What is called the value of a physical quantity. Basic physical quantities in mechanics, their measurement and units

Physical quantity

Physical quantity - physical property a material object, a physical phenomenon, a process that can be characterized quantitatively.

Meaning physical quantity - one or more (in the case of a tensor physical quantity) numbers characterizing this physical quantity, indicating the unit of measurement , on the basis of which they were obtained.

The size of a physical quantity- the values ​​of the numbers appearing in the value of a physical quantity.

For example, a car can be characterized as physical quantity like mass. Wherein, meaning this physical quantity will be, for example, 1 ton, and size- the number 1, or meaning will be 1000 kilograms, and size- the number 1000. The same car can be characterized using a different physical quantity- speed. Wherein, meaning this physical quantity will be, for example, a vector of a certain direction 100 km / h, and size- number 100.

Dimension of a physical quantity- unit of measurement, appearing in the value of a physical quantity. As a rule, a physical quantity has many different dimensions: for example, length has a nanometer, millimeter, centimeter, meter, kilometer, mile, inch, parsec, light year, etc. Some of these units of measurement (without taking into account their decimal factors) can enter various systems physical units - SI, CGS, etc.

Often a physical quantity can be expressed in terms of other, more fundamental physical quantities. (For example, force can be expressed in terms of the mass of a body and its acceleration). Which means respectively, and the dimension such a physical quantity can be expressed in terms of the dimensions of these more general quantities. (The dimension of force can be expressed in terms of the dimensions of mass and acceleration). (Often such a representation of the dimension of a certain physical quantity in terms of the dimensions of other physical quantities is an independent task, which in some cases has its own meaning and purpose.) The dimensions of such more general quantities are often already basic units one or another system of physical units, that is, those that themselves are no longer expressed through others, even more general quantities.

Example.
If the physical quantity power is written as

P= 42.3 × 10³ W = 42.3 kW, R is the generally accepted letter designation of this physical quantity, 42.3×10³ W- the value of this physical quantity, 42.3×10³ is the size of this physical quantity.

Tue is an abbreviation one of units of measurement of this physical quantity (watts). Litera to is the symbol for the decimal factor "kilo" of the International System of Units (SI).

Dimensional and dimensionless physical quantities

• Dimensional physical quantity- a physical quantity, to determine the value of which it is necessary to apply some unit of measurement of this physical quantity. The vast majority of physical quantities are dimensional.
• Dimensionless physical quantity- a physical quantity, to determine the value of which it is enough only to indicate its size. For example, relative permittivity is a dimensionless physical quantity.

Additive and non-additive physical quantities

• Additive physical quantity- physical quantity, different meanings which can be summed, multiplied by a numerical coefficient, divided by each other. For example, the physical quantity mass is an additive physical quantity.
• Non-additive physical quantity- a physical quantity for which summation, multiplication by a numerical coefficient or division by each other does not have its values physical sense. For example, the physical quantity temperature is a non-additive physical quantity.

Extensive and intensive physical quantities

The physical quantity is called

• extensive, if the magnitude of its value is the sum of the magnitudes of the values ​​of this physical quantity for the subsystems that make up the system (for example, volume, weight);
• intensive if the value of its value does not depend on the size of the system (for example, temperature, pressure).

Some physical quantities, such as angular momentum, area, force, length, time, are neither extensive nor intensive.

Derived quantities are formed from some extensive quantities:

• specific quantity is the quantity divided by the mass (for example, specific volume);
• molar quantity is the quantity divided by the amount of the substance (for example, molar volume).

Scalar, vector, tensor quantities

In the most general case we can say that a physical quantity can be represented by a tensor of a certain rank (valence).

System of units of physical quantities

The system of units of physical quantities is a set of units of measurement of physical quantities, in which there is a certain number of so-called basic units of measurement, and the remaining units of measurement can be expressed through these basic units. Examples of systems of physical units - International System of Units (SI), CGS.

