In principle, you can imagine anything big number different systems of units, but only a few are widely used. Around the world for scientific and technical measurements and in most countries in industry and everyday life they use the metric system.
Basic units.
In the system of units, for each measured physical quantity there must be a corresponding unit of measurement. Thus, a separate unit of measurement is needed for length, area, volume, speed, etc., and each such unit can be determined by choosing one or another standard. But the system of units turns out to be much more convenient if in it only a few units are selected as basic ones, and the rest are determined through the basic ones. So, if the unit of length is the meter, the standard of which is stored in the State Metrological Service, then the unit of area can be considered square meter, unit of volume - cubic meter, unit of speed - meter per second, etc.
The convenience of such a system of units (especially for scientists and engineers, who deal with measurements much more often than other people) is that the mathematical relationships between the basic and derived units of the system turn out to be simpler. In this case, a unit of speed is a unit of distance (length) per unit of time, a unit of acceleration is a unit of change in speed per unit of time, a unit of force is a unit of acceleration per unit of mass, etc. In mathematical notation it looks like this: v = l/t, a = v/t, F = ma = ml/t 2. The presented formulas show the “dimension” of the quantities under consideration, establishing relationships between units. (Similar formulas allow you to determine units for quantities such as pressure or force electric current.) Such relationships are general character and are carried out regardless of what units (meter, foot or arshin) the length is measured in and what units are chosen for other quantities.
In technology, the basic unit of measurement of mechanical quantities is usually taken not as a unit of mass, but as a unit of force. Thus, if in the system most commonly used in physical research, metal cylinder is taken as a standard of mass, then in the technical system it is considered as a standard of force that balances the force of gravity acting on it. But since gravity is not the same in different points on the surface of the Earth, for accurate implementation of the standard, an indication of the location is necessary. Historically, the location was sea level at geographical latitude 45° Currently, such a standard is defined as the force necessary to give the specified cylinder a certain acceleration. True, in technology measurements are carried out, as a rule, not so high accuracy, so that you need to take care of variations in gravity (unless we are talking about the calibration of measuring instruments).
There is a lot of confusion surrounding the concepts of mass, force and weight. The fact is that there are units of all these three quantities that have the same names. Mass is an inertial characteristic of a body, showing how difficult it is to remove it external force from a state of rest or uniform and rectilinear movement. A unit of force is a force that, acting on a unit of mass, changes its speed by one unit of speed per unit of time.
All bodies attract each other. Thus, any body near the Earth is attracted to it. In other words, the Earth creates the force of gravity acting on the body. This force is called its weight. The force of weight, as stated above, is not the same at different points on the surface of the Earth and at different altitudes above sea level due to differences in gravitational attraction and in the manifestation of the Earth's rotation. However, the total mass of a given amount of substance is unchanged; it is the same both in interstellar space and at any point on Earth.
Precise experiments have shown that the force of gravity acting on different bodies (i.e. their weight) is proportional to their mass. Consequently, masses can be compared on scales, and masses that turn out to be the same in one place will be the same in any other place (if the comparison is carried out in a vacuum to exclude the influence of displaced air). If a certain body is weighed on a spring scale, balancing the force of gravity with the force of an extended spring, then the results of measuring the weight will depend on the place where the measurements are taken. Therefore, spring scales must be adjusted at each new location so that they correctly indicate the mass. The simplicity of the weighing procedure itself was the reason that the force of gravity acting on the standard mass was adopted as an independent unit of measurement in technology. HEAT.
Metric system of units.
The metric system is the general name for the international decimal system of units, the basic units of which are the meter and the kilogram. Although there are some differences in details, the elements of the system are the same throughout the world.
Story.
The metric system grew out of regulations adopted by the French National Assembly in 1791 and 1795 defining the meter as one ten-millionth of the portion of the earth's meridian from the North Pole to the equator.
By decree issued on July 4, 1837, the metric system was declared mandatory for use in all commercial transactions in France. It gradually replaced the local and national systems in other European countries and has been legally recognized as acceptable in the UK and USA. An agreement signed on May 20, 1875 by seventeen countries created an international organization designed to preserve and improve the metric system.
It is clear that by defining the meter as a ten-millionth part of a quarter of the earth's meridian, the creators of the metric system sought to achieve invariance and accurate reproducibility of the system. They took the gram as a unit of mass, defining it as the mass of one millionth of a cubic meter of water at its maximum density. Since it would not be very convenient to carry out geodetic measurements of a quarter of the earth's meridian with each sale of a meter of cloth or to balance a basket of potatoes at the market with the appropriate amount of water, metal standards were created that reproduced these ideal definitions with extreme accuracy.
It soon became clear that metal length standards could be compared with each other, introducing much less error than when comparing any such standard with a quarter of the earth's meridian. In addition, it became clear that the accuracy of comparing metal mass standards with each other is much higher than the accuracy of comparing any such standard with the mass of the corresponding volume of water.
