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Lecture 1.Property. Magnitude. Basic measurement equation
2. Measurements
Quantities, measurements and measuring instruments are studied in detail in the course “Metrology”, which will be taught to you in the fourth year. Here we will look at the main points that we will need to know in the course “Geodetic Instruments and Measurements.”
1. Property. Magnitude. Basic measurement equation
All objects of the surrounding world are characterized by their properties.
For example, we can name such properties of objects as color, weight, length, height, density, hardness, softness, etc. However, from the fact that some object is colored or long, we learn nothing except that it has the property of color or length.
For a quantitative description of various properties, processes and physical bodies, the concept of quantity is introduced.
All quantities can be divided into two types:real And perfect .
Ideal quantities relate mainly to mathematics and are a generalization (model) of specific real concepts. We are not interested in them.
Real quantities are divided, in turn, byphysical And non-physical .
TO non-physical values inherent in social (non-physical) sciences - philosophy, sociology, economics, etc. should be included. We are not interested in these quantities.
Physical a quantity in the general case can be defined as a quantity characteristic of material objects (processes, phenomena) studied in the natural (physics, chemistry) and technical sciences. It is these quantities that are of interest to us.
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.
For example, every object on Earth has such a property as weight. If you take several apples, then each of them has weight. But at the same time, the weight of each apple will be different from the weight of other apples.
Physical quantities can be divided intomeasurable And evaluated.
Physical quantities for which, for one reason or another, a measurement cannot be performed or a unit of measurement cannot be entered, can only be estimated. Such physical quantities are called evaluable . Such physical quantities are assessed using conventional scales. For example, the intensity of earthquakes is estimated by Richter scale, mineral hardness - Mohs scale.
According to the degree of conditional independence from other quantities, physical quantities are divided into basic (conditionally independent),derivatives (conditionally dependent) andadditional .
All modern physics can be built on seven basic quantities that characterize the fundamental properties of the material world. These includeseven physical quantities selected inSI system as main , And two additional physical quantities.
With the help of the main seven and two additional quantities, introduced solely for convenience, the entire variety of derived physical quantities is formed and a description of the properties of physical objects and phenomena is provided.
According to the presence of dimension, physical quantities are divided intodimensional , i.e. having dimension, anddimensionless .
Concept dimensions of a physical quantity was introduced Fourier in 1822.
Dimension
quality
its characteristics and is indicated by the symbol 
, coming from the word dimension
(English - size, dimension). Dimension main
physical quantities are indicated by appropriate capital letters. For example, for length, mass and time
The dimension of a derivative physical quantity is expressed through the dimensions of the basic physical quantities using a power monomial:
Where 
, 
,
, … – dimensions of basic physical quantities;
, 
,
, … – indicators of dimension.
Moreover, each of the dimension indicators can be positive or negative, an integer or fractional number, as well as zero.
If all dimension indicators are equal to zero , then this quantity is called dimensionless .
Size the measured quantity isquantitative its characteristics.
For example, the length of a board is a quantitative characteristic of a board. The length itself can only be determined as a result of measurement.
A set of numbers representing homogeneous quantities of different sizes must be a set of identically named numbers. This naming is unit of physical quantity or its share. The same example with the length of the board. There is a set of numbers characterizing the length of various boards: 110, 115, 112, 120, 117. All numbers are called centimeters. The naming centimeter is a unit of physical quantity, in this case a unit of length.
For example, meter, kilogram, second.
For example, 54.3 meters, 76.8 kilograms, 516 seconds.
For example, 54.3, 76.8, 516.
All three listed parameters are interconnected by the relation
, (3.1) which is calledbasic measurement equation
.
2. Measurements
From the basic measurement equation it follows thatmeasurement - this is the determination of the value of a quantity or, in other words, it is the comparison of a quantity with its unit. Measurements of physical quantities are made using technical means. The following definition of measurement can be given.
This definition contains four characteristics of the concept of measurement.
1. Only physical quantities can be measured(i.e. properties of material objects, phenomena, processes).
2. Measurement is the estimation of a quantity experimentally, i.e. it's always an experiment.
The calculated determination of a quantity using formulas and known initial data cannot be called a measurement.
3. Measurement is carried out using special technical means - carriers of unit sizes or scales, called measuring instruments.
