuum, causes an interaction force on each section of the conductor 1 m long;

candela is equal to the luminous intensity in a given direction of a source emitting ion-protective radiation, the energetic luminous intensity of which in this direction is 1/683 W/sr;

a kelvin is equal to 1/273.16 of the thermodynamic temperature of the triple point of water;

mole equal to the quantity substances of a system containing the same number of structural elements as there are atoms in C 12 weighing 0.012 kg 2.

Additional units International system of units for measuring plane and solid angles:

radian (rad) - a flat angle between two radii of a circle, the arc between which is equal in length to the radius. In degrees, a radian is equal to 57°17"48"3;

steradian (sr) - a solid angle whose vertex is located at the center of the sphere and which cuts out an area on the surface of the sphere, equal to the area square with a side equal in length to the radius of the sphere.

Additional SI units are used to form the units of angular velocity, angular acceleration and some other quantities. The radian and steradian are used for theoretical constructions and calculations, since most practical values ​​of angles in radians that are important for practice are expressed as transcendental numbers.

Non-system units:

A tenth of a white is taken as a logarithmic unit - decibel (dB);

Diopter - luminous intensity for optical instruments;

Reactive power-var (VA);

Astronomical unit (AU) - 149.6 million km;

A light year is the distance a ray of light travels in 1 year;

Capacity - liter (l);

Area - hectare (ha).

Logarithmic units are divided into absolute, which represent the decimal logarithm of the ratio of a physical quantity to a normalized value, and relative, formed as a decimal logarithm of the ratio of any two homogeneous (same) quantities.

Non-SI units include degrees and minutes. The remaining units are derived.

Derived units SI are formed using the simplest equations that relate quantities and in which the numerical coefficients are equal to unity. In this case, the derived unit is called coherent.

Dimension is a qualitative display of measured quantities. The value of a quantity is obtained as a result of its measurement or calculation in accordance with basic equation frommeasurements:Q = q * [ Q]

where Q - quantity value; q- numerical value of the measured quantity in conventional units; [Q] - the unit chosen for measurement.

If the defining equation includes a numerical coefficient, then to form a derived unit, such numerical values ​​of the initial quantities should be substituted into the right side of the Equation so that the numerical value of the derived unit being determined is equal to one.

(For example, 1 ml is taken as a unit of measurement for the mass of a liquid, so on the packaging it is indicated: 250 ml, 750, etc., but if 1 liter is taken as a unit of measurement, then the same amount of liquid will be indicated 0.25 liters. , 075l. respectively).

As one of the ways to form multiples and submultiples, the decimal multiplicity between major and minor units, adopted in the metric system of measures, is used. In table 1.2 provides factors and prefixes for the formation of decimal multiples and submultiples and their names.

Table 2 - Factors and prefixes for the formation of decimal multiples and submultiples and their names

(Exabyte is a unit of measurement of the amount of information, equal to 1018 or 260 bytes. 1 EeV (exaelectronvolt) = 1018 electronvolt = 0.1602 joule)

It should be taken into account that when forming multiple and submultiple units of area and volume using prefixes, dual reading may arise depending on where the prefix is ​​added. For example, 1 m2 can be used as 1 square meter and as 100 square centimeters, which is far from the same thing, because 1 square meter that's 10,000 square centimeters.

According to international rules, multiples and submultiples of area and volume should be formed by adding prefixes to the original units. Degrees refer to those units that are obtained by attaching prefixes. For example, 1 km 2 = 1 (km) 2 = (10 3 m) 2 == 10 6 m 2.

To ensure the uniformity of measurements, it is necessary to have identical units in which all measuring instruments of the same physical quantity are calibrated. Unity of measurements is achieved by storing, accurately reproducing established units of physical quantities and transferring their sizes to all working measuring instruments using standards and reference measuring instruments.

Reference - a measuring instrument that ensures the storage and reproduction of a legal unit of physical quantity, as well as the transfer of its size to other measuring instruments.

The creation, storage and use of standards, monitoring their condition are subject to uniform rules established by GOST “GSI. Standards of units of physical quantities. Procedure for development, approval, registration, storage and application.”

By subordination standards are divided into primary and secondary and have the following classification.

