Physical quantity - a property of physical objects that is qualitatively common to many objects, but quantitatively individual for each of them. The qualitative side of the concept of “physical quantity” determines its type (for example, electrical resistance as a general property of electrical conductors), and the quantitative side determines its “size” (the value of the electrical resistance of a specific conductor, for example R = 100 Ohm). The numerical value of the measurement result depends on the choice of unit of physical quantity.
Physical quantities are assigned alphabetic symbols used in physical equations expressing relationships between physical quantities that exist in physical objects.
Size of physical quantity - quantitative determination of a value inherent in a specific object, system, phenomenon or process.
Physical quantity value- assessment of the size of a physical quantity in the form of a certain number of units of measurement accepted for it. Numerical value of a physical quantity- an abstract number expressing the ratio of the value of a physical quantity to the corresponding unit of a given physical quantity (for example, 220 V is the value of the voltage amplitude, and the number 220 itself is a numerical value). It is the term “value” that should be used to express the quantitative side of the property under consideration. It is incorrect to say and write “current value”, “voltage value”, etc., since current and voltage are themselves quantities (the correct use of the terms “current value”, “voltage value”).
With a selected assessment of a physical quantity, it is characterized by true, actual and measured values.
The true value of a physical quantity They call the value of a physical quantity that would ideally reflect the corresponding property of an object in qualitative and quantitative terms. It is impossible to determine it experimentally due to inevitable measurement errors.
This concept is based on two main postulates of metrology:
§ the true value of the quantity being determined exists and is constant;
§ the true value of the measured quantity cannot be found.
In practice, they operate with the concept of a real value, the degree of approximation of which to the true value depends on the accuracy of the measuring instrument and the error of the measurements themselves.
The actual value of a physical quantity they call it a value found experimentally and so close to the true value that for a certain purpose it can be used instead.
Under measured value understand the value of the quantity measured by the indicator device of the measuring instrument.
Unit of physical quantity - a fixed-size value, which is conventionally assigned a standard numerical value equal to one.
Units of physical quantities are divided into basic and derivative and combined into systems of units of physical quantities. The unit of measurement is established for each of the physical quantities, taking into account the fact that many quantities are interconnected by certain dependencies. Therefore, only some of the physical quantities and their units are determined independently of the others. Such quantities are called main. Other physical quantities - derivatives and they are found using physical laws and dependencies through the basic ones. A set of basic and derived units of physical quantities, formed in accordance with accepted principles, is called system of units of physical quantities. The unit of a basic physical quantity is basic unit systems.
International system of units (SI system; SI - French. Systeme International) was adopted by the XI General Conference on Weights and Measures in 1960.
The SI system is based on seven basic and two additional physical units. Basic units: meter, kilogram, second, ampere, kelvin, mole and candela (Table 1).
Table 1. International SI units
|
Name |
Dimension |
Name |
Designation |
|
|
international |
||||
|
Basic |
||||
|
kilogram |
||||
|
Electric current strength |
||||
|
Temperature |
||||
|
Quantity of substance |
||||
|
The power of light |
||||
|
Additional |
||||
|
Flat angle |
||||
|
Solid angle |
steradian |
Meter equal to the distance traveled by light in a vacuum in 1/299792458 of a second.
Kilogram- a unit of mass defined as the mass of the international prototype kilogram, representing a cylinder made of an alloy of platinum and iridium.
Second is equal to 9192631770 periods of radiation corresponding to the energy transition between two levels of the hyperfine structure of the ground state of the cesium-133 atom.
Ampere- the strength of a constant current, which, passing through two parallel straight conductors of infinite length and negligibly small circular cross-sectional area, located at a distance of 1 m from each other in a vacuum, would cause an interaction force equal to 210 -7 N (newton) on each section of the conductor 1 m long.
Kelvin- a unit of thermodynamic temperature equal to 1/273.16 of the thermodynamic temperature of the triple point of water, i.e., the temperature at which the three phases of water - vapor, liquid and solid - are in dynamic equilibrium.