4. Measurement is the determination of the value of a quantity, i.e. is the comparison of a quantity with its unit or scale. This approach has been developed through centuries of measurement practice. It fully corresponds to the content of the concept of “measurement”, which was given more than 200 years ago by L. Euler: “ It is impossible to define or measure one quantity except by taking as known another quantity of the same kind and indicating the ratio in which it is found to it » .
The measurement of a physical quantity includes two (in general, there may be several) stages:
A) comparison of a measured quantity with a unit;
b) transformation into a form convenient for use(various display methods).
The measurements distinguish:
A) measurement principle– this is a physical phenomenon or effect underlying the measurements;
b) measurement method– a technique or set of techniques for comparing a measured physical quantity with its unit in accordance with the implemented measurement principle. The measurement method is usually determined by the design of the measuring instruments.
All possible measurements encountered in human practice can be classified in several directions.
1. Classification by types of measurements :
A) direct measurement – a measurement in which the desired value of a physical quantity is obtained directly.
Examples: measuring the length of a line with a measuring tape, measuring horizontal or vertical angles with a theodolite;
b) indirect measurement – determination of the desired value of a physical quantity based on the results of direct measurements of other physical quantities that are functionally related to the desired quantity.
Example 1. Measuring the lengths of lines using the parallax method, in which the horizontal angle is measured on the marks of the base rail, the distance between which is known; the required length is calculated using formulas relating this length to the horizontal angle and basis.
Example 2. Measuring the length of a line with a range finder. In this case, it is not the line length itself that is directly measured, but the time of passage of the electromagnetic pulse between the emitter and the reflector installed above the points between which the line length is measured.
Example 3. Determination of the spatial coordinates of a point on the earth's surface using the Global Navigation Satellite System (GNSS). In this case, it is not coordinates or even lengths that are measured, but again the time it takes for the signal to travel from each satellite to the receiver. Using the measured time, the distances from the satellites to the receiver are indirectly determined, and then, again, in an indirect way, the coordinates of the standing point are determined.
V) joint measurements – simultaneous measurements of two or more different quantities to determine the relationship between them.
Example. Measuring the length of a metal rod and the temperature at which the length of the rod is measured. The result of such measurements is the determination of the coefficient of linear expansion of the metal from which the rod is made due to temperature changes.
G) aggregate measurements – measurements of several quantities of the same name carried out simultaneously, in which the desired values of the quantities are determined by solving a system of equations obtained by measuring these quantities in various combinations.
2. Classification by measurement methods :
A) direct assessment method– a method in which the value of a quantity is determined directly from the indicating measuring instrument;
examples of measuring pressure with a barometer or temperature with a thermometer;
b) comparison method with measure– a measurement method in which the measured value is compared with the value reproduced by the measure;
examples:
by applying a ruler with divisions to any part, they essentially compare its size with the unit stored by the ruler, and, having made a reading, obtain the value of the quantity (length, height, thickness and other parameters);
using a measuring device, the size of a quantity (for example, an angle), converted into the movement of a pointer (alidade), is compared with the unit stored by the scale of this device (a horizontal circle, dividing a circle is a measure), and a count is made.
A characteristic of measurement accuracy is its error or uncertainty.
When making measurements, the real object being measured is always replaced by its model, which, due to its imperfection, differs from the real object. As a result, the quantities characterizing a real object will also differ from similar quantities of the same object. This leads to inevitable measurement errors, which are generally divided into random and systematic.
Measurement method. The choice of measurement method is determined by the adopted model of the measurement object and the available measuring instruments. When choosing a measurement method, it is ensured that the error of the measurement method, i.e. the component of the systematic measurement error, due to the imperfection of the adopted model and measurement method (otherwise the theoretical error), did not noticeably affect the resulting measurement error, i.e. did not exceed 30% from her.
Object model. Changes in the measured parameters of the model during the observation cycle, as a rule, should not exceed 10% from the specified measurement error. If alternatives are possible, then economic considerations are also taken into account: unnecessary overestimation of the accuracy of the model and measurement method leads to unreasonable costs. The same applies to the choice of measuring instruments.
Measuring instruments. The choice of measuring instruments and auxiliary devices is determined by the quantity being measured, the adopted measurement method and the required accuracy of the measurement results (accuracy standards). Measurements using measuring instruments of insufficient accuracy are of little value (even meaningless), since they can cause incorrect conclusions. The use of overly precise measuring instruments is not economically profitable. The range of changes in the measured quantity, measurement conditions, performance characteristics of measuring instruments, and their cost are also taken into account.