Primary standard ensures storage, reproduction of units and transmission of dimensions with the highest accuracy in the country achievable in this field of measurement:

- special primary standards- are intended to reproduce the unit in conditions in which direct transmission of the unit size from the primary standard with the required accuracy is technically infeasible, for example, for low and high voltages, microwave and HF. They are approved as state standards. In view of the special importance of state standards and to give them the force of law, GOST is approved for each state standard. The State Committee for Standards creates, approves, stores and applies state standards.

Secondary standard reproduces the unit in special conditions and replaces the primary standard under these conditions. It is created and approved to ensure the least wear and tear on the state standard. Secondary standards in turn divided according to purpose:

Copy standards - designed to transfer unit sizes to working standards;

Comparison standards - designed to check the safety of the state standard and to replace it in case of damage or loss;

Witness standards - used for comparison of standards that, for one reason or another, cannot be directly compared with each other;

Working standards - reproduce a unit from secondary standards and serve to transfer the size to a standard of a lower rank. Secondary standards are created, approved, stored and used by ministries and departments.

Unit standard - one instrument or set of measuring instruments that provide storage and reproduction of a unit for the purpose of transferring its size to subordinate measuring instruments in the verification scheme, made according to a special specification and officially approved in in the prescribed manner as a standard.

Reproduction of units, depending on the technical and economic requirements, is carried out by two ways:

- centralized- using a single state standard for the entire country or group of countries. All basic units and most of the derivatives are reproduced centrally;

- decentralized- applicable to derived units, the size of which cannot be conveyed by direct comparison with the standard and provide the necessary accuracy.

The standard establishes a multi-stage procedure for transferring the dimensions of a unit of a physical quantity from the state standard to all working means of measuring a given physical quantity using secondary standards and exemplary means of measuring various categories from the highest first to the lowest and from exemplary means to working ones.

Size transfer is carried out by various verification methods, mainly by well-known measurement methods. Transferring a size in a stepwise manner is accompanied by a loss of accuracy, however, multi-stepping allows you to save standards and transfer the unit size to all working measuring instruments.

INTRODUCTION

A physical quantity is a characteristic of one of the properties of a physical object (physical system, phenomenon or process), which is qualitatively common to many physical objects, but quantitatively individual for each object.

Individuality is understood in the sense that the value of a quantity or the size of a quantity can be for one object a certain number of times greater or less than for another.

The value of a physical quantity is an estimate of its size in the form of a certain number of units accepted for it or a number on a scale accepted for it. For example, 120 mm is a linear value; 75 kg is the value of body weight.

There are true and actual values ​​of a physical quantity. The true value is a value that ideally reflects the property of an object. Real value is a value of a physical quantity found experimentally that is close enough to the true value that it can be used instead.

Measurement of a physical quantity is a set of operations involving the use of a technical means that stores a unit or reproduces a scale of a physical quantity, which consists of comparing (explicitly or implicitly) the measured quantity with its unit or scale in order to obtain the value of this quantity in the form most convenient for use.

There are three types of physical quantities, the measurement of which is carried out according to fundamentally different rules.

The first type of physical quantities includes quantities on the set of sizes of which only relations of order and equivalence are defined. These are relationships like “softer”, “harder”, “warmer”, “colder”, etc.

Quantities of this kind include, for example, hardness, defined as the ability of a body to resist the penetration of another body into it; temperature, as the degree of body heating, etc.

The existence of such relationships is established theoretically or experimentally using special means comparison, as well as based on observations of the results of the impact of a physical quantity on any objects.

For the second type of physical quantities, the relation of order and equivalence occurs both between sizes and between differences in pairs of their sizes.

A typical example is the time interval scale. Thus, differences in time intervals are considered equal if the distances between the corresponding marks are equal.

The third type consists of additive physical quantities.

Additive physical quantities are quantities on the set of sizes of which not only the relations of order and equivalence, but also the operations of addition and subtraction are defined

Such quantities include, for example, length, mass, current, etc. They can be measured in parts, as well as reproduced using a multivalued measure based on the summation of individual measures.

The sum of the masses of two bodies is the mass of the body that is balanced on equal-armed scales by the first two.