In this regard, the International Commission on the Meter in 1872 decided to accept the “archival” meter stored in Paris “as it is” as the standard of length. Similarly, the members of the Commission accepted the archival platinum-iridium kilogram as the standard of mass, “considering that the simple relationship established by the creators of the metric system between the unit of weight and the unit of volume is represented by the existing kilogram with an accuracy sufficient for ordinary applications in industry and commerce, and the exact Sciences do not need a simple numerical relationship of this kind, but an extremely perfect definition of this relationship.” In 1875, many countries around the world signed a meter agreement, and this agreement established a procedure for coordinating metrological standards for the world scientific community through the International Bureau of Weights and Measures and the General Conference on Weights and Measures.
The new international organization immediately began developing international standards for length and mass and transmitting copies of them to all participating countries.
Standards of length and mass, international prototypes.
The international prototypes of the standards of length and mass - the meter and the kilogram - were deposited with the International Bureau of Weights and Measures, located in Sèvres, a suburb of Paris. The meter standard was a ruler made of a platinum alloy with 10% iridium, the cross-section of which was given a special X-shape to increase bending rigidity with a minimum volume of metal. In the groove of such a ruler there was a longitudinal flat surface, and the meter was defined as the distance between the centers of two strokes applied across the ruler at its ends, at a standard temperature of 0 ° C. The mass of a cylinder made of the same platinum was taken as the international prototype of the kilogram. iridium alloy, the same as the standard meter, with a height and diameter of about 3.9 cm. The weight of this standard mass, equal to 1 kg at sea level at latitude 45°, is sometimes called kilogram-force. Thus, it can be used either as a standard of mass for an absolute system of units, or as a standard of force for a technical system of units in which one of the basic units is the unit of force.
The international prototypes were selected from a large batch of identical standards produced simultaneously. Other standards of this batch were transferred to all participating countries as national prototypes (state primary standards), which are periodically returned to the International Bureau for comparison with international standards. Comparisons made at various times since then show that they do not show deviations (from international standards) beyond the limits of measurement accuracy.
International SI system.
The metric system was very favorably received by scientists of the 19th century. partly because it was proposed as an international system of units, partly because its units were theoretically assumed to be independently reproducible, and also because of its simplicity. Scientists began to develop new units for the various physical quantities they dealt with, based on the elementary laws of physics and linking these units to the metric units of length and mass. The latter increasingly conquered various European countries, in which previously there were many unrelated units for different quantities in use.
Although in all countries that adopted the metric system of units, the standards of metric units were almost the same, various discrepancies in derived units arose between different countries and different disciplines. In the field of electricity and magnetism, two separate systems of derived units emerged: electrostatic, based on the force with which two electric charges act on each other, and electromagnetic, based on the force of interaction between two hypothetical magnetic poles.
The situation became even more complicated with the advent of the so-called system. practical electrical units introduced in the mid-19th century. by the British Association for the Advancement of Science to meet the demands of rapidly developing wire telegraph technology. Such practical units do not coincide with the units of both systems mentioned above, but differ from the units of the electromagnetic system only by factors equal to whole powers of ten.
Thus, for such ordinary electrical quantities, such as voltage, current and resistance, there were several options for accepted units of measurement, and each scientist, engineer, teacher had to decide for himself which of these options was best for him to use. In connection with the development of electrical engineering in the second half of the 19th and first half of the 20th centuries. Practical units were increasingly used and eventually came to dominate the field.
To eliminate such confusion at the beginning of the 20th century. a proposal was put forward to combine practical electrical units with corresponding mechanical ones based on metric units of length and mass, and build some kind of coherent system. In 1960, the XI General Conference on Weights and Measures adopted a unified International System of Units (SI), defined the basic units of this system and prescribed the use of certain derived units, “without prejudice to others that may be added in the future.” Thus, for the first time in history, an international coherent system of units was adopted by international agreement. It is currently accepted as legal system units of measurement in most countries of the world.
The International System of Units (SI) is a harmonized system that provides one and only one unit of measurement for any physical quantity, such as length, time, or force. Some of the units are given special names, an example is the unit of pressure pascal, while the names of others are derived from the names of the units from which they are derived, for example the unit of speed - meter per second. The basic units, together with two additional geometric ones, are presented in Table. 1. Derived units for which special names are adopted are given in table. 2. Of all derived mechanical units, the most important The unit of force is newton, the unit of energy is joule and the unit of power is watt. Newton is defined as the force that imparts an acceleration of one meter per second squared to a mass of one kilogram. A joule is equal to the work done when the point of application of a force equal to one Newton moves a distance of one meter in the direction of the force. A watt is the power at which one joule of work is done in one second. Electrical and other derived units will be discussed below. The official definitions of major and minor units are as follows.