The main attention is paid to the errors of measuring instruments. It is necessary that the total error of the measurement result 
was less than the maximum permissible measurement error 
, i.e.
— maximum error due to the operator.<
A physical quantity is one of the properties of a physical object (phenomenon, process), which is qualitatively common to many physical objects, while differing in quantitative value.
The purpose of measurements is to determine the value of a physical quantity - a certain number of units accepted for it (for example, the result of measuring the mass of a product is 2 kg, the height of a building is 12 m, etc.).
Depending on the degree of approximation to objectivity, true, actual and measured values of a physical quantity are distinguished.
This is a value that ideally reflects the corresponding property of an object in qualitative and quantitative terms. Due to the imperfection of measurement tools and methods, it is practically impossible to obtain the true values of quantities. They can only be imagined theoretically. And the values obtained during measurement only approach the true value to a greater or lesser extent.
This is a value of a quantity found experimentally that is so close to the true value that it can be used instead for a given purpose.
This is the value obtained by measurement using specific methods and measuring instruments.
9. Classification of measurements according to the dependence of the measured value on time and according to sets of measured values.
According to the nature of the change in the measured value - static and dynamic measurements.
Dynamic measurement - a measurement of a quantity whose size changes over time. A rapid change in the size of the measured quantity requires its measurement with the most accurate determination of the moment in time. For example, measuring the distance to the Earth's surface from a balloon or measuring the constant voltage of an electric current. Essentially, a dynamic measurement is a measurement of the functional dependence of the measured quantity on time.
Static measurement - measurement of a quantity that is taken into account in accordance with the assigned measurement task and does not change throughout the measurement period. For example, measuring the linear size of a manufactured product at normal temperature can be considered static, since temperature fluctuations in the workshop at the level of tenths of a degree introduce a measurement error of no more than 10 μm/m, which is insignificant compared to the manufacturing error of the part. Therefore, in this measurement task, the measured quantity can be considered unchanged. When calibrating a line length measure against the state primary standard, thermostatting ensures the stability of maintaining the temperature at the level of 0.005 °C. Such temperature fluctuations cause a thousand times smaller measurement error - no more than 0.01 μm/m. But in this measurement task it is essential, and taking into account temperature changes during the measurement process becomes a condition for ensuring the required measurement accuracy. Therefore, these measurements should be carried out using the dynamic measurement technique.
Based on existing sets of measured values on electrical ( current, voltage, power) , mechanical ( mass, number of products, effort); , thermal power(temperature, pressure); , physical(density, viscosity, turbidity); chemical(composition, chemical properties, concentration) , radio engineering etc.
Classification of measurements according to the method of obtaining the result (by type).
According to the method of obtaining measurement results, they are distinguished: direct, indirect, cumulative and joint measurements.
Direct measurements are those in which the desired value of the measured quantity is found directly from experimental data.
Indirect measurements are those in which the desired value of the measured quantity is found on the basis of a known relationship between the measured quantity and quantities determined using direct measurements.
Cumulative measurements are those in which several quantities of the same name are simultaneously measured and the determined value is found by solving a system of equations that is obtained on the basis of direct measurements of quantities of the same name.
Measurements of two or more different quantities to find the relationship between them are called joint.
Classification of measurements according to the conditions that determine the accuracy of the result and the number of measurements to obtain the result.
According to the conditions that determine the accuracy of the result, measurements are divided into three classes:
1. Measurements of the highest possible accuracy achievable with the existing level of technology.
These include, first of all, standard measurements related to the highest possible accuracy of reproducing established units of physical quantities, and, in addition, measurements of physical constants, primarily universal ones (for example, the absolute value of the acceleration of gravity, the gyromagnetic ratio of a proton, etc.).
This class also includes some special measurements that require high accuracy.
2. Control and verification measurements, the error of which, with a certain probability, should not exceed a certain specified value.
These include measurements performed by laboratories for state supervision of the implementation and compliance with standards and the state of measuring equipment and factory measurement laboratories, which guarantee the error of the result with a certain probability not exceeding a certain predetermined value.
3. Technical measurements in which the error of the result is determined by the characteristics of the measuring instruments.
Examples of technical measurements are measurements performed during the production process at machine-building enterprises, on switchboards of power plants, etc.
