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 of the technical system of the ICSC and some off-system units also find some use.

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	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	A		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 per 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, electric voltage	volt	V (W/A)	kg×m 2 x x s –3 ×A –1	1SGSE u = =300 V 1SGSM u = =10 –8 V
Electric field strength	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
Magnetic field strength	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	A	A	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

Physics. Subject and tasks.

2.Physical quantities and their measurement. SI system.

3. Mechanics. The tasks of mechanics.

.

5. Kinematics of the MT point. Methods for describing the movement of MT.

6. Move. Path.

7. Speed. Acceleration.

8. Tangential and normal accelerations.

9. Kinematics of rotational motion.

10. Law of inertia of Galileo. Inertial reference systems.

11. Galilean transformations. Galileo's law of addition of velocities. Acceleration invariance. The principle of relativity.

12. Strength. Weight.

13. Second law. Pulse. The principle of independence of action of forces.

14. Newton's third law.

15. Types of fundamental interactions. The law of universal gravitation. Coulomb's law. Lorentz force. Van der Waals forces. Forces in classical mechanics.

16. System of material points (SMT).

17. Impulse of the system. The law of conservation of momentum in a closed system.

18. Center of mass. Equation of motion of SMT.

19. Equation of motion of a body of variable mass. Tsiolkovsky formula.

20. Work of forces. Power.

21. Potential field of forces. Potential energy.

22. Kinetic energy of MT in a force field.

23. Total mechanical energy. The law of conservation of energy in mechanics.

24. Angular moment. Moment of power. Equation of moments.

25. Law of conservation of angular momentum.

26. Own angular momentum.

27. The moment of inertia of the TT about the axis. Hugens-Steiner theorem.

28. The equation of motion of a TT rotating around a fixed axis.

29. Kinetic energy of TT, performing translational and rotational motion.

30. Place of oscillatory motion in nature and technology.

31. Free harmonic vibrations. Method of vector diagrams.

32. Harmonic oscillator. Spring, physical and mathematical pendulums.

33. Dynamic and statistical regularities in physics. Thermodynamic and statistical methods.

34. Properties of liquids and gases. Mass and surface forces. Pascal's law.

35. Law of Archimedes. Swimming tel.

36. Thermal motion. macroscopic parameters. Ideal gas model. Gas pressure from the point of view of molecular-kinetic theory. The concept of temperature.

37. Equation of state.

38. Experimental gas laws.

39. Basic equation of the MKT.

40. Average kinetic energy of translational motion of molecules.

41. Number of degrees of freedom. The law of uniform distribution of energy over degrees of freedom.

42. Internal energy of an ideal gas.

43. The length of the gas free path.

44. Ideal gas in a force field. barometric formula. Boltzmann's law.

45. The internal energy of the system is a function of the state.

46. ​​Work and heat as a function of the process.

47. The first law of thermodynamics.

48. Heat capacity of polyatomic gases. Robert-Meyer equation.

49. Application of the first law of thermodynamics to isoprocesses.

50 Speed ​​of sound in gas.

51. Reversible and irreversible processes. circular processes.

52. Heat engines.

53. Carnot cycle.

54. The second law of thermodynamics.

55. The concept of entropy.

56. Carnot's theorems.

57. Entropy in reversible and irreversible processes. Entropy increase law.

58. Entropy as a measure of disorder in a statistical system.

59. The third law of thermodynamics.

60. Thermodynamic flows.

61. Diffusion in gases.

62. Viscosity.

63. Thermal conductivity.

64. Thermal diffusion.

65. Surface tension.

66. Wetting and non-wetting.

67. Pressure under the curved surface of a liquid.

68. Capillary phenomena.

Physics. Subject and tasks.

Physics is a natural science. It is based on an experimental study of natural phenomena, and its task is to formulate the laws that explain these phenomena. Physics is focused on the study of fundamental and simplest phenomena and on answers to simple questions: what matter consists of, how particles of matter interact with each other, according to what rules and laws particles move, etc.

The subject of its study is matter (in the form of matter and fields) and the most general forms of its movement, as well as the fundamental interactions of nature that control the movement of matter.

Physics is closely related to mathematics: mathematics provides the apparatus by which physical laws can be formulated precisely. Physical theories are almost always formulated as mathematical equations, using more complex branches of mathematics than is usual in other sciences. Conversely, the development of many areas of mathematics was stimulated by the needs of physical science.