Mole- the amount of substance containing as many structural elements as are contained in carbon-12 weighing 0.012 kg.
Candela- the intensity of light in a given direction of a source emitting monochromatic radiation with a frequency of 54010 12 Hz (wavelength about 0.555 microns), whose energy radiation intensity in this direction is 1/683 W/sr (sr - steradian).
Additional units SI systems are intended only to form units of angular velocity and angular acceleration. Additional physical quantities of the SI system include plane and solid angles.
Radian (glad) - the angle between two radii of a circle whose arc length is equal to this radius. In practical cases, the following units of measurement of angular quantities are often used:
degree - 1 _ = 2p/360 rad = 1.745310 -2 rad;
minute - 1" = 1 _ /60 = 2.9088 10 -4 rad;
second - 1"= 1"/60= 1 _ /3600 = 4.848110 -6 rad;
radian - 1 rad = 57 _ 17 "45" = 57.2961 _ = (3.4378 10 3)" = (2.062710 5)".
Steradian (Wed) - a solid angle with a vertex at the center of the sphere, cutting out an area on its surface equal to the area of a square with a side equal to the radius of the sphere.
Measure solid angles using plane angles and calculation
Where b- solid angle; ts- a plane angle at the vertex of a cone formed inside a sphere by a given solid angle.
Derived units of the SI system are formed from basic and supplementary units.
In the field of measurements of electrical and magnetic quantities, there is one basic unit - ampere (A). Through the ampere and the unit of power - watt (W), common for electrical, magnetic, mechanical and thermal quantities, all other electrical and magnetic units can be determined. However, today there are no sufficiently accurate means of reproducing watts using absolute methods. Therefore, electrical and magnetic units are based on units of current and the ampere-derived unit of capacitance, the farad.
Physical quantities derived from ampere also include:
§ unit of electromotive force (EMF) and electrical voltage - volt (V);
§ unit of frequency - hertz (Hz);
§ unit of electrical resistance - ohm (Ohm);
§ unit of inductance and mutual inductance of two coils - henry (H).
In table 2 and 3 show the derived units most used in telecommunication systems and radio engineering.
Table 2. Derived SI units
|
Magnitude |
||||
|
Name |
Dimension |
Name |
Designation |
|
|
international |
||||
|
Energy, work, amount of heat |
||||
|
Strength, weight |
||||
|
Power, energy flow |
||||
|
Amount of electricity |
||||
|
Electrical voltage, electromotive force (EMF), potential |
||||
|
Electrical capacity |
L -2 M -1 T 4 I 2 |
|||
|
Electrical resistance |
||||
|
Electrical conductivity |
L -2 M -1 T 3 I 2 |
|||
|
Magnetic induction |
||||
|
Magnetic induction flux |
||||
|
Inductance, mutual inductance |
Table 3. SI units used in measurement practice
|
Magnitude |
||||
|
Name |
Dimension |
Unit |
Designation |
|
|
international |
||||
|
Electric current density |
ampere per square meter |
|||
|
Electric field strength |
volt per meter |
|||
|
Absolute dielectric constant |
L 3 M -1 T 4 I 2 |
farad per meter |
||
|
Electrical resistivity |
ohm per meter |
|||
|
Total power of the electrical circuit |
volt-ampere |
|||
|
Reactive power of an electrical circuit |
||||
|
Magnetic field strength |
ampere per meter |
Abbreviations for units, both international and Russian, named after great scientists, are written in capital letters, for example ampere - A; om - Om; volt - V; farad - F. For comparison: meter - m, second - s, kilogram - kg.
In practice, the use of whole units is not always convenient, since very large or very small values are obtained as a result of measurements. Therefore, the SI system has its decimal multiples and submultiples, which are formed using multipliers. Multiple and submultiple units of quantities are written together with the name of the main or derived unit: kilometer (km), millivolt (mV); megaohm (MΩ).