Based on the number of measurements, measurements are divided into single and multiple.
A single measurement is a measurement of one quantity made once. In practice, single measurements have a large error; therefore, to reduce the error, it is recommended to perform measurements of this type at least three times, and take their arithmetic average as the result.
Multiple measurements are measurements of one or more quantities performed four or more times. A multiple measurement is a series of single measurements. The minimum number of measurements at which a measurement can be considered multiple is four. The result of multiple measurements is the arithmetic average of the results of all measurements taken. With repeated measurements, the error is reduced.
Classification of random measurement errors.
Random error is a component of measurement error that changes randomly during repeated measurements of the same quantity.
1) Rough - does not exceed the permissible error
2) A miss is a gross error, depends on the person
3) Expected - obtained as a result of the experiment during creation. conditions
Concept of metrology
Metrology– the science of measurements, methods and means of ensuring their unity and methods of achieving the required accuracy. It is based on a set of terms and concepts, the most important of which are given below.
Physical quantity- a property that is qualitatively common to many physical objects, but quantitatively individual for each object. Physical quantities are length, mass, density, force, pressure, etc.
Unit of physical quantity is considered to be the quantity that, by definition, is assigned a value equal to 1. For example, mass 1 kg, force 1 N, pressure 1 Pa. In different systems of units, units of the same quantity may differ in size. For example, for a force of 1 kgf ≈ 10 N.
Physical quantity value– numerical assessment of the physical size of a specific object in accepted units. For example, the mass of a brick is 3.5 kg.
Technical Dimension– determination of the values of various physical quantities using special technical methods and means. During laboratory tests, the values of geometric dimensions, mass, temperature, pressure, force, etc. are determined. All technical measurements must meet the requirements of unity and accuracy.
Direct measurement– experimental comparison of a given value with another, taken as unit, by means of reading on the instrument scale. For example, measuring length, mass, temperature.
Indirect measurements– results obtained using the results of direct measurements by calculations using known formulas. For example, determining the density and strength of a material.
Unity of measurements– a state of measurements in which their results are expressed in legal units and measurement errors are known with a given probability. Unity of measurements is necessary in order to be able to compare the results of measurements taken in different places, at different times, using a variety of instruments.
Accuracy of measurements– quality of measurements, reflecting the closeness of the results obtained to the true value of the measured value. Distinguish between true and actual values of physical quantities.
True meaning physical quantity ideally reflects the corresponding properties of the object in qualitative and quantitative terms. The true value is free from measurement errors. Since all values of a physical quantity are found empirically and they contain measurement errors, the true value remains unknown.
Real value physical quantities are found experimentally. It is so close to the true value that for certain purposes it can be used instead. In technical measurements, the value of a physical quantity found with an error acceptable by technical requirements is taken as the actual value.
Measurement error– deviation of the measurement result from the true value of the measured value. Since the true value of the measured quantity remains unknown, in practice the measurement error is only approximately estimated by comparing the measurement results with the value of the same quantity obtained with an accuracy several times higher. Thus, the error in measuring the dimensions of a sample with a ruler, which is ± 1 mm, can be estimated by measuring the sample with a caliper with an error of no more than ± 0.5 mm.
Absolute error expressed in units of the measured quantity.
Relative error- the ratio of the absolute error to the actual value of the measured value.
Measuring instruments are technical means used in measurements and having standardized metrological properties. Measuring instruments are divided into measures and measuring instruments.
Measure– a measuring instrument designed to reproduce a physical quantity of a given size. For example, a weight is a measure of mass.
Measuring device– a measuring instrument that serves to reproduce measurement information in a form accessible to perception by an observer. The simplest measuring instruments are called measuring instruments. For example, a ruler, a caliper.
The main metrological indicators of measuring instruments are:
The scale division value is the difference in the values of the measured quantity, corresponding to two adjacent scale marks;
The initial and final values of the scale are, respectively, the smallest and largest values of the measured value indicated on the scale;
Measurement range is the range of values of the measured value for which permissible errors are normalized.
Measurement error– the result of mutual superposition of errors caused by various reasons: errors of the measuring instruments themselves, errors arising when using the device and reading measurement results and errors from non-compliance with measurement conditions. With a sufficiently large number of measurements, the arithmetic mean of the measurement results approaches the true value, and the error decreases.
