The numerical value of a physical quantity. Value size. The value of the quantity

The object of metrology are physical quantities. There are various physical objects that have a variety of physical properties, the number of which is unlimited. A person in his desire to know physical objects - objects of knowledge - identifies a certain limited number of properties that are common to a number of objects in qualitatively, but individual for each of them in quantitative terms. Such properties are called physical quantities. The concept of "physical quantity" in metrology, as in physics, a physical quantity is interpreted as a property of physical objects (systems), which is qualitatively common to many objects, but quantitatively individual for each object, i.e. as a property that can be for one object one or another number of times more or less than for another (for example, length, mass, density, temperature, force, speed). The quantitative content of the property corresponding to the concept of "physical quantity" in this object is the size of the physical quantity. The size of a physical quantity exists objectively, regardless of what we know about it.

A set of quantities interconnected by dependencies form a system of physical quantities. Objectively existing dependencies between physical quantities are represented by a number of independent equations. Number of Equations T always less than the number of values P. That's why T quantities of a given system are determined through other quantities, and i quantities - independently of others. The last quantities are usually called the basic physical quantities, and the rest - derivative physical quantities.

The presence of a number of systems of units of physical quantities, as well as a significant number of non-systemic units, the inconvenience associated with recalculation during the transition from one system of units to another, required the unification of units of measurement. The growth of scientific, technical and economic ties between different countries necessitated such unification on an international scale.

A unified system of units of physical quantities was required, practically convenient and covering various areas measurements. At the same time, she had to maintain the principle coherence(equality to unity of the coefficient of proportionality in the equations of connection between physical quantities).

In 1954, the 10th General Conference on Weights and Measures established the six basic units (meter, kilogram, second, ampere, kelvin, and candle) of a practical system of units. The system, based on the six basic units approved in 1954, was called the International System of Units, abbreviated SI (SI- initial letters of the French name Systeme International di Unites). A list of six basic, two additional and the first list of 27 derived units was approved, as well as prefixes for the formation of multiples and submultiples.

In Russia, there is GOST 8.417-2002, which prescribes the mandatory use of SI. It lists units of measurement, their Russian and international titles and established 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, either international or Russian designations can be used (but not both at the same time).

The basic SI units with abbreviations in Russian and Latin letters are given in Table. 9.1.

The definitions of base units, in accordance with the decisions of the General Conference on Weights and Measures, are as follows.

Meter is equal to the length of the path traveled by light in vacuum in

/299792458 For a few seconds.

Kilogram equal to the mass of the international prototype of the kilogram.

Second is equal to 9192631770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.

Ampere equal to the strength of an unchanging current, which, when passing through two parallel rectilinear conductors of infinite length and negligible circular cross-sectional area, located at a distance of 1 m from one another in vacuum, causes an interaction force equal to 2-10-7 in each section of the conductor 1 m long N.

Kelvin equals 1/273.16 of the thermodynamic temperature of the triple point of water.

mole is equal to the amount of substance of a system containing as many structural elements as there are atoms in carbon-12 weighing 0.012 kg.

Candela equal to the 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.

Table 9.1 Basic SI units

Derived units of the International System of Units are formed using the simplest equations between quantities in which the numerical coefficients are equal to one. Yes, for linear speed as a defining equation, you can use the expression for the speed of uniform rectilinear motion v = l/t.

With the length of the path traveled (in meters) and the time t for which this path has been traveled (in seconds), the speed is expressed in meters per second (m / s). Therefore, the SI unit of speed is meter per second is the speed of a rectilinearly and uniformly moving point at which it during the time t moves at a distance of 1 m.

If a numerical coefficient is included in the defining equation, 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.

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

In table. 9.2 provides multipliers and prefixes for the formation of decimal multiples and submultiples and their names.

Table 9.2 Formation of decimal multiples And valley units of measurement

10^-18_________________|atto _______________|____________A ____________|_____________A _____________

It should be borne in mind that when forming multiple and submultiple units of area and volume with the help of prefixes, a dual reading may occur, depending on where the prefix is ​​​​added. So, the abbreviation I km 2 can also be interpreted as 1 square kilometer and as 1,000 square meters, which is obviously not the same thing (1 square kilometer = 1,000,000 square meters). In accordance with international rules, multiples and submultiples of area and volume units should be formed by adding prefixes to the original units. Thus, degrees refer to those units that are obtained as a result of the addition of prefixes. Therefore, 1 km 2 - 1 (km) -= (10 3 m) 2 = 10 6 m 2.