Symbols for physical quantities

Literature

• RMG 29-99 Metrology. Basic terms and definitions.
• Burdun G. D., Bazakutsa V. A. Units of physical quantities. - Kharkiv: Vishcha school,.

In science and technology, units of measurement of physical quantities are used, forming certain systems. The set of units established by the standard for mandatory use is based on the units of the International System (SI). In the theoretical branches of physics, units of the CGS systems are widely used: CGSE, CGSM and the symmetric Gaussian CGS system. Units also find some use technical system MKGSS and some non-systemic units.

The international system (SI) is built on 6 basic units (meter, kilogram, second, kelvin, ampere, candela) and 2 additional ones (radian, steradian). In the final version of the draft standard "Units of Physical Quantities" are given: units of the SI system; units allowed for use on a par with SI units, for example: ton, minute, hour, degree Celsius, degree, minute, second, liter, kilowatt-hour, revolution per second, revolution per minute; units of the CGS system and other units used in theoretical sections of physics and astronomy: light year, parsec, barn, electron volt; units temporarily allowed for use such as: angstrom, kilogram-force, kilogram-force-meter, kilogram-force per square centimeter, millimeter of mercury, horsepower, calorie, kilocalorie, roentgen, curie. The most important of these units and the ratios between them are given in Table P1.

The abbreviations of units given in the tables are used only after the numerical value of the quantity or in the headings of the columns of the tables. You cannot use abbreviations instead of the full names of units in the text without the numerical value of the quantities. When using both Russian and international unit designations, a roman font is used; designations (abbreviated) of units whose names are given by the names of scientists (newton, pascal, watt, etc.) should be written with a capital letter (N, Pa, W); in the notation of units, the dot as a sign of reduction is not used. The designations of the units included in the product are separated by dots as multiplication signs; a slash is usually used as a division sign; if the denominator includes a product of units, then it is enclosed in brackets.

For the formation of multiples and submultiples, decimal prefixes are used (see Table P2). The use of prefixes, which are a power of 10 with an indicator that is a multiple of three, is especially recommended. It is advisable to use submultiples and multiples of units derived from SI units and resulting in numerical values ​​between 0.1 and 1000 (for example: 17,000 Pa should be written as 17 kPa).

It is not allowed to attach two or more prefixes to one unit (for example: 10 -9 m should be written as 1 nm). To form mass units, a prefix is ​​attached to the main name “gram” (for example: 10 -6 kg = = 10 -3 g = 1 mg). If the complex name of the original unit is a product or a fraction, then the prefix is ​​\u200b\u200battached to the name of the first unit (for example, kN∙m). In necessary cases, it is allowed to use submultiple units of length, area and volume (for example, V / cm) in the denominator.

Table P3 shows the main physical and astronomical constants.

Table P1

UNITS OF PHYSICAL MEASUREMENTS IN THE SI SYSTEM

AND THEIR RELATION WITH OTHER UNITS

Name of quantities	Units	Abbreviation	The size	Coefficient for conversion to SI units
GHS	ICSU and non-systemic units
Basic units
Length	meter	m		1 cm=10 -2 m	1 Å \u003d 10 -10 m 1 light year \u003d 9.46 × 10 15 m
Weight	kg	kg		1g=10 -3 kg
Time	second	with			1 h=3600 s 1 min=60 s
Temperature	kelvin	To			1 0 C=1 K
Current strength	ampere	BUT		1 SGSE I \u003d \u003d 1 / 3 × 10 -9 A 1 SGSM I \u003d 10 A
The power of light	candela	cd
Additional units
flat corner	radian	glad			1 0 \u003d p / 180 rad 1¢ \u003d p / 108 × 10 -2 rad 1² \u003d p / 648 × 10 -3 rad
Solid angle	steradian	Wed			Full solid angle=4p sr
Derived units
Frequency	hertz	Hz	s –1