Multiple unit of physical quantity- a unit greater than an integer number of times the system one, for example kilohertz (10 3 Hz). Submultiple unit of physical quantity- a unit that is an integer times smaller than the system one, for example a microhenry (10 -6 H).
The names of multiple and submultiple units of the SI system contain a number of prefixes corresponding to the factors (Table 4).
Table 4. Factors and prefixes for the formation of decimal multiples and submultiples of SI units
|
Factor |
Console |
Prefix designation |
|
|
international |
|||
For a quantitative description of various properties of physical objects, physical systems, phenomena or processes, RMG 29-99 (Recommendations for interstate standardization) introduced the concept quantities.
Magnitude- this is a property that can be distinguished from other properties and assessed in one way or another, including quantitatively.
The quantities are divided into perfect And real .
Ideal values mainly relate to the field of mathematics and are a generalization (model) of specific real concepts. They are calculated in one way or another.
Real values are divided into physical and non-physical.
Physical quantity in the general case, it can be defined as a quantity characteristic of certain material objects (processes, phenomena) studied in the natural (physics, chemistry) and technical sciences. Physical quantities include mass, temperature, time, length, voltage, pressure, speed, etc.
TO non-physical These include quantities inherent in social (non-physical) sciences - philosophy, sociology, economics, etc. Non-physical quantities for which a unit of measurement cannot be entered can only be estimated. Examples of non-physical quantities: student assessment on a 5-point scale, the number of employees in an organization, the price of a product, tax rate, etc. The assessment of non-physical quantities is not part of the tasks of theoretical metrology.
Physical quantity– one of the properties of a physical object, common in a qualitative sense for many physical objects, but quantitatively individual for each of them (the qualitative side determines the “kind” of a quantity, for example, electrical resistance as a general property of conductors of electricity, and the quantitative side – its “size” ", for example, the resistance of a particular conductor).
There are physical quantities measurable And assessed.
Measured physical quantities can be expressed quantitatively in terms of a specific number of established units of measurement.
Estimated physical quantities– quantities for which, for some reason, a unit of measurement cannot be entered, and they can only be estimated.
Assessment– the operation of assigning a certain number of units accepted for it to a given physical quantity, carried out according to established rules. Assessment is carried out using scales.
To express the quantitative content of a property of a particular object, the concept of “size of physical quantity” is used, the assessment of which is established during the measurement process.
Size of physical quantity(size of a quantity) is the quantitative determination of a physical quantity inherent in a specific material object, system, phenomenon or process.
For example, each person has a certain height and weight, as a result of which people can be distinguished by their height or weight, i.e. according to the sizes of the physical quantities that interest us.
Size is an objective quantitative characteristic that does not depend on the choice of units of measurement.
For example, if we write 3.5 kg and 3500 g, then these are two representations of the same size. Each of them is meaning physical quantity (in this case, mass).
Physical quantity value is an expression of the size of a physical quantity in the form of a certain number of units accepted for it.
Physical quantity value Q obtained as a result of measurement and calculated in accordance with basic measurement equation:
Q = q[Q], (1)
where q is an abstract number called numerical value, and [Q] – unit size measurement of a given physical quantity.
Numerical value of a physical quantity– an abstract number expressing the ratio of the value of a quantity to the corresponding unit of a given physical quantity.
Numeric value The measurement result will depend on the choice of unit of physical quantity. (Example about a boa constrictor from a cartoon).
The numbers 3.5 and 3500 are abstract numbers included in the value of a physical quantity and indicating the numerical values of a physical quantity. In the example given, the mass of the object is given in numbers - 3.5 and 3500, and the units are kilogram (kg) and gram (g).
Meaning values should not be confused with size. The size of the physical quantity of a given object really exists and regardless of whether we know it or not, whether we express it in any units or not. The value of a physical quantity appears only after the size of the quantity of a given object is expressed using some unit.