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 have their own names.

Physical quantities, depending on the set of sizes that they can have when changing in a limited range, are divided into continuous (analog) and quantized (discrete) in size (level).

The analog value can have in the given range infinite set sizes. This is the overwhelming number of physical quantities (voltage, current, temperature, length, etc.). The quantized value has only a countable set of sizes in the given range. An example of such a quantity can be a small electric charge, the size of which is determined by the number of electron charges included in it. The dimensions of a quantized quantity can correspond only to certain levels - quantization levels. The difference between two adjacent quantization levels is called the quantization step (quantum). The value of an analog quantity is determined by measurement with an inevitable error. A quantized quantity can be determined by counting its quanta if they are constant.

Physical quantities can be constant or variable in time. When measuring a time-constant quantity, it is sufficient to determine one of its instantaneous values. Time-variable quantities can have a quasi-deterministic or random nature of change. A quasi-deterministic physical quantity is a quantity for which the type of dependence on time is known, but the measured parameter of this dependence is unknown. A random physical quantity is a quantity whose size changes randomly over time. How special case variables in time, it is possible to distinguish quantities discrete in time, i.e. quantities whose dimensions are different from zero only in certain moments time.

Physical quantities are divided into active and passive. Active quantities (e.g. mechanical force, EMF source electric current) are capable of generating measurement information signals without auxiliary energy sources. Passive quantities (for example, mass, electrical resistance, inductance) cannot themselves

generate measurement information signals. To do this, they must be activated using auxiliary energy sources, for example, when measuring the resistance of a resistor, a current must flow through it. Depending on the objects of study, one speaks of electrical, magnetic or non-electrical quantities.

A physical quantity, which, by definition, is assigned a numerical value equal to one, is called a unit of a physical quantity. The size of a unit of a physical quantity can be any. However, measurements must be made in generally accepted units. The community of units on an international scale is established by international agreements.

Physics, as we have already established, studies the general patterns in the world around us. To do this, scientists conduct observations of physical phenomena. However, when describing phenomena, it is customary to use not everyday language, but special words that have a strictly defined meaning - terms. Some physical terms have already met you in the previous paragraph. Many terms you just have to learn and remember their meanings.

In addition, physicists need to describe various properties (characteristics) of physical phenomena and processes, and characterize them not only qualitatively, but also quantitatively. Let's take an example.

We investigate the dependence of the time of the fall of the stone from the height from which it falls. Experience shows what more height, the longer the fall time. This is a qualitative description, it does not allow a detailed description of the result of the experiment. To understand the regularity of such a phenomenon as a fall, you need to know, for example, that with a fourfold increase in height, the time it takes for a stone to fall usually doubles. This is an example of quantitative characteristics of the properties of a phenomenon and the relationship between them.

In order to quantitatively describe the properties (characteristics) of physical objects, processes or phenomena, physical quantities are used. Examples of physical quantities known to you are length, time, mass, speed.

Physical quantities quantitatively describe the properties of physical bodies, processes, phenomena.

Some of the quantities you have encountered before. In mathematics lessons, when solving problems, you measured the lengths of segments, determined the distance traveled. In this case, you used the same physical quantity - length. In other cases, you found the duration of the movement of various objects: a pedestrian, a car, an ant - and also used only one physical quantity for this - time. As you have already noticed, for different objects the same physical quantity takes various meanings. For example, the lengths of different segments may not be the same. Therefore, the same value can take different meanings and be used to characterize a variety of objects and phenomena.

The need to introduce physical quantities also lies in the fact that they are used to write down the laws of physics.

In formulas and calculations, physical quantities are denoted by letters of the Latin and Greek alphabets. There are generally accepted designations, for example, length - l or L, time - t, mass - m or M, area - S, volume - V, etc.

If you write down the value of a physical quantity (the same length of the segment, having received it as a result of the measurement), you will notice that this value is not just a number. Having said that the length of the segment is 100, it is imperative to clarify in what units it is expressed: in meters, centimeters, kilometers, or something else. Therefore, they say that the value of a physical quantity is a named number. It can be represented as a number followed by the name of the unit of this quantity.

The value of a physical quantity = Number * Unit of quantity.