The sizes of any two homogeneous PVs or any two sizes of the same PV can be compared with each other, i.e., you can find how many times one is larger (or smaller) than the other. To compare m sizes Q", Q", ..., Q (m) with each other, it is necessary to consider C m 2 of their relations. It is easier to compare each of them with one size [Q] of a homogeneous PV, if we take it as a unit of PV size (abbreviated as a unit of PV). As a result of this comparison, we obtain expressions for the dimensions Q", Q", ... , Q (m) in the form of some numbers n", n", .. . ,n (m) PV units: Q" = n" [Q]; Q" = n"[Q]; ...; Q(m) = n(m)[Q]. If the comparison is carried out experimentally, then only m experiments will be required (instead of C m 2), and a comparison of the sizes Q", Q", ... , Q (m) with each other can only be performed by calculations like

where n (i) / n (j) are abstract numbers.

Type equality

called the basic measurement equation, where n [Q] is the value of the PV size (abbreviated as PV value). The PV value is a named number made up of the numerical value of the PV size (abbreviated as the numeric value of the PV) and the name of the PV unit. For example, with n = 3.8 and [Q] = 1 gram the size of the mass is Q = n [Q] = 3.8 grams, with n = 0.7 and [Q] = 1 ampere the size of the current Q = n [Q ] = 0.7 ampere. Usually, instead of “the size of the mass is 3.8 grams”, “the size of the current is 0.7 amperes”, etc., they say and write more briefly: “the mass is 3.8 grams”, “the current is 0.7 amperes” " and so on.

The size of the PV is most often determined by measuring it. Measuring the size of the PV (abbreviated as measuring the PV) consists of experimentally using special technical means find the value of the PV and evaluate the proximity of this value to the value that ideally reflects the size of this PV. The PV value found in this way will be called nominal.

The same size Q can be expressed different meanings with different numerical values ​​depending on the choice of PV unit (Q = 2 hours = 120 minutes = 7200 seconds = = 1/12 days). If we take two different units and , then we can write Q = n 1 and Q = n 2, from which

n 1 /n 2 = /,

that is, the numerical values ​​of the PV are inversely proportional to its units.

From the fact that the size of the PV does not depend on its chosen unit, the condition for the unambiguity of measurements follows, which consists in the fact that the ratio of two values ​​of a certain PV should not depend on which units were used in the measurement. For example, the ratio of the speeds of a car and a train does not depend on whether these speeds are expressed in kilometers per hour or in meters per second. This condition, which seems immutable at first glance, unfortunately, has not yet been met when measuring certain PVs (hardness, photosensitivity, etc.).

1. THEORETICAL PART

1.1 Concept of physical quantity

Weight objects of the surrounding world are characterized by their properties. Property - philosophical category, expressing such an aspect of an object (phenomenon, process) that determines its difference or commonality with other objects (phenomena, processes) and is revealed in its relations to them. Property - quality category. To quantitatively describe various properties of processes and physical bodies, the concept of quantity is introduced. Magnitude is a property of something that can be distinguished from other properties and assessed in one way or another, including quantitatively. A quantity does not exist on its own; it exists only insofar as there is an object with properties expressed by a given quantity.

Analysis of the quantities allows us to divide them (Fig. 1) into two types: quantities material form(real) and values ​​of ideal models of reality (ideal), which relate mainly to mathematics and are a generalization (model) of specific real concepts.

Real quantities, in turn, are divided into physical and non-physical. A physical quantity in the most general case can be defined as a quantity characteristic of material objects (processes, phenomena) studied in the natural (physics, chemistry) and technical sciences. Non-physical quantities include quantities inherent in social (non-physical) sciences - philosophy, sociology, economics, etc.

Rice. 1. Classification of quantities.

Document RMG 29-99 interprets a physical quantity as one of the properties of a physical object, which is qualitatively common for many physical objects, but quantitatively individual for each of them. Individuality in quantitative terms is understood in the sense that a property can be a certain number of times greater or less for one object than for another.

It is advisable to divide physical quantities into measured and estimated. Measured EF can be expressed quantitatively in the form of a certain number of established units of measurement. The ability to introduce and use such units is important hallmark measured PV. Physical quantities for which, for one reason or another, a unit of measurement cannot be introduced, can only be estimated. Estimation is understood as the operation of assigning a certain number to a given value, carried out according to established rules. Values ​​are assessed using scales. A quantity scale is an ordered set of values ​​of a quantity that serves as the initial basis for measuring a given quantity.

Non-physical quantities, for which a unit of measurement cannot in principle be introduced, can only be estimated. It should be noted that the assessment of non-physical quantities is not part of the tasks of theoretical metrology.