Systematic error- an error that remains constant or changes naturally with repeated measurements and arises for well-known reasons. For example, the shift of the instrument scale.
Random error is an error in which there is no natural connection with previous or subsequent errors. Its appearance is caused by many random reasons, the influence of which on each measurement cannot be taken into account in advance. The reasons leading to the appearance of a random error include, for example, heterogeneity of the material, irregularities during sampling, and errors in instrument readings.
If the so-called gross error, which significantly increases the error expected under given conditions, then such measurement results are excluded from consideration as unreliable.
The unity of all measurements is ensured by the establishment of units of measurement and the development of their standards. Since 1960, the International System of Units (SI) has been in force, which replaced the complex set of systems of units and individual non-system units developed on the basis of the metric system of measures. In Russia, the SI system has been adopted as standard, and its use in the field of construction has been regulated since 1980.
Lecture 2. PHYSICAL QUANTITIES. UNITS OF MEASUREMENT
2.1 Physical quantities and scales
2.2 Units of physical quantities
2.3. International System of Units (SI System)
2.4 Physical quantities of technological processes
food production
2.1 Physical quantities and scales
A physical quantity is a property that is qualitatively common to many physical objects (physical systems, their states and processes occurring in them), but quantitatively individual for each of them.
Individual in quantitative terms should be understood in such a way that the same property for one object can be a certain number of times greater or less than for another.
Typically, the term "physical quantity" is used to refer to properties or characteristics that can be quantified. Physical quantities include mass, length, time, pressure, temperature, etc. All of them determine qualitatively common physical properties; their quantitative characteristics may be different.
It is advisable to distinguish physical quantities into measured and assessed. Measured EF can be expressed quantitatively in the form of a certain number of established units of measurement. The possibility of introducing and using the latter is an important distinguishing feature of measured EF.
However, there are properties such as taste, smell, etc., for which units cannot be entered. Such quantities can be estimated. Values are assessed using scales.
By accuracy of the result There are three types of values of physical quantities: true, actual, measured.
True value of a physical quantity(true value of a quantity) - the value of a physical quantity that, in qualitative and quantitative terms, would ideally reflect the corresponding property of the object.
The postulates of metrology include
The true value of a certain quantity exists and it is constant
The true value of the measured quantity cannot be found.
The true value of a physical quantity can only be obtained as a result of an endless process of measurements with endless improvement of methods and measuring instruments. For each level of development of measuring technology, we can only know the actual value of a physical quantity, which is used instead of the true one.
Real value of a physical quantity– the value of a physical quantity found experimentally and so close to the true value that it can replace it for the given measurement task. A typical example illustrating the development of measurement technology is the measurement of time. At one time, the unit of time, the second, was defined as 1/86400 of the average solar day with an error of 10 -7 . Currently, the second is determined with an error of 10 -14 , i.e., we are 7 orders of magnitude closer to the true value of determining time at the reference level.
The actual value of a physical quantity is usually taken to be the arithmetic mean of a series of quantity values obtained with equal-precision measurements, or the weighted arithmetic mean with unequal-precision measurements.
Measured value of a physical quantity– the value of a physical quantity obtained using a specific technique.
By type of PV phenomena divided into the following groups :
- real , those. describing the physical and physicochemical properties of substances. Materials and products made from them. These include mass, density, etc. These are passive PVs, because to measure them, it is necessary to use auxiliary energy sources, with the help of which a signal of measurement information is generated.
- energy – describing the energy characteristics of the processes of transformation, transmission and use of energy (energy, voltage, power. These quantities are active. They can be converted into measurement information signals without the use of auxiliary energy sources;
- characterizing the flow of time processes . This group includes various kinds of spectral characteristics, correlation functions, etc.
According to the degree of conditional dependence on other values of PV divided into basic and derivative
Basic physical quantity– a physical quantity included in a system of quantities and conventionally accepted as independent of other quantities of this system.
The choice of physical quantities accepted as basic and their number is carried out arbitrarily. First of all, the quantities that characterize the basic properties of the material world were chosen as the main ones: length, mass, time. The remaining four basic physical quantities are chosen in such a way that each of them represents one of the branches of physics: current strength, thermodynamic temperature, amount of matter, light intensity.