A meter is the length of the path traveled by light in a vacuum in 1/299,792,458 of a second. This definition was adopted in October 1983.
A kilogram is equal to the mass of the international prototype of the kilogram.
A second is the duration of 9,192,631,770 periods of radiation oscillations corresponding to transitions between two levels of the hyperfine structure of the ground state of the cesium-133 atom.
Kelvin is equal to 1/273.16 of the thermodynamic temperature of the triple point of water.
A mole is equal to the amount of a substance that contains the same number of structural elements as atoms in the carbon-12 isotope weighing 0.012 kg.
A radian is a plane angle between two radii of a circle, the length of the arc between which is equal to the radius.
A steradian is equal to a solid angle with its vertex at the center of the sphere, cutting out on its surface an area equal to the area of a square with a side equal to the radius spheres.
To form decimal multiples and submultiples, a number of prefixes and factors are prescribed, indicated in the table. 3.
|
Table 3. Prefixes and multipliers of the international system of units |
|||||
| exa | deci | ||||
| peta | centi | ||||
| tera | Milli | ||||
| giga | micro |
mk |
|||
| mega | nano | ||||
| kilo | pico | ||||
| hecto | femto | ||||
| soundboard |
Yes |
atto | |||
Thus, a kilometer (km) is 1000 m, and a millimeter is 0.001 m. (These prefixes apply to all units, such as kilowatts, milliamps, etc.)
It was originally intended that one of the base units should be the gram, and this was reflected in the names of the units of mass, but nowadays the base unit is the kilogram. Instead of the name megagram, the word “ton” is used. In physics disciplines, such as measuring the wavelength of visible or infrared light, a millionth of a meter (micrometer) is often used. In spectroscopy, wavelengths are often expressed in angstroms (Å); An angstrom is equal to one tenth of a nanometer, i.e. 10 - 10 m. For radiation with a shorter wavelength, such as X-rays, in scientific publications it is allowed to use a picometer and an x-unit (1 x-unit = 10 –13 m). A volume equal to 1000 cubic centimeters (one cubic decimeter) is called a liter (L).
Mass, length and time.
All basic SI units, except the kilogram, are currently defined in terms of physical constants or phenomena that are considered immutable and reproducible with high accuracy. As for the kilogram, a way to implement it with the degree of reproducibility that is achieved in procedures for comparing various mass standards with the international prototype of the kilogram has not yet been found. Such a comparison can be carried out by weighing on a spring balance, the error of which does not exceed 1H 10 –8. Standards of multiple and submultiple units for a kilogram are established by combined weighing on scales.
Since the meter is defined in terms of the speed of light, it can be reproduced independently in any well-equipped laboratory. Thus, using the interference method, line and end length measures, which are used in workshops and laboratories, can be checked by comparing directly with the wavelength of light. The error with such methods is optimal conditions does not exceed one billionth (1H 10 –9). With the development of laser technology, such measurements have become very simplified, and their range has expanded significantly.
Likewise, the second, according to its modern definition, can be independently realized in a competent laboratory in an atomic beam facility. The beam atoms are excited by a high-frequency generator tuned to the atomic frequency, and electronic circuit measures time by counting periods of oscillation in the generator circuit. Such measurements can be carried out with an accuracy of the order of 1H 10 -12 - much higher than was possible with previous definitions of the second, based on the rotation of the Earth and its revolution around the Sun. Time and its reciprocal, frequency, are unique in that their standards can be transmitted by radio. Thanks to this, anyone who has the appropriate radio receiving equipment can receive signals of exact time and reference frequency, almost no different in accuracy from those transmitted over the air.
Mechanics.
Temperature and warmth.
Mechanical units do not allow solving all scientific and technical problems without involving any other relationships. Although the work done when moving a mass against the action of a force, and the kinetic energy of a certain mass are equivalent in nature to the thermal energy of a substance, it is more convenient to consider temperature and heat as separate quantities that do not depend on mechanical ones.
Thermodynamic temperature scale.
The unit of thermodynamic temperature Kelvin (K), called kelvin, is determined by the triple point of water, i.e. the temperature at which water is in equilibrium with ice and steam. This temperature is taken to be 273.16 K, which determines the thermodynamic temperature scale. This scale, proposed by Kelvin, is based on the second law of thermodynamics. If there are two thermal reservoirs with a constant temperature and a reversible heat engine, transferring heat from one of them to the other in accordance with the Carnot cycle, then the ratio of the thermodynamic temperatures of the two reservoirs is given by the equality T 2 /T 1 = –Q 2 Q 1 where Q 2 and Q 1 – the amount of heat transferred to each of the reservoirs (the minus sign indicates that heat is taken from one of the reservoirs). Thus, if the temperature of the warmer reservoir is 273.16 K, and the heat taken from it is twice as much as the heat transferred to the other reservoir, then the temperature of the second reservoir is 136.58 K. If the temperature of the second reservoir is 0 K, then it no heat will be transferred at all, since all the energy of the gas has been converted into mechanical energy in the area of adiabatic expansion in the cycle. This temperature is called absolute zero. The thermodynamic temperature commonly used in scientific research coincides with the temperature included in the equation of state of an ideal gas PV = RT, Where P- pressure, V– volume and R– gas constant. The equation shows that for an ideal gas, the product of volume and pressure is proportional to temperature. This law is not exactly satisfied for any of the real gases. But if corrections are made for virial forces, then the expansion of gases allows us to reproduce the thermodynamic temperature scale.