Continuation of Table P1

Angular velocity	radians per second	rad/s	s –1		1 rpm=2p rad/s 1 rpm==0.105 rad/s
Volume	cubic meter	m 3	m 3	1cm 2 \u003d 10 -6 m 3	1 l \u003d 10 -3 m 3
Speed	meters per second	m/s	m×s –1	1cm/s=10 -2 m/s	1km/h=0.278m/s
Density	kilogram per cubic meter	kg / m 3	kg×m -3	1g / cm 3 \u003d \u003d 10 3 kg / m 3
Force	newton	H	kg×m×s –2	1 dyne = 10 -5 N	1 kg=9.81N
Work, energy, amount of heat	joule	J (N×m)	kg × m 2 × s -2	1 erg \u003d 10 -7 J	1 kgf×m=9.81 J 1 eV=1.6×10 –19 J 1 kW×h=3.6×10 6 J 1 cal=4.19 J 1 kcal=4.19×10 3 J
Power	watt	W (J/s)	kg × m 2 × s -3	1erg/s=10 -7 W	1hp=735W
Pressure	pascal	Pa (N / m 2)	kg∙m –1 ∙s –2	1 din / cm 2 \u003d 0.1 Pa	1 atm \u003d 1 kgf / cm 2 \u003d \u003d \u003d 0.981 ∙ 10 5 Pa 1 mm Hg \u003d 133 Pa 1 atm \u003d \u003d 760 mm Hg \u003d \u003d 1.013 10 5 Pa
Moment of power	newton meter	N∙m	kgm 2 ×s -2	1 dyne cm = = 10 –7 N × m	1 kgf×m=9.81 N×m
Moment of inertia	kilogram square meter	kg × m 2	kg × m 2	1 g × cm 2 \u003d \u003d 10 -7 kg × m 2
Dynamic viscosity	pascal second	Pa×s	kg×m –1 ×s –1	1P / poise / \u003d \u003d 0.1 Pa × s

Continuation of Table P1

Kinematic viscosity	square meter for a second	m 2 /s	m 2 × s -1	1St / stokes / \u003d \u003d 10 -4 m 2 / s
Heat capacity of the system	joule per kelvin	J/K	kg×m 2 x x s –2 ×K –1		1 cal / 0 C = 4.19 J / K
Specific heat	joule per kilogram kelvin	J/ (kg×K)	m 2 × s -2 × K -1		1 kcal / (kg × 0 C) \u003d \u003d 4.19 × 10 3 J / (kg × K)
Electric charge	pendant	Cl	A×s	1SGSE q = =1/3×10 –9 C 1SGSM q = =10 C
Potential, electrical voltage	volt	V (W/A)	kg×m 2 x x s –3 ×A –1	1SGSE u = =300 V 1SGSM u = =10 –8 V
tension electric field	volt per meter	V/m	kg×m x x s –3 ×A –1	1 SGSE E \u003d \u003d 3 × 10 4 V / m
Electrical displacement (electrical induction)	pendant per square meter	C/m 2	m –2 ×s×A	1SGSE D \u003d \u003d 1 / 12p x x 10 -5 C / m 2
Electrical resistance	ohm	Ohm (V/A)	kg × m 2 × s -3 x x A -2	1SGSE R = 9×10 11 Ohm 1SGSM R = 10 –9 Ohm
Electrical capacitance	farad	F (C/V)	kg -1 ×m -2 x s 4 ×A 2	1SGSE C \u003d 1 cm \u003d \u003d 1 / 9 × 10 -11 F

End of table P1

magnetic flux	weber	Wb (W×s)	kg × m 2 × s -2 x x A -1	1SGSM f = =1 μs (maxwell) = =10 –8 Wb
Magnetic induction	tesla	T (Wb / m 2)	kg×s –2 ×A –1	1SGSM B = =1 Gs (gauss) = =10 –4 T
tension magnetic field	ampere per meter	A/m	m –1 ×A	1SGSM H \u003d \u003d 1E (oersted) \u003d \u003d 1 / 4p × 10 3 A / m
Magnetomotive force	ampere	BUT	BUT	1SGSM Fm
Inductance	Henry	Hn (Wb/A)	kg×m 2 x x s –2 ×A –2	1SGSM L \u003d 1 cm \u003d \u003d 10 -9 H
Light flow	lumen	lm	cd
Brightness	candela per square meter	cd/m2	m–2 ×cd
illumination	luxury	OK	m–2 ×cd