Each basic physical quantity of a system of quantities is assigned a symbol in the form of a lowercase letter of the Latin or Greek alphabet: length - L, mass - M, time - T, electric current - I, temperature - O, amount of substance - N, light intensity - J. These symbols are included in the name of the system of physical quantities. Thus, the system of physical quantities of mechanics, the main quantities of which are length, mass and time, is called the “LMT system”.
Derived physical quantity– a physical quantity included in a system of quantities and determined through the basic quantities of this system.
1.3 Physical quantities and their measurements
Physical quantity – one of the properties of a physical object (physical system, phenomenon or process), common in qualitative terms for many physical objects, but quantitatively individual for each of them. We can also say that a physical quantity is a quantity that can be used in the equations of physics, and by physics here we mean science and technology in general.
Word " magnitude" is often used in two senses: as a general property to which the concept of more or less is applicable, and as the quantity of this property. In the latter case, we would have to talk about the “magnitude of a quantity,” so in what follows we will talk about quantity precisely as a property of a physical object, and in the second sense, as the meaning of a physical quantity.
Recently, the division of quantities into physical and non-physical , although it should be noted that there is no strict criterion for such a division of values. At the same time, under physical understand quantities that characterize the properties of the physical world and are used in physical sciences and technology. There are units of measurement for them. Physical quantities, depending on the rules of their measurement, are divided into three groups:
Quantities characterizing the properties of objects (length, mass);
quantities characterizing the state of the system (pressure,
temperature);
Quantities characterizing processes (speed, power).
TO non-physical refer to quantities for which there are no units of measurement. They can characterize both the properties of the material world and concepts used in social sciences, economics, and medicine. In accordance with this division of quantities, it is customary to distinguish between measurements of physical quantities and non-physical measurements . Another expression of this approach is two different understandings of the concept of measurement:
measurement in in the narrow sense as an experimental comparison
one measurable quantity with another known quantity
the same quality adopted as a unit;
measurement in in a broad sense how to find matches
between numbers and objects, their states or processes according to
known rules.
The second definition appeared in connection with the recent widespread use of measurements of non-physical quantities that appear in biomedical research, in particular in psychology, economics, sociology and other social sciences. In this case, it would be more correct to talk not about measurement, but about estimating quantities , understanding assessment as establishing the quality, degree, level of something in accordance with established rules. In other words, this is an operation of attributing by calculating, finding or determining a number to a quantity characterizing the quality of an object, according to established rules. For example, determining the strength of wind or earthquake, grading figure skaters or assessing student knowledge on a five-point scale.
Concept assessment quantities should not be confused with the concept of estimating quantities, associated with the fact that as a result of measurements we actually do not receive the true value of the measured quantity, but only its assessment, to one degree or another close to this value.
The concept discussed above measurement", which presupposes the presence of a unit of measurement (measure), corresponds to the concept of measurement in the narrow sense and is more traditional and classical. In this sense, it will be understood below - as a measurement of physical quantities.
Below are about basic concepts , related to a physical quantity (hereinafter, all basic concepts in metrology and their definitions are given according to the above-mentioned recommendation on interstate standardization RMG 29-99):
- size of a physical quantity - quantitative certainty of a physical quantity inherent in a specific material object, system, phenomenon or process;
- physical quantity value - expression of the size of a physical quantity in the form of a certain number of units accepted for it;
- true value of a physical quantity - the value of a physical quantity that ideally characterizes the corresponding physical quantity in qualitative and quantitative terms (can be correlated with the concept of absolute truth and is obtained only as a result of an endless process of measurements with endless improvement of methods and measuring instruments);
actual value of a physical quantity 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;
unit of measurement of physical quantity a physical quantity of a fixed size, which is conventionally assigned a numerical value equal to 1, and used for the quantitative expression of physical quantities similar to it;
system of physical quantities a set of physical quantities formed in accordance with accepted principles, when some quantities are taken as independent, while others are defined as functions of these independent quantities;
main physical quantity – a physical quantity included in a system of quantities and conventionally accepted as independent of other quantities of this system.
derived physical quantity – a physical quantity included in a system of quantities and determined through the basic quantities of this system;
system of units of physical units a set of basic and derived units of physical quantities, formed in accordance with the principles for a given system of physical quantities.
Metrology, standardization and certification Demidova N.V.