International temperature scale.
In accordance with the definition outlined above, temperature can be measured with very high accuracy (up to approximately 0.003 K near the triple point) by gas thermometry. A platinum resistance thermometer and a gas reservoir are placed in a thermally insulated chamber. When the chamber is heated, the electrical resistance of the thermometer increases and the gas pressure in the reservoir increases (in accordance with the equation of state), and when cooled, the opposite picture is observed. By measuring resistance and pressure simultaneously, you can calibrate the thermometer by gas pressure, which is proportional to temperature. The thermometer is then placed in a thermostat in which the liquid water can be kept in equilibrium with its solid and vapor phases. By measuring its electrical resistance at this temperature, a thermodynamic scale is obtained, since the temperature of the triple point is assigned a value equal to 273.16 K.
There are two international temperature scales - Kelvin (K) and Celsius (C). Temperature on the Celsius scale is obtained from temperature on the Kelvin scale by subtracting 273.15 K from the latter.
Accurate temperature measurements using gas thermometry require a lot of labor and time. Therefore, in 1968, the International Practical Practice was introduced temperature scale(MPTS). Using this scale, thermometers different types can be calibrated in the laboratory. This scale was established using a platinum resistance thermometer, a thermocouple and a radiation pyrometer, used in the temperature intervals between certain pairs of constant reference points (temperature benchmarks). The MPTS was supposed to correspond to the thermodynamic scale with the greatest possible accuracy, but, as it turned out later, its deviations were very significant.
Fahrenheit temperature scale.
The Fahrenheit temperature scale, which is widely used in combination with the British technical system units, as well as in non-scientific measurements in many countries, are usually determined by two constant reference points - the melting temperature of ice (32° F) and the boiling point of water (212° F) at normal (atmospheric) pressure. Therefore, to get the Celsius temperature from the Fahrenheit temperature, you need to subtract 32 from the latter and multiply the result by 5/9.
Units of heat.
Since heat is a form of energy, it can be measured in joules, and this metric unit has been adopted by international agreement. But since the amount of heat was once determined by the change in temperature of a certain amount of water, a unit called a calorie became widespread and is equal to the amount of heat required to increase the temperature of one gram of water by 1 ° C. Due to the fact that the heat capacity of water depends on temperature , I had to clarify the calorie value. At least two different calories appeared - “thermochemical” (4.1840 J) and “steam” (4.1868 J). The “calorie” used in dietetics is actually a kilocalorie (1000 calories). The calorie is not an SI unit and has fallen into disuse in most fields of science and technology.
Electricity and magnetism.
All commonly accepted electrical and magnetic units of measurement are based on the metric system. In accordance with modern definitions of electrical and magnetic units, they are all derived units, derived by certain physical formulas from the metric units of length, mass and time. Since most electrical and magnetic quantities are not so easy to measure using the standards mentioned, it was found that it is more convenient to establish, through appropriate experiments, derivative standards for some of the indicated quantities, and to measure others using such standards.
SI units.
Below is a list of SI electrical and magnetic units.
The ampere, a unit of electric current, is one of the six SI base units. Ampere is the strength of a constant current, which, when passing through two parallel straight conductors of infinite length, with negligible small area circular cross-section, located in a vacuum at a distance of 1 m from one another, would cause on each section of a conductor 1 m long an interaction force equal to 2H 10 - 7 N.
Volt, a unit of potential difference and electromotive force. Volt is the electrical voltage in a section of an electrical circuit with a direct current of 1 A with a power consumption of 1 W.
Coulomb, a unit of quantity of electricity (electric charge). Coulomb is the amount of electricity passing through cross section conductor at DC with a force of 1 A for a time of 1 s.
Farad, a unit of electrical capacitance. Farad is the capacitance of a capacitor on the plates of which, when charged at 1 C, an electric voltage of 1 V appears.
Henry, unit of inductance. Henry is equal to the inductance of the circuit in which a self-inductive emf of 1 V occurs when the current in this circuit changes uniformly by 1 A in 1 s.
Weber unit of magnetic flux. Weber - a magnetic flux, when it decreases to zero, a circuit connected to it, having a resistance of 1 Ohm, flows electric charge, equal to 1 C.