The dimension of a physical quantity is determined by the system of physical quantities used, which is a set of physical quantities interconnected by dependencies, and in which several quantities are chosen as the main ones. A unit of a physical quantity is such a physical quantity that, by agreement, has been assigned a numerical value equal to one. A system of units of physical quantities is a set of basic and derived units based on a certain system of quantities. The tables below show the physical quantities and their units adopted in the International system of units (SI) based on the International System of Units.

Physical quantities and units of their measurement. SI system.

Physical quantity		Unit of measurement of a physical quantity
Mechanics
Weight	m	kilogram	kg
Density		kilogram per cubic meter	kg / m 3
Specific volume	v	cubic meter per kilogram	m 3 /kg
Mass flow	Qm	kilogram per second	kg/s
Volume flow	Q V	cubic meter per second	m 3 / s
Pulse	P	kilogram meter per second	kg m/s
angular momentum	L	kilogram meter squared per second	kg m 2 /s
Moment of inertia	J	kilogram meter squared	kg m 2
Strength, weight	F, Q	newton	H
Moment of power	M	newton meter	N m
Impulse of force	I	newton second	N s
Pressure, mechanical stress	p,	pascal	Pa
work, energy	A, E, U	joule	J
Power	N	watt	Tue

The International System of Units (SI) is a system of units based on the International System of Units, together with names and symbols, as well as a set of prefixes and their names and symbols, together with the rules for their use, adopted by the General Conference on Weights and Measures (CGPM).

International Dictionary of Metrology
The SI was adopted by the XI General Conference on Weights and Measures (CGPM) in 1960; some subsequent conferences made a number of changes to the SI.
SI defines seven basic units of physical quantities and derived units (abbreviated as SI units or units), as well as a set of prefixes. The SI also establishes standard unit abbreviations and rules for writing derived units.
Basic units: kilogram, meter, second, ampere, kelvin, mole and candela. Within the SI, these units are considered to have independent dimensionality, that is, none of the base units can be derived from the others.
Derived units are obtained from base units using algebraic operations such as multiplication and division. Some of the derived units in the SI have their own names, such as the unit radian.
Prefixes can be used before unit names. They mean that the unit 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.

Mechanics. The tasks of mechanics.

Mechanics is a branch of physics that studies the laws of mechanical motion, as well as the causes that cause or change motion.

The main task of mechanics is to describe the mechanical movement of bodies, that is, to establish a law (equation) of body movement based on characteristics that describe (coordinates, displacement, distance traveled, angle of rotation, speed, acceleration, etc.). In other words, if with using the compiled law (equation) of motion, you can determine the position of the body at any time, then the main problem of mechanics is considered solved. Depending on the chosen physical quantities and methods for solving the main problem of mechanics, it is divided into kinematics, dynamics and statics.

4.Mechanical movement. Space and time. Coordinate systems. Time measurement. Reference system. Vectors .

Mechanical movement called the change in the position of bodies in space relative to other bodies over time. Mechanical motion is divided into translational, rotational and oscillatory.

Translational called such a movement in which any straight line drawn in the body moves parallel to itself. rotational called a movement in which all points of the body describe concentric circles about a certain point, called the center of rotation. oscillatory called a movement in which the body makes periodically repeating movements around the middle position, that is, it oscillates.

To describe mechanical motion, the concept is introduced reference systems .types of reference systems can be different, for example, a fixed frame of reference, a moving frame of reference, an inertial frame of reference, a non-inertial frame of reference. It includes a body of reference, a coordinate system, and a clock. Reference body is the body to which the coordinate system is “attached”. coordinate system, which is a reference point (origin). The coordinate system has 1, 2 or 3 axes depending on the driving conditions. The position of a point on a line (1 axis), a plane (2 axes) or in space (3 axes) is determined by one, two or three coordinates, respectively. To determine the position of the body in space at any time, it is also necessary to set the origin of time. Different coordinate systems are known: Cartesian, polar, curvilinear, etc. In practice, Cartesian and polar coordinate systems are most often used. Cartesian coordinate system- these are (for example, in the two-dimensional case) two mutually perpendicular rays coming out of one point, called the origin, with a scale applied to them (Fig. 2.1a). Polar coordinate system- in the two-dimensional case, this is the radius-vector coming out of the origin and the angle θ, by which the radius-vector rotates (Fig. 2.1b). Clocks are needed to measure time.