Unit of physical quantity- a physical quantity of a fixed size, which is conventionally assigned a numerical value equal to one. It is used for the quantitative expression of homogeneous physical quantities.
Homogeneous physical quantities are physical quantities that are expressed in the same units and can be compared with each other (for example, the length and diameter of a part).
Physical quantities are combined into system.
System of physical quantities(system of quantities) is a set of physical quantities formed in accordance with accepted principles, when some quantities are taken as independent, and others are determined as functions of these independent quantities.
All quantities included in the system of physical quantities are divided into basic And derivatives.
Basic 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.
A formalized reflection of the qualitative difference in physical quantities is their dimension.
Dimension of a physical quantity - this is an expression reflecting the relationship of a given quantity with physical quantities accepted in a given system of units as basic ones with a proportionality coefficient equal to one.
The dimension of a physical quantity is indicated by the symbol dim (from the Latin dimension - dimension).
The dimensions of basic physical quantities are indicated by the corresponding capital letters:
length - dim l = L
mass - dim m = M
time - dim t = T
electric current strength – dim i= I
thermodynamic temperature – dim Q = Q
amount of substance - dim n = N
luminous intensity – dim j = J
Dimension dim x any derivative of a physical quantity X determined through the equation of connection between quantities. It has the form of a product of basic quantities raised to the appropriate powers:
dim x = L a M b T g I e Qi N v J t ,(2)
where L, M, T, I... - symbols of the main quantities of this system;
a, b, g, e... - indicators of dimension, each of which can be positive or negative, an integer or fractional number, as well as zero.
Dimension indicator - exponent to which the dimension of a basic physical quantity included in the dimension of a derivative physical quantity is raised.
According to the presence of dimension, physical quantities are divided into dimensional And dimensionless.
Dimensional physical quantity– a physical quantity in the dimension of which at least one of the basic physical quantities is raised to a power not equal to zero.
Dimensionless physical quantity– all dimension indicators are equal to zero. They do not have units of measurement, that is, they are not measured in anything ( For example, friction coefficient).
Measurement scales
Assessment and measurement of physical quantities is carried out using various scales.
Measurement scale is an ordered set of values of a physical quantity that serves as the basis for its measurement.
Let us explain this concept using the example of temperature scales. In the Celsius scale, the melting temperature of ice is taken as the starting point, and the boiling point of water is taken as the main interval (reference point). One hundredth of this interval is the unit of temperature (degree Celsius).
The following main types are distinguished: measurement scales: names, order, differences (intervals), ratios and absolute scales.
Name scales reflect quality properties. The elements of these scales are characterized only by relations of equivalence (equality) and similarity of specific qualitative manifestations of properties.
An example of such scales is the scale for classifying (evaluating) the color of objects by name (red, orange, yellow, green, etc.), based on standardized color atlases, systematized by similarity. Measurements in the color scale are made by comparing, under certain lighting, color samples from the atlas with the color of the object under study and establishing the equality (equivalence) of their colors.
The naming scales do not contain such concepts as “zero”, “unit of measurement”, “dimension”, “more” or “less”. The naming scale can consist of any symbols (number, name, other symbols). The numbers or numbers of such a scale are nothing more than code signs.
The naming scale allows you to make classifications, identify and distinguish objects.
Order scale(rank scale) - arranges objects relative to any of their properties in descending or ascending order.
The resulting ordered series is called ranked. He can give answers to the questions: “What is more or less?”, “What is worse or better?”. The order scale cannot provide more detailed information - how much more or less, how many times better or worse.
An example of an order scale is a group of people built by height, where each subsequent one is lower than all the previous ones; knowledge scoring; athlete's place; wind (Beaufort scale) and earthquake (Richter scale) scales; scales of hardness numbers (Rockwell, Brinell, Vickers scales), etc.
Order scales may or may not have a zero element ( for example, ranked accuracy classes of instruments (0,1 and 2)).