Tesla, a unit of magnetic induction. Tesla is the magnetic induction of a uniform magnetic field, in which the magnetic flux through a flat area of 1 m2, perpendicular to the induction lines, is equal to 1 Wb.
Practical standards.
Light and illumination.
Luminous intensity and illuminance units cannot be determined based on mechanical units alone. We can express the energy flux in a light wave in W/m2, and the intensity of the light wave in V/m, as in the case of radio waves. But the perception of illumination is a psychophysical phenomenon in which not only the intensity of the light source is significant, but also the sensitivity of the human eye to the spectral distribution of this intensity.
By international agreement, the unit of luminous intensity is the candela (previously called a candle), equal to the luminous intensity in a given direction of a source emitting monochromatic radiation of frequency 540H 10 12 Hz ( l= 555 nm), the energy force of light radiation of which in this direction is 1/683 W/sr. This roughly corresponds to the luminous intensity of a spermaceti candle, which once served as a standard.
If the luminous intensity of the source is one candela in all directions, then the total luminous flux is 4 p lumens. Thus, if this source is located at the center of a sphere with a radius of 1 m, then the illumination inner surface sphere is equal to one lumen per square meter, i.e. one suite.
X-ray and gamma radiation, radioactivity.
X-ray (R) is an obsolete unit of exposure dose of x-ray, gamma and photon radiation, equal to the amount of radiation that, taking into account secondary electron radiation, forms ions in 0.001 293 g of air that carry a charge equal to one unit of the CGS charge of each sign. The SI unit of absorbed radiation dose is the gray, equal to 1 J/kg. The standard for absorbed radiation dose is a setup with ionization chambers that measure the ionization produced by radiation.
- 1 General information
- 2 History
- 3 SI units
- 3.1 Basic units
- 3.2 Derived units
- 4 Non-SI units
- Consoles
General information
The SI system was adopted by the XI General Conference on Weights and Measures, and some subsequent conferences made a number of changes to the SI.
The SI system defines seven main And derivatives units of measurement, as well as a set of . Standard abbreviations for units of measurement and rules for recording derived units have been established.
In Russia, GOST 8.417-2002 is in force, which prescribes the mandatory use of SI. It lists the units of measurement, gives their Russian and international names and establishes the rules for their use. According to these rules in international documents and only international designations may be used on instrument scales. In internal documents and publications, you can use either international or Russian designations (but not both at the same time).
Basic units: kilogram, meter, second, ampere, kelvin, mole and candela. Within the SI framework, these units are considered to have independent dimensions, that is, none of the basic units can be obtained from the others.
Derived units are obtained from the basic ones using algebraic operations such as multiplication and division. Some of the derived units in the SI System are given their own names.
Consoles can be used before names of units of measurement; they mean that a unit of measurement must be multiplied or divided by a certain integer, a power of 10. For example, the prefix “kilo” means multiplying by 1000 (kilometer = 1000 meters). SI prefixes are also called decimal prefixes.
Story
The SI system is based on the metric system of measures, which was created by French scientists and was first widely adopted after the French Revolution. Before the introduction of the metric system, units of measurement were chosen randomly and independently of each other. Therefore, conversion from one unit of measurement to another was difficult. In addition, different units of measurement were used in different places, sometimes with the same names. The metric system was supposed to become a convenient and uniform system of measures and weights.
In 1799, two standards were approved - for the unit of length (meter) and for the unit of weight (kilogram).
In 1874, the GHS system was introduced, based on three units of measurement - centimeter, gram and second. Decimal prefixes from micro to mega were also introduced.
In 1889, the 1st General Conference on Weights and Measures adopted a system of measures similar to the GHS, but based on the meter, kilogram and second, since these units were considered more convenient for practical use.
Subsequently, basic units were introduced for measuring physical quantities in the field of electricity and optics.
In 1960, the XI General Conference on Weights and Measures adopted a standard that was first called the International System of Units (SI).
In 1971, the IV General Conference on Weights and Measures amended the SI, adding, in particular, a unit for measuring the amount of a substance (mole).
SI is now accepted as the legal system of units of measurement by most countries in the world and is almost always used in the scientific field (even in countries that have not adopted SI).
SI units
There is no dot after the designations of SI units and their derivatives, unlike usual abbreviations.
Basic units
| Magnitude | Unit | Designation | ||
|---|---|---|---|---|
| Russian name | international name | Russian | international | |
| Length | meter | meter (meter) | m | m |
| Weight | kilogram | kilogram | kg | kg |
| Time | second | second | With | s |
| Electric current strength | ampere | ampere | A | A |
| Thermodynamic temperature | kelvin | kelvin | TO | K |
| The power of light | candela | candela | cd | CD |
| Quantity of substance | mole | mole | mole | mol |
Derived units
Derived units can be expressed in terms of base units using the mathematical operations of multiplication and division. Some of the derived units are given their own names for convenience; such units can also be used in mathematical expressions to form other derived units.