The units of many physical quantities (for example, length, time, mass) originally arose from the needs of everyday life. For them in different times different peoples invented different units. It is interesting that the names of many units of quantities are the same among different peoples, because when choosing these units, the dimensions of the human body were used. For example, a unit of length called a cubit was used in Ancient Egypt, Babylon, the Arab world, England, Russia.

But the length was measured not only in cubits, but also in inches, feet, leagues, etc. It should be said that even with the same names, units of the same size were different for different peoples. In 1960, scientists developed the International System of Units (SI, or SI). This system has been adopted by many countries, including Russia. Therefore, the use of units of this system is mandatory.
It is customary to distinguish between basic and derived units of physical quantities. In SI, the basic mechanical units are length, time, and mass. Length is measured in meters (m), time - in seconds (s), mass - in kilograms (kg). Derived units are formed from the basic ones, using the ratios between physical quantities. For example, a unit of area - a square meter (m 2) - is equal to the area of ​​​​a square with a side length of one meter.

In measurements and calculations, one often has to deal with physical quantities whose numerical values ​​differ many times from the unit of magnitude. In such cases, a prefix is ​​added to the name of the unit, meaning the multiplication or division of the unit by a certain number. Very often they use the multiplication of the accepted unit by 10, 100, 1000, etc. (multiple values), as well as the division of the unit by 10, 100, 1000, etc. (multiple values, i.e., fractions). For example, a thousand meters is one kilometer (1000 m = 1 km), the prefix is ​​​​kilo-.

Prefixes, meaning the multiplication and division of units of physical quantities by ten, one hundred and one thousand, are shown in Table 1.
Results

A physical quantity is a quantitative characteristic of the properties of physical objects, processes or phenomena.

A physical quantity characterizes the same property of a variety of physical objects and processes.

The value of a physical quantity is a named number.
The value of a physical quantity = Number * Unit of quantity.

Questions

1. What are physical quantities for? Give examples of physical quantities.
2. Which of the following terms are physical quantities and which are not? Ruler, car, cold, length, speed, temperature, water, sound, mass.
3. How are physical quantities recorded?
4. What is SI? What is it for?
5. Which units are called basic and which are derivatives? Give examples.
6. The mass of a body is 250 g. Express the mass of this body in kilograms (kg) and milligrams (mg).
7. Express the distance 0.135 km in meters and millimeters.
8. In practice, an off-system unit of volume is often used - a liter: 1 l \u003d 1 dm 3. In SI, the unit of volume is called the cubic metre. How many liters are in one cubic meter? Find the volume of water contained in a cube with an edge of 1 cm, and express this volume in liters and cubic meters, using the necessary prefixes.
9. Name the physical quantities that are necessary to describe the properties of such physical phenomenon like the wind. Use the information received in science lessons, as well as the results of your observations. Plan a physical experiment to measure these quantities.
10. What old and modern units length and time you know?

Physics, as a science that studies natural phenomena, uses a standard research methodology. The main stages can be called: observation, putting forward a hypothesis, conducting an experiment, substantiating a theory. During the observation, distinctive features phenomena, the course of its course, possible reasons and consequences. The hypothesis allows you to explain the course of the phenomenon, to establish its patterns. The experiment confirms (or does not confirm) the validity of the hypothesis. Allows you to establish a quantitative ratio of values ​​in the course of the experiment, which leads to an accurate establishment of dependencies. The hypothesis confirmed in the course of the experiment forms the basis of a scientific theory.

No theory can claim to be reliable if it has not received full and unconditional confirmation during the experiment. Carrying out the latter is associated with measurements of physical quantities characterizing the process. is the basis of measurements.

What it is

Measurement refers to those quantities that confirm the validity of the hypothesis of regularities. A physical quantity is a scientific characteristic physical body, the qualitative ratio of which is common for many similar bodies. For each body, such a quantitative characteristic is purely individual.

If we turn to the special literature, then in the reference book by M. Yudin et al. (1989 edition) we read that a physical quantity is: “a characteristic of one of the properties of a physical object (physical system, phenomenon or process), which is qualitatively common for many physical objects, but quantitatively individual for each object.

Ozhegov's Dictionary (1990 edition) claims that a physical quantity is "the size, volume, length of an object."