4 The concept of physical quantity The meaning of systems of physical units
A physical quantity is a concept of at least two sciences: physics and metrology. By definition, a physical quantity is a certain property of an object or process, common to a number of objects in terms of qualitative parameters, but differing, however, in quantitative terms (individual for each object). There are a number of classifications created according to various criteria. The main ones are divided into:
1) active and passive physical quantities - when divided in relation to measurement information signals. Moreover, the first (active) in this case are quantities that, without the use of auxiliary energy sources, have the probability of being converted into a measurement information signal. And the second (passive) are quantities for which it is necessary to use auxiliary energy sources that create a signal of measurement information;
2) additive (or extensive) and non-additive (or intensive) physical quantities - when dividing on the basis of additivity. It is believed that the first (additive) quantities are measured in parts; in addition, they can be accurately reproduced using a multivalued measure based on the summation of the sizes of individual measures. But the second (non-additive) quantities are not directly measured, since they are converted into a direct measurement of a quantity or a measurement by indirect measurements. In 1791, the first ever system of units of physical quantities was adopted by the French National Assembly. It was a metric system of measures. It included: units of length, area, volume, capacity and weight. And they were based on two now well-known units: the meter and the kilogram.
The scientist based his methodology on three main independent quantities: mass, length, time. And the mathematician took the milligram, millimeter and second as the main units of measurement for these quantities, since all other units of measurement can be easily calculated using the minimum ones. Thus, at the present stage of development, the following main systems of units of physical quantities are distinguished:
1) GHS system(1881);
2) MKGSS system(end of the 19th century);
3) MKSA system(1901)
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Physical quantity and its characteristics.
All objects of the material world have a number of properties that allow us to distinguish one object from another.
Property an object is an objective feature that manifests itself during its creation, operation and consumption.
The property of an object must be expressed qualitatively - in the form of a verbal description, and quantitatively - in the form of graphs, figures, diagrams, tables.
Metrological science deals with measuring the quantitative characteristics of material objects - physical quantities.
Physical quantity- ϶ᴛᴏ a property that is qualitatively inherent in many objects, and quantitatively is individual for each of them.
Eg, mass have all material objects, but each of them mass value individual.
Physical quantities are divided into measurable And assessed.
Measurable physical quantities can be expressed quantitatively in the form of a certain number of established units of measurement.
Eg, the network voltage value is 220 IN.
Physical quantities that do not have a unit of measurement can only be estimated. For example, smell, taste. Their assessment is carried out by tasting.
Some quantities can be estimated on a scale. For example: hardness of the material - on the Vickers, Brinel, Rockwell scale, earthquake strength - on the Richter scale, temperature - on the Celsius (Kelvin) scale.
Physical quantities can be qualified by metrological criteria.
By types of phenomena they are divided into
A) real, describing the physical and physico-chemical properties of substances, materials and products made from them.
For example, mass, density, electrical resistance (to measure the resistance of a conductor, current must pass through it, this measurement is called passive).
b) energy, describing the characteristics of the processes of transformation, transmission and use of energy.
These include: current, voltage, power, energy. These physical quantities are called active. They do not require an auxiliary energy source.
There is a group of physical quantities that characterize the course of processes over time, for example, spectral characteristics, correlation functions.
By accessories to various groups of physical processes, the quantities are
· spatio-temporal,
· mechanical,
· electrical,
· magnetic,
· thermal,
· acoustic,
· light,
· physical and chemical,
· ionizing radiation, atomic and nuclear physics.
By degrees of conditional independence physical quantities are divided into
· main (independent),
· derivatives (dependent),
· additional.
By presence of dimension physical quantities are divided into dimensional and dimensionless.
Example dimensional magnitude is force, dimensionless- level sound power.
To quantify a physical quantity, the concept is introduced size physical quantity.
Size of physical quantity- this is the quantitative certainty of a physical quantity inherent in a specific material object, system, process or phenomenon.
Eg, each body has a certain mass, therefore, they can be distinguished by mass, ᴛ.ᴇ. by physical size.
The expression of the size of a physical quantity in the form of a certain number of units accepted for it is defined as the value of a physical quantity.
The value of a physical quantity is This is an expression of a physical quantity in the form of a certain number of units of measurement accepted for it.
The measurement process is a procedure for comparing an unknown quantity with a known physical quantity (compared) and in this regard the concept is introduced true meaning physical quantity.
True value of a physical quantity- ϶ᴛᴏ the value of a physical quantity, ĸᴏᴛᴏᴩᴏᴇ ideally characterizes the corresponding physical quantity in qualitative and quantitative ratio.