The mathematical expression for a derived unit of measurement follows from the physical law by which this unit of measurement is defined or the definition of the physical quantity for which it is introduced. For example, speed is the distance a body travels per unit time. Accordingly, the unit of measurement for speed is m/s (meter per second).
Often the same unit of measurement can be written in different ways, using a different set of base and derived units (see, for example, the last column in the table ). However, in practice, established (or simply generally accepted) expressions are used, which the best way reflect the physical meaning of the measured quantity. For example, to write the value of a moment of force, you should use N×m, and you should not use m×N or J.
| Magnitude | Unit | Designation | Expression | ||
|---|---|---|---|---|---|
| Russian name | international name | Russian | international | ||
| Flat angle | radian | radian | glad | rad | m×m -1 = 1 |
| Solid angle | steradian | steradian | Wed | sr | m 2 ×m -2 = 1 |
| Temperature in Celsius | degrees Celsius | °C | degree Celsius | °C | K |
| Frequency | hertz | hertz | Hz | Hz | s -1 |
| Force | newton | newton | N | N | kg×m/s 2 |
| Energy | joule | joule | J | J | N×m = kg×m 2 /s 2 |
| Power | watt | watt | W | W | J/s = kg × m 2 / s 3 |
| Pressure | pascal | pascal | Pa | Pa | N/m 2 = kg? m -1 ? s 2 |
| Light flow | lumen | lumen | lm | lm | kd×sr |
| Illumination | luxury | lux | OK | lx | lm/m 2 = cd×sr×m -2 |
| Electric charge | pendant | coulomb | Cl | C | А×с |
| Potential difference | volt | volt | IN | V | J/C = kg×m 2 ×s -3 ×A -1 |
| Resistance | ohm | ohm | Ohm | Ω | V/A = kg×m 2 ×s -3 ×A -2 |
| Capacity | farad | farad | F | F | C/V = kg -1 ×m -2 ×s 4 ×A 2 |
| Magnetic flux | weber | weber | Wb | Wb | kg×m 2 ×s -2 ×A -1 |
| Magnetic induction | tesla | tesla | Tl | T | Wb/m 2 = kg × s -2 × A -1 |
| Inductance | Henry | Henry | Gn | H | kg×m 2 ×s -2 ×A -2 |
| Electrical conductivity | Siemens | siemens | Cm | S | Ohm -1 = kg -1 ×m -2 ×s 3 A 2 |
| Radioactivity | becquerel | becquerel | Bk | Bq | s -1 |
| Absorbed dose of ionizing radiation | Gray | gray | Gr | Gy | J/kg = m 2 / s 2 |
| Effective dose of ionizing radiation | sievert | sievert | Sv | Sv | J/kg = m 2 / s 2 |
| Catalyst activity | rolled | catal | cat | kat | mol×s -1 |
Units not included in the SI System
Some units of measurement not included in the SI System are, by decision of the General Conference on Weights and Measures, “allowed for use in conjunction with SI.”
| Unit | International name | Designation | Value in SI units | |
|---|---|---|---|---|
| Russian | international | |||
| minute | minute | min | min | 60 s |
| hour | hour | h | h | 60 min = 3600 s |
| day | day | days | d | 24 h = 86,400 s |
| degree | degree | ° | ° | (P/180) glad |
| arcminute | minute | ′ | ′ | (1/60)° = (P/10,800) |
| arcsecond | second | ″ | ″ | (1/60)′ = (P/648,000) |
| liter | liter (liter) | l | l, L | 1 dm 3 |
| ton | tons | T | t | 1000 kg |
| neper | neper | Np | Np | |
| white | bel | B | B | |
| electron-volt | electronvolt | eV | eV | 10 -19 J |
| atomic mass unit | unified atomic mass unit | A. eat. | u | =1.49597870691 -27 kg |
| astronomical unit | astronomical unit | A. e. | ua | 10 11 m |
| nautical mile | nautical mile | mile | 1852 m (exactly) | |
| node | knot | bonds | 1 nautical mile per hour = (1852/3600) m/s | |
| ar | are | A | a | 10 2 m 2 |
| hectare | hectare | ha | ha | 10 4 m 2 |
| bar | bar | bar | bar | 10 5 Pa |
| angstrom | ångström | Å | Å | 10 -10 m |
| barn | barn | b | b | 10 -28 m 2 |
Consider the physical record m=4kg. In this formula "m"- designation of a physical quantity (mass), "4" - numerical value or size, "kg"- unit of measurement of a given physical quantity.
There are different types of quantities. Here are two examples:
1) The distance between points, the lengths of segments, broken lines - these are quantities of the same kind. They are expressed in centimeters, meters, kilometers, etc.
2) The durations of time intervals are also quantities of the same kind. They are expressed in seconds, minutes, hours, etc.