For a more detailed study of PVs, it is necessary to classify and identify the general metrological features of their individual groups. Possible classifications of PV are shown in Fig. 2.

According to the types of phenomena, PVs are divided into:

Real, i.e. quantities that describe the physical and physicochemical properties of substances, materials and products made from them. This group includes mass, density, electrical resistance, capacitance, inductance, etc. Sometimes these PVs are called passive. To measure them, it is necessary to use an auxiliary energy source, with the help of which a measurement information signal is generated. In this case, passive PVs are converted into active ones, which are measured;

Energy, i.e. quantities describing the energy characteristics of the processes of transformation, transmission and use of energy. These include current, voltage, power, energy. These quantities are called active.

They can be converted into measurement information signals without the use of auxiliary energy sources;

Characterizing the course of processes over time, this group includes various types spectral characteristics, correlation functions and other parameters.

Physical quantity- this is a property that is qualitatively common to many objects (systems, their states and processes occurring in them), but quantitatively individual for each object.

Individuality in quantitative terms should be understood in the sense that a property can be for one object a certain number of times greater or less than for another.

As a rule, the term “quantity” is used in relation to properties or their characteristics that can be quantified, that is, measured. There are properties and characteristics that we have not yet learned to evaluate quantitatively, but we are striving to find a way to quantify them, for example, smell, taste, etc. Until we learn to measure them, we should call them not quantities, but properties.

The standard contains only the term “physical quantity”, and the word “quantity” is given as a short form of the main term, which is allowed to be used in cases that exclude the possibility of different interpretations. In other words, you can briefly call a physical quantity a quantity if it is obvious even without an adjective that we are talking about a physical quantity. In the rest of this book short form The term "quantity" is used only in the sense indicated.

In metrology, the word “quantity” is given a terminological meaning by imposing a limitation in the form of the adjective “physical”. The word “quantity” is often used to express the size of a given physical quantity. They say: the amount of pressure, the amount of speed, the amount of voltage. This is incorrect, since pressure, speed, tension in the correct understanding of these words are quantities, and it is impossible to talk about the magnitude of a quantity. In the above cases, the use of the word “magnitude” is unnecessary. Indeed, why talk about a large or small “magnitude” of pressure, when you can say: large or small pressure, etc.

A physical quantity displays properties of objects that can be expressed quantitatively in accepted units. Every measurement implements the operation of comparing homogeneous properties of physical quantities on the basis of “more or less.” As a result of comparison, each size of the measured quantity is assigned a positive real number:

x = q[x], (1.1)

where q - the numerical value of a quantity or the result of a comparison; [X] - unit of magnitude.

Unit of physical quantity- a physical quantity that, by definition, is given a value equal to one. We can also say that a unit of a physical quantity is its value that is taken as the basis for comparing physical quantities of the same kind with it when quantifying them.

Equation (1.1) is the basic measurement equation. The numerical value of q is found as follows

therefore, it depends on the unit of measurement adopted.

1. Systems of units of physical quantities

When carrying out any measurements, the measured quantity is compared with another homogeneous quantity, taken as a unit. To construct a system of units, several physical quantities are chosen arbitrarily. They are called basic. Quantities determined through fundamental quantities are called derivatives. The set of basic and derived quantities is called a system of physical quantities.

IN general view relationship between derivative quantity Z and the main ones can be represented by the following equation:

Z = L  M  T  I    J  ,

Where L, M, T,I, ,J- basic quantities; , , , , ,  - dimensional indicators. This formula is called the dimension formula. A system of quantities can consist of both dimensional and dimensionless quantities. A dimensional quantity is a quantity in the dimension of which at least one of the basic quantities is raised to a power not equal to zero. A dimensionless quantity is a quantity whose dimension includes the basic quantities to a degree equal to zero. A dimensionless quantity in one system of quantities can be a dimensional quantity in another system. A system of physical quantities is used to construct a system of units of physical quantities.

A unit of a physical quantity is the value of this quantity, taken as the basis for comparing with it the values ​​of quantities of the same kind when quantifying them. By definition, it is assigned a numerical value equal to 1.