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 in certain number times more 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 have not yet been learned to quantify, but seek to find a way to quantify them, such as smell, taste, etc. Until we learn how to measure them, we should not call them 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, one can call a physical quantity briefly a quantity if it is obvious without an adjective that we are talking about a physical quantity. In the following text of this book short form the term "quantity" is used only in the indicated sense.

In metrology, the word "value" is given a terminological meaning by imposing a restriction in the form of the adjective "physical". The word "value" is often used to express the size of a given physical quantity. They say: pressure value, speed value, voltage value. This is wrong, since pressure, speed, voltage in the correct sense 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 "value" is superfluous. Indeed, why talk about a large or small "value" of pressure, when you can say: large or small pressure, etc..

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

x = q [x] , (1.1)

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

Unit of physical quantity- a physical quantity, which, by definition, is given a value, equal to one. It can also be said that the unit of a physical quantity is its value, which is taken as a basis for comparing physical quantities of the same kind with it in their quantitative assessment.

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

therefore, it depends on the accepted unit of measurement .

1. Systems of units of physical quantities

When carrying out any measurements, the measured value is compared with another value that is homogeneous with it, taken as a unit. To build a system of units, several physical quantities are chosen arbitrarily. They are called basic. The values ​​determined through the main ones are called derivatives. The set of basic and derived quantities is called a system of physical quantities.

AT general view relationship between derived quantity Z and basic can be represented by the following equation:

Z = L  M  T  I    J  ,

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

The 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 in their quantitative assessment. It is assigned a numerical value of 1 by definition.

Units of basic and derived quantities are called basic and derived units, respectively, their totality is called a system of units. The choice of units within a system is somewhat arbitrary. However, as the basic units, they choose 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 certain areas of science and technology or regions and therefore have become widespread. Non-systemic units include: a unit of power - horsepower, a unit of energy - a kilowatt-hour, units of time - an hour, a day, a unit of temperature - degrees Celsius and many others. They arose during the development of measurement technology to meet practical needs or were introduced for the convenience of using them in 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 greater than a system or off-system unit: kilohertz, megawatt. A fractional unit is one that is an integer number of times less than a system or off-system unit: milliampere, microvolt. Strictly speaking, many off-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, in percent, in ppm. The logarithmic value is the logarithm (usually decimal in radio electronics) of the dimensionless ratio of two quantities of the same name. The unit of the logarithmic value is bel (B), defined by the ratio:

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 flux, etc.); F 1 , F 2 - power quantities of the same name (voltage, current strength, intensity electromagnetic field etc.).

As a rule, a submultiple unit from a bel 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 \u003d 10 corresponds to a logarithmic unit of 20 dB .

There is a tendency to use natural systems of units based on universal physical constants (constants) that could be taken as basic units: the speed of light, Boltzmann's constant, Planck's constant, electron charge, etc. . The advantage of such a system is the constancy of the basis of the system 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 present level of development of technology, 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, invariability in time, independence from location stimulate work on studying the possibility of their practical application.

For the first time, a set of basic and derived units that form 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 a millimeter, a milligram and a 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 entry into force of GOST 8.417-81 “GSI. Units of Physical Quantities" - and as mandatory in all areas of science, technology, the national economy, as well as in all educational institutions.

As the main international system units (SI) the following seven units are selected: meter, kilogram, second, ampere, Kelvin, candela, mole.

The international system of units includes two additional units - for measuring flat and solid angles. These units cannot be introduced into 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 in the center of the sphere and which cuts out on the surface. spheres have an area equal to the area of ​​a square with a side, along the length equal to the radius spheres.

In accordance with the Law on Ensuring the Uniformity of Measurements in the Russian Federation, units 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 application 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 for use, along with units of quantities of the International System of Units, non-systemic units of quantities.