Quantities of the same kind can be compared and added:
BUT! It makes no sense to ask what is greater: 1 meter or 1 hour, and you cannot add 1 meter to 30 seconds. The duration of time intervals and distance are quantities of different kinds. They cannot be compared or added together.
Quantities can be multiplied by positive numbers and zero. 
Taking any value e per unit of measurement, you can use it to measure any other quantity A same kind. As a result of the measurement we obtain that A=x e, where x is a number. This number x is called the numerical value of the quantity A with unit of measurement e.
There are dimensionless physical quantities. They do not have units of measurement, that is, they are not measured in anything. For example, friction coefficient.
What is SI?
According to data from Professor Peter Cumpson and Dr Naoko Sano from the University of Newcastle, published in the journal Metrology, the standard kilogram gains on average about 50 micrograms per hundred years, which ultimately can significantly affect many physical quantities.
The kilogram is the only SI unit that is still defined using a standard. All other measures (meter, second, degree, ampere, etc.) can be determined with the necessary accuracy in a physical laboratory. The kilogram is included in the definition of other quantities, for example, the unit of force is the newton, which is defined as a force that changes the speed of a body weighing 1 kg by 1 m/s in 1 second in the direction of the force. Other physical quantities depend on the value of Newton, so in the end the chain can lead to a change in the value of many physical units.
The most important kilogram is a cylinder with a diameter and height of 39 mm, consisting of an alloy of platinum and iridium (90% platinum and 10% iridium). It was cast in 1889 and is kept in a safe at the International Bureau of Weights and Measures in Sèvres near Paris. The kilogram was originally defined as the mass of one cubic decimeter (liter) clean water at 4 °C and standard atmospheric pressure at sea level.
From the standard kilogram, 40 exact copies were initially made, which were distributed throughout the world. Two of them are located in Russia, at the All-Russian Research Institute of Metrology named after. Mendeleev. Later another series of replicas was cast. Platinum was chosen as the main material for the standard because it is highly resistant to oxidation, high density and low magnetic susceptibility. The standard and its replicas are used to standardize mass in a variety of industries. Including where micrograms are significant.
Physicists believe that weight fluctuations were the result of atmospheric pollution and changes chemical composition on the surface of the cylinders. Despite the fact that the standard and its replicas are stored in special conditions, this does not save the metal from interaction with environment. Exact weight kilogram was determined using X-ray photoelectron spectroscopy. It turned out that the kilogram “gained” by almost 100 micrograms.
At the same time, copies of the standard differed from the original from the very beginning and their weight also changes differently. Thus, the main American kilogram initially weighed 39 micrograms less than the standard, and a check in 1948 showed that it had increased by 20 micrograms. The other American copy, on the contrary, is losing weight. In 1889, kilogram number 4 (K4) weighed 75 mcg less than the standard, and in 1989 it was already 106 mcg.
IN modern world there are many units of measurement for various quantities. Not all of them are often used, but they all have a right to exist. Most often, the use of a particular unit of measurement depends on the location. For example, we are used to measuring length in millimeters, centimeters, meters, kilometers. However, when buying a foreign-made TV, we inevitably come across such a unit of length as an inch, because it is usually the diagonal length of a TV that is indicated in inches. Imagine, for example, you are buying a TV, as is now fashionable, through an online store. The website states that its diagonal is 24 inches. And here the problem arises: how much is 24 inches? And mathematics comes to the rescue. Another example: any student studying physics has heard about the SI system of units of measurement. Moreover, from every student modern program requires the ability to convert units of measurement to the SI system when solving school problems in physics. There are many such examples. The point is that you need to be able to navigate the units of measurement of various quantities and, if necessary, be able to convert one unit of measurement to another.
We present the most common units of measurement of basic quantities.
Mass: milligram, gram, kilogram (SI), centner, ton.
1 ton = 10 quintals = 1,000 kg = 1,000,000 g = 1,000,000,000 mg.
Length: millimeter, centimeter, meter (SI), kilometer, foot, inchm.
1 km = 1,000 m = 100,000 cm = 1,000,000 mm
1 m = 3.2808399 feet = 39.3707 inches
Area: cm2, m2 (SI), acre, foot2, hectare, in2.
1 m 2 = 10,000 cm 2 = 0.00024711 acres = 10.764 feet = 0.0001 hectares = 1,550 inches 2.
Volume: 3 centimeter, 3 meter (SI), 3 foot, gallon, 3 inch, liter.
1 m 3 = 1,000,000 cm 3 = 35.32 ft 3 = 220 gallons = 61,024 in 3 = 1,000 liters (dm 3).
As a rule, schoolchildren do not have problems converting large units of measurement into smaller ones.
For example:
23 m = 2,300 cm = 23,000 mm.
43 kg = 43,000 g.
When it comes to converting smaller units into larger ones, problems usually arise. Let's figure out how best to act in such situations.