Using order scales, you can measure qualitative indicators that do not have a strict quantitative measure. These scales are used especially widely in the humanities: pedagogy, psychology, sociology.
Difference scale(intervals) contains the difference between the values of a physical quantity. For these scales, relations of equivalence, order, and summation of intervals (differences) between quantitative manifestations of properties make sense.
This scale consists of identical intervals, has a conventional (accepted by agreement) unit of measurement and an arbitrarily chosen reference point - zero.
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Books
- Hydraulics. Textbook and workshop for academic bachelor's degree, V.A. Kudinov. The textbook outlines the basic physical and mechanical properties of liquids, issues of hydrostatics and hydrodynamics, provides the basics of the theory of hydrodynamic similarity and mathematical modeling...
- Hydraulics 4th ed., trans. and additional Textbook and workshop for academic bachelor's degree, Eduard Mikhailovich Kartashov. The textbook outlines the basic physical and mechanical properties of liquids, issues of hydrostatics and hydrodynamics, provides the basics of the theory of hydrodynamic similarity and mathematical modeling...
Physical quantity- this is a physical quantity that, by agreement, is assigned a numerical value equal to one.
The tables show basic and derived physical quantities and their units adopted in the International System of Units (SI).
Correspondence of a physical quantity in the SI system
Basic quantities
| Magnitude | Symbol | SI unit | Description |
| Length | l | meter (m) | The extent of an object in one dimension. |
| Weight | m | kilogram (kg) | A quantity that determines the inertial and gravitational properties of bodies. |
| Time | t | second (s) | Duration of the event. |
| Electric current strength | I | ampere (A) | Charge flowing per unit time. |
| Thermodynamic temperature | T | kelvin (K) | The average kinetic energy of the object's particles. |
| The power of light | candela (cd) | The amount of light energy emitted in a given direction per unit time. | |
| Quantity of substance | ν | mole (mol) | Number of particles divided by the number of atoms in 0.012 kg 12 C |
Derived quantities
| Magnitude | Symbol | SI unit | Description |
| Square | S | m 2 | The extent of an object in two dimensions. |
| Volume | V | m 3 | The extent of an object in three dimensions. |
| Speed | v | m/s | The speed of changing body coordinates. |
| Acceleration | a | m/s² | The rate of change in the speed of an object. |
| Pulse | p | kg m/s | Product of mass and speed of a body. |
| Force | kg m/s 2 (newton, N) | An external cause of acceleration acting on an object. | |
| Mechanical work | A | kg m 2 /s 2 (joule, J) | Dot product of force and displacement. |
| Energy | E | kg m 2 /s 2 (joule, J) | The ability of a body or system to do work. |
| Power | P | kg m 2 /s 3 (watt, W) | Rate of change of energy. |
| Pressure | p | kg/(m s 2) (pascal, Pa) | Force per unit area. |
| Density | ρ | kg/m 3 | Mass per unit volume. |
| Surface density | ρA | kg/m2 | Mass per unit area. |
| Linear density | ρl | kg/m | Mass per unit length. |
| Quantity of heat | Q | kg m 2 /s 2 (joule, J) | Energy transferred from one body to another by non-mechanical means |
| Electric charge | q | A s (coulomb, Cl) | |
| Voltage | U | m 2 kg/(s 3 A) (volt, V) | Change in potential energy per unit charge. |
| Electrical resistance | R | m 2 kg/(s 3 A 2) (ohm, Ohm) | resistance of an object to the passage of electric current |
| Magnetic flux | Φ | kg/(s 2 A) (Weber, Wb) | A value that takes into account the intensity of the magnetic field and the area it occupies. |
| Frequency | ν | s −1 (hertz, Hz) | The number of repetitions of an event per unit of time. |
| Corner | α | radian (rad) | The amount of change in direction. |
| Angular velocity | ω | s −1 (radians per second) | Angle change rate. |
| Angular acceleration | ε | s −2 (radians per second squared) | Rate of change of angular velocity |
| Moment of inertia | I | kg m 2 | A measure of the inertia of an object during rotation. |
| Momentum | L | kg m 2 /s | A measure of the rotation of an object. |
| Moment of power | M | kg m 2 /s 2 | The product of a force and the length of a perpendicular drawn from a point to the line of action of the force. |
| Solid angle | Ω | steradian (avg) |
Physical size is a physical property of a material object, process, physical phenomenon, characterized quantitatively.