The study of physical phenomena and their regularities, as well as the use of these regularities in human practical activity, is associated with the measurement of physical quantities.

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 object.

A physical quantity is, for example, mass. Different physical objects have mass: all bodies, all particles of matter, particles of the electromagnetic field, etc. Qualitatively, all specific realizations of mass, i.e., the masses of all physical objects, are the same. But the mass of one object can be a certain number of times greater or less than the mass of another. And in this quantitative sense, mass is a property that is individual for each object. Physical quantities are also length, temperature, electric field strength, oscillation period, etc.

Specific realizations of the same physical quantity are called homogeneous quantities. For example, the distance between the pupils of your eyes and the height eiffel tower there are specific realizations of one and the same physical quantity - length, and therefore they are homogeneous quantities. The mass of this book and the mass of the Earth's satellite Kosmos-897 are also homogeneous physical quantities.

Homogeneous physical quantities differ from each other in size. The size of a physical quantity is

the quantitative content in this object of a property corresponding to the concept of "physical quantity".

The sizes of homogeneous physical quantities of various objects can be compared with each other if the values ​​of these quantities are determined.

The value of a physical quantity is an estimate of a physical quantity in the form of a certain number of units accepted for it (see p. 14). For example, the value of the length of a certain body, 5 kg is the value of the mass of a certain body, etc. An abstract number included in the value of a physical quantity (in our examples 10 and 5) is called a numerical value. In the general case, the value X of a certain quantity can be expressed as the formula

where is the numerical value of the quantity, its unit.

It is necessary to distinguish between the true and actual values ​​of a physical quantity.

The true value of a physical quantity is the value of the quantity that would ideally reflect the corresponding property of the object in qualitative and quantitative terms.

The actual value of a physical quantity is the value of the quantity found experimentally and so close to the true value that it can be used instead of it for a given purpose.

Finding the value of a physical quantity empirically using special technical means called measurement.

The true values ​​of physical quantities are, as a rule, unknown. For example, no one knows the true values ​​of the speed of light, the distance from the Earth to the Moon, the mass of an electron, a proton, and others. elementary particles. We do not know the true value of our height and body weight, we do not know and cannot find out the true value of the air temperature in our room, the length of the table at which we work, etc.

However, using special technical means, it is possible to determine the actual

all these and many other values. At the same time, the degree of approximation of these actual values ​​to the true values ​​of physical quantities depends on the perfection of the technical means of measurement used in this case.

Measuring instruments include measures, measuring instruments, etc. A measure is understood as a measuring instrument designed to reproduce a physical quantity of a given size. For example, a weight is a measure of mass, a ruler with millimeter divisions is a measure of length, a measuring flask is a measure of volume (capacity), a normal element is a measure of electromotive force, a quartz oscillator is a measure of the frequency of electrical oscillations, etc.

A measuring device is a measuring instrument designed to generate a signal of measuring information in a form accessible for direct perception by observation. To measuring instruments include dynamometer, ammeter, manometer, etc.

There are direct and indirect measurements.

A direct measurement is a measurement in which the desired value of a quantity is found directly from experimental data. Direct measurements include, for example, the measurement of mass on an equal-arm scale, temperature - with a thermometer, length - with a scale ruler.

Indirect measurement is a measurement in which the desired value of a quantity is found on the basis of a known relationship between it and the quantities subjected to direct measurements. Indirect measurements are, for example, finding the density of a body by its mass and geometric dimensions, finding the specific electrical resistance conductor by its resistance, length and cross-sectional area.

Measurements of physical quantities are based on various physical phenomena. For example, thermal expansion of bodies or the thermoelectric effect is used to measure temperature, gravity is used to measure the mass of bodies by weighing, etc. The set of physical phenomena on which measurements are based is called the principle of measurement. Measurement principles are not covered in this manual. Metrology deals with the study of the principles and methods of measurements, types of measuring instruments, measurement errors and other issues related to measurements.