For example, length is a physical quantity. Mechanics interprets the length as the distance traveled, electrodynamics uses the length of the wire, in thermodynamics a similar value determines the thickness of the walls of the vessels. The essence of the concept does not change: the units of quantities can be the same, but the value can be different.

A distinctive feature of a physical quantity, say, from a mathematical one, is the presence of a unit of measurement. Meter, foot, arshin are examples of length units.

Units

To measure a physical quantity, it should be compared with a quantity taken as a unit. Remember the wonderful cartoon "Forty-Eight Parrots". To determine the length of the boa constrictor, the heroes measured its length either in parrots, or in elephants, or in monkeys. In this case, the length of the boa constrictor was compared with the height of other cartoon characters. The result quantitatively depended on the standard.

Values ​​- a measure of its measurement in a certain system of units. The confusion in these measures arises not only because of the imperfection and heterogeneity of the measures, but sometimes also because of the relativity of the units.

Russian measure of length - arshin - the distance between the index and thumb fingers. However, the hands of all people are different, and the arshin measured by the hand of an adult man differs from the arshin on the hand of a child or a woman. The same discrepancy between measures of length applies to the fathom (the distance between the tips of the fingers of the arms spread apart) and the elbow (the distance from the middle finger to the elbow of the hand).

It is interesting that men of small stature were taken into the shops as clerks. Cunning merchants saved fabric with the help of several smaller measures: arshin, cubit, fathom.

Systems of measures

Such a variety of measures existed not only in Russia, but also in other countries. The introduction of units of measurement was often arbitrary, sometimes these units were introduced only because of the convenience of their measurement. For example, to measure atmospheric pressure entered mmHg. The famous one, which used a tube filled with mercury, allowed such an unusual value to be introduced.

Engine power was compared with (which is practiced in our time).

Various physical quantities made the measurement of physical quantities not only difficult and unreliable, but also complicating the development of science.

Unified system of measures

A single system of physical quantities, convenient and optimized in every industrial developed country has become an urgent need. The idea of ​​choosing as few units as possible was adopted as a basis, with the help of which other quantities could be expressed in mathematical relations. Such basic quantities should not be related to each other, their meaning is determined unambiguously and clearly in any economic system.

This problem was tried to be solved in various countries. The creation of a unified GHS, ISS and others) was undertaken repeatedly, but these systems were inconvenient either with scientific point vision, or in domestic, industrial use.

The task, set at the end of the 19th century, was solved only in 1958. At the meeting International Committee legal metrology was presented with a unified system.

Unified system of measures

The year 1960 was marked by the historic meeting of the General Conference on Weights and Measures. A unique system called "Systeme internationale d" units "(abbreviated as SI) was adopted by the decision of this honorary meeting. In Russian version this system is called System International (abbreviation SI).

7 basic units and 2 additional units are taken as a basis. Their numerical value is determined in the form of a standard

Table of physical quantities SI

The system itself cannot consist of only seven units, since diversity physical processes in nature requires the introduction of more and more new quantities. The structure itself provides for not only the introduction of new units, but also their relationship in the form of mathematical relationships (they are often called dimension formulas).

The unit of a physical quantity is obtained by multiplying and dividing the basic units in the dimension formula. The absence of numerical coefficients in such equations makes the system not only convenient in all respects, but also coherent (consistent).

Derived units

Units of measurement, which are formed from the seven basic ones, are called derivatives. In addition to the basic and derived units, it became necessary to introduce additional ones (radians and steradians). Their dimension is considered to be zero. Absence measuring instruments to determine them makes it impossible to measure them. Their introduction is due to the use in theoretical studies. For example, the physical quantity "force" in this system is measured in newtons. Since force is a measure of the mutual action of bodies on each other, which is the cause of varying the speed of a body of a certain mass, it can be defined as the product of a unit of mass per unit of speed divided by a unit of time:

F = k٠M٠v/T, where k is the proportionality factor, M is the unit of mass, v is the unit of speed, T is the unit of time.

SI gives the following formula dimensions: H \u003d kg m / s 2, where three units are used. And the kilogram, and the meter, and the second are classified as basic. The proportionality factor is 1.

It is possible to introduce dimensionless quantities, which are defined as a ratio of homogeneous quantities. These include, as is known, equal to the ratio of the friction force to the force of normal pressure.