The true value of independent physical quantities is reproduced in their standards.
The true meaning is rarely used, more used real value physical quantity.
Real value of a physical quantity- ϶ᴛᴏ value obtained experimentally and somewhat close to the true value.
Previously, there was the concept of “measurable parameters,” but now, according to the regulatory document RMG 29-99, the concept of “measurable quantities” is recommended.
There are many physical quantities and they are systematized. A system of physical quantities is a set of physical quantities formed in accordance with accepted rules, when some quantities are taken as independent, while others are defined as functions of independent quantities.
In the name of a system of physical quantities, symbols of quantities accepted as basic ones are used.
For example, in mechanics, where lengths are taken as basic - L , weight - m and time - t , the name of the system accordingly is Lm t .
The system of base quantities corresponding to the international system of SI units is expressed by symbols LmtIKNJ , ᴛ.ᴇ. symbols of basic quantities are used: length - L , weight - M , time - t , current strength - I , temperature - K, the amount of substance - N , the power of light - J .
Basic physical quantities do not depend on the values of other quantities of this system.
Derived physical quantity- ϶ᴛᴏ physical quantity included in a system of quantities and determined through the basic quantities of this system. For example, force is defined as mass times acceleration.
3. Units of measurement of physical quantities.
A unit of measurement of a physical quantity is usually called a quantity that, by definition, is assigned a numerical value equal to 1 and which is used for the quantitative expression of physical quantities homogeneous with it.
Units of physical quantities are combined into a system. The first system was proposed by Gauss K (millimeter, milligram, second). Now the SI system is in force; previously there was a standard of the CMEA countries.
Units of measurement are divided into basic, additional, derivative and non-systemic.
In the SI system seven basic units:
· length (meter),
· weight (kilogram),
· time (second),
· thermodynamic temperature (kelvin),
· amount of substance (mol),
· electric current strength (ampere),
· luminous intensity (candela).
Table 1
Designation of SI base units
| Physical quantity | Unit of measurement | |||
| Name | Designation | 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 | A |
| Thermodynamic temperature | T | kelvin | TO | TO |
| Quantity of substance | n, v | mole | mole | mol |
| Power of light | J | candela | cd | cd |
| additional | ||||
| Flat angle | - | radian | glad | rad |
| Solid angle | - | steradian | Wed | sr |
Note. A radian is the 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 0 17 ’ 48 ’’ .
Steradian is a solid angle, the vertex of which is located at the center of the sphere and which cuts out on the surface of the sphere an area equal to the area of a square with a side length equal to the radius of the sphere. The solid angle is measured by determining plane angles and carrying out additional calculations using the formula:
Q = 2p (1 - cosa/2),
Where Q- solid angle,a - a plane angle at the vertex of a cone formed inside a sphere by a given solid angle.
Solid angle 1 Wed corresponds to a plane angle equal to 65 0 32 ’ , cornerp avg - flat angle 120 0 , corner2pср - 180 0 .
Additional SI units are used to form the units of angular velocity, angular acceleration and some other quantities.
The radian and steradian themselves are used mainly for theoretical constructions and calculations, because Most practical angle values (full angle, right angle, etc.) in radians are expressed by transcendental numbers ( 2p, p/2).
Derivatives are called units of measurement obtained using equations of connection between physical quantities. For example, the SI unit of force is newton ( N ):
N = kg∙m/s 2 .
Despite the fact that the SI system is universal, it allows the use of some non-systemic units, which have found wide practical application (for example, a hectare).
They are called non-systemic units that are not included in any of the generally accepted systems of units of physical quantities.
For many practical cases, the selected sizes of physical quantities are inconvenient - too small or large. For this reason, in measurement practice they often use multiples And sub-multiple units.
Multiple It is customary to call a unit an integer number of times larger than a systemic or non-systemic unit. For example, a multiple of one 1km = 1000 m.
Dolnoy It is customary to call a unit an integer number of times less than a systemic or non-systemic unit. For example, a submultiple unit 1 cm = 0,01 m.
After the adoption of the metric system of measures, a decimal system for the formation of multiples and submultiples was adopted, corresponding to the decimal system of our numerical counting. Eg, 10 6 – mega, A 10 -6 – micro.
Physical quantity and its characteristics. - concept and types. Classification and features of the category "Physical quantity and its characteristics." 2017, 2018.