Physical quantity value 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 numbers appearing in the value of a physical quantity.
Units of measurement of physical quantities.
Unit of measurement of physical quantity is a quantity of fixed size that is assigned a numerical 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 a 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, the mass of a body with a unit of weight, etc. But if one researcher measures the length in fathoms and another in feet, it will be difficult for them to compare the two values. Therefore, all physical quantities throughout 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 there must be a corresponding unit of measurement. Standard units is its physical implementation.
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 serves as the duration of any regularly repeating process, for which the movement of the Earth around the Sun is chosen: the Earth makes one revolution per year. But the unit of time is taken not to be a year, but give me a sec.
For a unit speed take the speed of such uniform rectilinear motion at which the body moves 1 m in 1 s.
A separate unit of measurement is used for area, volume, length, etc. Each unit is determined when choosing a particular standard. But the system of units is much more convenient if only a few units are selected 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 will be a square meter, volume will be a cubic meter, speed will be a meter per second, etc.
Basic units The physical quantities in the International System of Units (SI) are: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), candela (cd) and mole (mol).
|
Basic SI units |
|||
|
Magnitude |
Unit |
Designation |
|
|
Name |
Russian |
international |
|
|
Electric current strength |
|||
|
Thermodynamic temperature |
|||
|
The power of light |
|||
|
Quantity of substance |
|||
There are also derived SI units that have their own names:
|
Derived SI units with their own names |
||||
|
Unit |
Derived unit expression |
|||
|
Magnitude |
Name |
Designation |
Through other SI units |
Through SI major and supplementary units |
|
Pressure |
m -1 ChkgChs -2 |
|||
|
Energy, work, amount of heat |
m 2 ChkgChs -2 |
|||
|
Power, energy flow |
m 2 ChkgChs -3 |
|||
|
Amount of electricity, electric charge |
||||
|
Electrical voltage, electrical potential |
m 2 ChkgChs -3 ChA -1 |
|||
|
Electrical capacity |
m -2 Chkg -1 Ch 4 Ch 2 |
|||
|
Electrical resistance |
m 2 ChkgChs -3 ChA -2 |
|||
|
Electrical conductivity |
m -2 Chkg -1 Ch 3 Ch 2 |
|||
|
Magnetic induction flux |
m 2 ChkgChs -2 ChA -1 |
|||
|
Magnetic induction |
kgHs -2 HA -1 |
|||
|
Inductance |
m 2 ChkgChs -2 ChA -2 |
|||
|
Light flow |
||||
|
Illumination |
m 2 ChkdChsr |
|||
|
Radioactive source activity |
becquerel |
|||
|
Absorbed radiation dose |
||||
ANDmeasurements. To obtain an accurate, objective and easily reproducible description of a physical quantity, measurements are used. Without measurements, a physical quantity cannot be characterized quantitatively. Definitions such as “low” or “high” pressure, “low” or “high” temperature reflect only subjective opinions and do not contain comparisons with reference values. When measuring a physical quantity, a certain numerical value is assigned to it.
Measurements are carried out using measuring instruments. There are quite a large number of measuring instruments and devices, 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: by the method of presenting information (displaying or recording), by the method of measurement (direct action and comparison), by the form of presentation of readings (analog and digital), etc.
The following parameters are typical for measuring instruments:
Measuring range- the range of values of the measured quantity for 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- connects the value of the measured parameter and the corresponding change in the 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.