Table of physical quantities derived from the main ones

Off-system units

The use of historically established values ​​that are not included in the SI or differ only by a numerical coefficient is allowed when measuring values. These are non-systemic units. For example, mmHg, X-ray and others.

Numeric coefficients are used to introduce submultiples and multiples. Prefixes correspond to a certain number. An example is centi-, kilo-, deca-, mega- and many others.

1 kilometer = 1000 meters,

1 centimeter = 0.01 meters.

Typology of values

Let's try to point out a few basic features that allow you to set the type of value.

1. Direction. If the action of a physical quantity is directly related to the direction, it is called vector, others are called scalar.

2. The presence of dimension. The existence of a formula for physical quantities makes it possible to call them dimensional. If in the formula all units have a zero degree, then they are called dimensionless. It would be more correct to call them quantities with a dimension equal to 1. After all, the concept of a dimensionless quantity is illogical. The main property - dimension - has not been canceled!

3. If possible, addition. An additive quantity whose value can be added, subtracted, multiplied by a coefficient, etc. (for example, mass) is a physical quantity that is summable.

4. In relation to the physical system. Extensive - if its value can be composed of the values ​​of the subsystem. An example is the area measured in square meters. Intensive - a quantity whose value does not depend on the system. These include temperature.

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

Physical quantity, as mentioned above, this is a characteristic that is qualitatively common for a variety of objects, processes, phenomena, and quantitatively - 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 the object is the size of the physical quantity, numerical assessment of its size called the value of the physical quantity.

A physical quantity that expresses the same qualitative property is called homogeneous (of the same name ).

The 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 value is the value perfect way reflecting qualitatively and quantitatively the corresponding properties of the object.

Actual value is a value found experimentally and so close to the true that it can be taken instead.

Physical quantities are classified according to a number of criteria. There are the following classification:

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

2) on the basis of additivity, physical quantities are divided into: additive , or extensive, which can be measured in parts, as well as 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 a quantity or a measurement by indirect measurements. (Additivity (lat. additivus - added) is a property of quantities, consisting in the fact that the value of the quantity corresponding to the whole object is equal to the sum of the values ​​of the quantities corresponding to its parts).

Development evolution systems of physical units.

Metric- the first system of units of physical quantities

was adopted in 1791 by the National Assembly of France. She included units of length, area, volume, capacity and weight , which were based on two units - meter and kilogram . It differed 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 of 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, who called it an absolute system. As a basis, he took three quantities independent of each other - mass, length, time .

For the main units these values ​​he took 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 according to 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 base 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;

ICSS 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: a meter - a unit of length, a kilogram - force - a unit of force, a 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 J. Giorgi.

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

SystemSI. In 1954, the commission for the development of 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 as SI) took its name from the initial letters of the French name System International.

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

Table 1 - International system of units

Source: Tyurin N.I. Introduction to metrology. Moscow: 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;

the 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;

ampere is equal to the strength of an unchanging current, which, when passing through two parallel rectilinear conductors of infinite length and negligible circular cross-sectional area, located at a distance of 1 m from one another in vacuum, causes an interaction force on each section of the conductor 1 m long;

candela is equal to the intensity of light in a given direction of a source emitting ionoprotective radiation, the energy intensity of which in this direction is 1/683 W/sr;

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

a mole is equal to the amount of substance of a system containing as many structural elements as there are atoms in C 12 weighing 0.012 kg 2.

Additional units International system of units for measuring flat 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 57°17"48"3;

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

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

Off-system units:

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

Diopter - light intensity for optical instruments;

Reactive power-var (VA);

Astronomical unit (au) - 149.6 million km;

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

Capacity - liter (l);

Area - hectare (ha).

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

The non-SI units are 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 one. In this case, the derived unit is called coherent.

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

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

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

(For example, 1 ml is taken as a unit for measuring the mass of a liquid, therefore it is indicated on the package: 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 l. , 075 liters respectively).

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

Table 2 - Multipliers 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 electronvolts = 0.1602 joules)

It should be borne in mind that when forming multiple and submultiple units of area and volume with the help of prefixes, a dual reading may occur depending on where the prefix is ​​​​added. For example, 1 m 2 can be used as 1 square meter and as 100 square centimeters, which is far from the same thing, because 1 square meter is 10,000 square centimeters.