Units of basic and derived quantities are called basic and derived units, respectively, and their combination is called a system of units. The choice of units within the system is to some extent arbitrary. However, the basic units are those that, firstly, can be reproduced with the highest accuracy, and secondly, are convenient in the practice of measurements or their reproduction. The units of quantities included in the system are called system units. In addition to system units, non-system units are also used. Non-system units are units that are not part of the system. They are convenient for individual areas science and technology or regions and therefore have become widespread. Non-system units include: power unit - horsepower, energy unit - kilowatt-hour, time units - hour, day, temperature unit - degree Celsius and many others. They arose in the process of developing measurement technology to satisfy practical needs or were introduced for ease of use during measurements. For the same purposes, multiple and submultiple units of quantities are used.

A multiple unit is one that is an integer number of times larger than a system or extra-system unit: kilohertz, megawatt. A submultiple unit is one that is an integer number of times smaller than a system or extra-system unit: milliampere, microvolt. Strictly speaking, many non-system units can be considered as multiples or submultiples.

In science and technology, relative and logarithmic quantities and their units are also widely used, which characterize the amplification and attenuation of electrical signals, modulation coefficients, harmonics, etc. Relative values ​​can be expressed in dimensionless relative units, as a percentage, or in ppm. A logarithmic quantity is the logarithm (usually decimal in radio electronics) of the dimensionless ratio of two quantities of the same name. The unit of logarithmic value is bel (B), determined by the relation:

N = lg P 1/ / P 2 = 2 lg F 1 / F 2 , (1.2)

Where P 1 ,P 2 - energy quantities of the same name (values ​​of power, energy, power density flow, etc.); F 1 , F 2 - power quantities of the same name (voltage, current, electromagnetic field strength, etc.).

As a rule, a submultiple unit of white is used, called a decibel, equal to 0.1 B. In this case, in formula (1.2) an additional factor of 10 is added after the equal signs. For example, the voltage ratio U 1 /U 2 = 10 corresponds to a logarithmic unit of 20 dB .

There is a tendency to use natural systems units based on universal physical constants (constants), which could be taken as basic units: speed of light, Boltzmann's constant, Planck's constant, electron charge, etc. . The advantage of such a system is the constancy of the system base and the high stability of the constants. In some standards, such constants are already used: the standard of the unit of frequency and length, the standard of the unit of constant voltage. But the sizes of units of quantities based on constants, at the current level of technology development, are inconvenient for practical measurements and do not provide the necessary accuracy in obtaining all derived units. However, such advantages of the natural system of units as indestructibility, immutability over time, and independence from location stimulate work to study the possibility of their practical application.

For the first time, a set of basic and derivative units forming a system was proposed in 1832 by K. F. Gauss. The basic units in this system are three arbitrary units - length, mass and time, respectively equal to the millimeter, milligram and second. Later, other systems of units of physical quantities were proposed, based on the metric system of measures and differing in basic units. But all of them, while satisfying some experts, aroused objections from others. This required the creation new system units. To some extent, it was possible to resolve the existing contradictions after the adoption in 1960 by the XI General Conference on Weights and Measures of the International System of Units, abbreviated as SI (SI). In Russia, it was first adopted as preferable (1961), and then after the introduction of GOST 8.417-81 “GSI. Units of physical quantities" - and as mandatory in all areas of science, technology, national economy, as well as in all educational institutions.

The following seven units have been selected as base units in the International System of Units (SI): meter, kilogram, second, ampere, Kelvin, candela, mole.

The International System of Units includes two additional units - for measuring plane and solid angles. These units cannot be included in the category of basic ones, since they are determined by the ratio of two quantities. At the same time, they are not derived units, since they do not depend on the choice of basic units.

Radian (rad) - the angle between two radii of a circle, the arc between which is equal in length to the radius.

Steradian (sr) is a solid angle whose vertex is located at the center of the sphere and which cuts out on the surface. sphere has an area equal to the area of ​​a square with a side equal in length to the radius of the sphere.

In accordance with the Law on Ensuring the Uniformity of Measurements in the Russian Federation, units of quantities of the International System of Units adopted by the General Conference on Weights and Measures recommended by the International Organization of Legal Metrology are allowed to be used in the prescribed manner.

The names, designations and rules for writing units of quantities, as well as the rules for their use on the territory of the Russian Federation, are established by the government of the Russian Federation, with the exception of cases provided for by acts of legislation of the Russian Federation.

The Government of the Russian Federation may allow non-systemic units of quantities to be used on a par with units of quantities of the International System of Units.