Example.
Suppose we need to convert 28 mm to meters. This problem often arises in physics when it is necessary to convert units of measurement to the SI system.
Solution.
We proceed as follows:
1) We build a chain of units of measurement from largest to smallest: 
m -> cm -> mm.
2) Remember: 1 m = 100 cm, 1 cm = 10 mm.
3) Now let's go to reverse order: 1 mm = 0.1 cm, 1 cm = 0.01 m.
This means 1 mm = 0.1 cm = 0.1 · 0.01 = 0.001 m.
4) 28 mm = 28 0.001 = 0.028 m.
Answer. 28 mm = 0.028 m.
Example.
Suppose we need to convert 25 liters to 3 meters.
Solution.
We use the same scheme.
1) We build a chain of units of measurement from largest to smallest, but for now without cubes.
2) Remember: 1 m = 10 dm.
3) Now we go in reverse order: 1 dm = 0.1 m.
This means 1 liter = 1 dm 3 = 0.001 m 3.
4) 25 liters = 25 dm3 = 25 · 0.001 = 0.025 m3.
Answer. 25 liters = 0.025 m3.
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Unit– a physical quantity of a certain size, adopted for the quantitative display of quantities homogeneous with it.Distinguish basic units of measurement, which are determined using standards, and derived units, defined using basic ones. The choice of the value and number of basic units of measurement can be arbitrary and is determined only by traditions or agreements. There is a large number various systems units of measurement that differ in the choice of base units of measurement.
To determine the quantitative characteristics of a certain object, it is easy to compare it with another object. For example, to determine the length of a python, you can compare it to a parrot and say that a boa constrictor is equal to 39 and a half parrots. However, the parrot is not a very good standard for measuring length. Parrots are different. Therefore, there is a need to establish precise standards. Historically, length was measured in feet (feet), elbows, but over time the units of measurement became standardized and became more and more accurate. The need to establish a single standard began to be recognized at the state level. The science of metrology arose. To support international activities, measurement systems that would be recognized on a global scale began to emerge.
Practical needs and scientific research are increasingly demanding standards for the standards with which measured quantities are compared. The standard must be associated with an unchanging, fundamental value, which, in addition, would not be difficult to reproduce. Thus, if during the Great French Revolution the standard of the meter was established as the length of an arbitrarily chosen rod, then in our time the meter is associated with the road that light travels through the void in a certain time. Thus, to accurately establish a unit of length, it is necessary to accurately establish a unit of time (second), which in our time is defined as a period of time in which a certain number of oscillations of a certain electromagnetic wave, which is emitted by a strictly defined atom under strictly defined conditions. This definition allows you to reproduce the time standard with high accuracy, up to the eleventh decimal place.
Unit of measurement. RELATIONSHIP BETWEEN UNIT OF MEASUREMENT OF THE SAME QUANTITY
Meaning of decimal prefixes
To designate units of different quantities, prefixes are used that show how many times the basic unit of measurement has increased or decreased.
Prefixes increase and their designations:
Decrease prefixes:
For example, a deciliter is a value that is 10 times larger than 1 liter. Since 1 liter is denoted 1 liter, and the short designation is deca, we get: 1 dal = 10 liters or 1 liter = 0.1 dal.
Another example. A millimeter is a value that is 1000 times smaller than 1 meter. Since one meter is briefly written as 1 m, and a milli is also briefly written as m, it turns out that 1 mm = 0.001 m, and 1 m = 1000 mm.
Units of length
The basic unit of length is the meter. The meter is briefly denoted m, that is, 1 meter is written 1 m.
The last entry means, for example, that 1 meter is equal to 1,000,000 microns. It follows that:
These relationships can be written differently:
The length of a significant value is usually written in kilometers, a short notation is 1 km.
There is
Very small quantities are measured in angstroms:
Mass units
The basic unit of mass is the gram, shortened to g. When denoting other units of mass, the prefixes mole and kilo are used.
Larger quantities are measured in tons (t) and centners (c):
Area units
The basic unit of measurement of area is the square meter: m2 affects.
When measuring land plots The units used are ap and hectare (denoted a and ha).
Another name for the macaw is weaving. 1 weave is 1 are, or 100 m2.
Volume units
The basic unit of volume measurement is the cubic decimeter; dm 3 affects. 1 dm 3 is also called 1 liter, that is, 1 dm 3 = 1 liter.
A thousandth of a liter is a milliliter, i.e. 1 l = 1000 ml, and 1 ml = 0.001 l.
Thus, 1 ml = 1000 mm 3, and 1 mm 3 = 0.001 ml. Since 1 cm 3 = 1000 mm 3, then 1 ml = 1 cm 3.
Large volumes are measured in deciliters (dal): 1 dal = 10 l; and cubic meters (m3): 1 m3 = 1000 l, i.e. 1 m 3 = 100 dal.