According to international rules, multiples and submultiples of area and volume units should be formed by adding prefixes to the original units. Degrees refer to those units that are obtained as a result of the addition of prefixes. For example, 1 km 2 \u003d 1 (km) 2 \u003d (10 3 m) 2 \u003d= 10 6 m 2.

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

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

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

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

primary standard provides storage, reproduction of the unit and transmission of dimensions with the highest accuracy in the country, achievable in this area of ​​​​measurement:

- special primary standards- designed to reproduce the unit in conditions in which the direct transfer of the size of the unit from the primary standard with the required accuracy is technically unfeasible, for example, for low and high voltages, microwave and high frequency. They are approved as state standards. In view of the special importance of state standards and in order to give them the force of law, GOST is approved for each state standard. Creates, approves, stores and applies state standards State Committee for 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 of the state standard. Secondary standards in turn divided according to purpose:

Copy standards - designed to transfer the sizes of units 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 - are used to compare standards that, for one reason or another, cannot be directly compared with each other;

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

unit reference - one means or a set of measuring instruments that ensure the storage and reproduction of the unit in order to transfer its size to the lower-level measuring instruments according to the verification scheme, made according to a special specification and officially approved 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 whole country or a 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 transferred 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 workers.

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

Physical quantity called physical property material object, process, physical phenomenon, characterized quantitatively.

The value of a physical quantity expressed by one or more numbers characterizing this physical quantity, indicating the unit of measurement.

The size of a physical quantity are the values ​​of the numbers appearing in the meaning of the physical quantity.

Units of measurement of physical quantities.

The unit of measurement of a physical quantity is a fixed size value that is assigned a numeric value equal to one. It is used for the quantitative expression of physical quantities homogeneous with it. A system of units of physical quantities is a set of basic and derived units based on a certain system of quantities.

Only a few systems of units have become widespread. In most cases, many countries use the metric system.

Basic units.

Measure physical quantity - means to compare it with another similar physical quantity, taken as a unit.

The length of an object is compared with a unit of length, body weight - with a unit of weight, etc. But if one researcher measures the length in sazhens, and another in feet, it will be difficult for them to compare these two values. Therefore, all physical quantities around the world are usually measured in the same units. In 1963, the International System of Units SI (System international - SI) was adopted.

For each physical quantity in the system of units, an appropriate unit of measurement must be provided. Standard units is its physical realization.

The length standard is meter- the distance between two strokes applied on a specially shaped rod made of an alloy of platinum and iridium.

Standard time is the duration of any correctly repeating process, which is chosen as the movement of the Earth around the Sun: the Earth makes one revolution per year. But the unit of time is not a year, but give me a sec.

For a unit speed take the speed of such uniform rectilinear motion, at which the body makes a movement of 1 m in 1 s.

A separate unit of measurement is used for area, volume, length, etc. Each unit is determined when choosing one or another standard. But the system of units is much more convenient if only a few units are chosen as the main ones, and the rest are determined through the main ones. For example, if the unit of length is a meter, then the unit of area is a square meter, volume is a cubic meter, speed is a meter per second, and so on.

Basic units physical quantities in international system units (SI) are: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), candela (cd) and mole (mole).

There are also derived SI units, which have their own names:

ANDmeasurements. To obtain an accurate, objective and easily reproducible description of a physical quantity, measurements are used. Without measurements, a physical quantity cannot be quantified. Definitions such as "low" or "high" pressure, "low" or "high" temperature reflect only subjective opinions and do not contain comparison with reference values. When measuring a physical quantity, it is assigned a certain numerical value.

Measurements are made using measuring instruments. There is quite a large number of measuring instruments and fixtures, from the simplest to the most complex. For example, length is measured with a ruler or tape measure, temperature with a thermometer, width with calipers.

Measuring instruments are classified: according to the method of presenting information (indicating or recording), according to the method of measurement (direct action and comparison), according to the form of presentation of indications (analog and digital), etc.

The measuring instruments are characterized by the following parameters:

Measuring range- the range of values ​​of the measured quantity, on which the device is designed during its normal operation (with a given measurement accuracy).

Sensitivity threshold- the minimum (threshold) value of the measured value, distinguished by the device.

Sensitivity- relates the value of the measured parameter and the corresponding change in instrument readings.

Accuracy- the ability of the device to indicate the true value of the measured indicator.

Stability- the ability of the device to maintain a given measurement accuracy for a certain time after calibration.