The line that a material point describes in space is called trajectory. For two-dimensional motion on the plane (x, y), this is the function y(x). The distance traveled by a material point along the trajectory is called path length(fig.2.2). Vector connecting the initial position of a moving material point r (t 1) with any of its subsequent position r (t 2) is called moving(fig.2.2):

.

Rice. 2.2. Path length (highlighted by a thick line); is the displacement vector.

Each of the coordinates of the body depends on the time x=x(t), y=y(t), z=z(t). These functions of changing coordinates depending on time are called kinematic law of motion, for example, for x \u003d x (t) (Fig. 2.3).

Fig.2.3. An example of the kinematic law of motion x=x(t).

A vector-directed segment for which its beginning and end are indicated. Space and time are concepts denoting the main forms of the existence of matter. Space expresses the order of coexistence of individual objects. Time determines the order of change of phenomena.

Topic: VALUES AND THEIR MEASUREMENTS

Target: Give the concept of quantity, its measurement. To acquaint with the history of the development of the system of units of quantities. Summarize knowledge about the quantities that preschoolers get acquainted with.

Plan:

The concept of magnitude, their properties. The concept of measuring a quantity. From the history of the development of the system of units of quantities. International system of units. The quantities that preschoolers get acquainted with and their characteristics.

1. The concept of magnitude, their properties

The value is one of the basic mathematical concepts that arose in antiquity and underwent a number of generalizations in the process of long development.

The initial idea of ​​the size is associated with the creation of a sensory basis, the formation of ideas about the size of objects: show and name the length, width, height.

The value refers to the special properties of real objects or phenomena of the surrounding world. The size of an object is its relative characteristic, emphasizing the length of individual parts and determining its place among homogeneous ones.

Values ​​that have only a numerical value are called scalar(length, mass, time, volume, area, etc.). In addition to scalars in mathematics, they also consider vector quantities, which are characterized not only by number, but also by direction (force, acceleration, electric field strength, etc.).

Scalars can be homogeneous or heterogeneous. Homogeneous quantities express the same property of objects of a certain set. Heterogeneous quantities express different properties of objects (length and area)

Scalar properties:

§ any two quantities of the same kind are comparable or they are equal, or one of them is less (greater than) the other: 4t5ts …4t 50kgÞ 4t5c=4t500kg Þ 4t500kg>4t50kg, because 500kg>50kg

4t5c >4t 50kg;

§ Values ​​of the same genus can be added, resulting in a value of the same genus:

2km921m+17km387mÞ 2km921m=2921m, 17km387m=17387m Þ 17387m+2921m=20308m; Means

2km921m+17km387m=20km308m

§ A value can be multiplied by a real number, resulting in a value of the same kind:

12m24cm× 9 Þ 12m24m=1224cm, 1224cm×9=110m16cm, so

12m24cm× 9=110m16cm;

4kg283g-2kg605gÞ 4kg283g=4283g, 2kg605g=2605g Þ 4283g-2605g=1678g, so

4kg283g-2kg605g=1kg678g;

§ quantities of the same kind can be divided, resulting in a real number:

8h25min: 5 Þ 8h25min=8×60min+25min=480min+25min=505min, 505min : 5=101min, 101min=1h41min, so 8h25min: 5=1h41min.

The value is a property of an object perceived by different analyzers: visual, tactile and motor. In this case, most often the value is perceived simultaneously by several analyzers: visual-motor, tactile-motor, etc.

The perception of magnitude depends on:

§ the distance from which the object is perceived;

§ the size of the object with which it is compared;

§ its location in space.

The main properties of the quantity:

§ Comparability- the definition of the value is possible only on the basis of comparison (directly or by comparing with a certain way).

§ Relativity- the characteristic of the magnitude is relative and depends on the objects chosen for comparison; the same object can be defined by us as larger or smaller, depending on the size of the object it is compared with. For example, a bunny is smaller than a bear, but larger than a mouse.

§ Variability- the variability of quantities is characterized by the fact that they can be added, subtracted, multiplied by a number.

§ measurability- measurement makes it possible to characterize the magnitude of the comparison of numbers.

2. The concept of measuring a quantity

The need to measure all kinds of quantities, as well as the need to count objects, arose in the practical activity of man at the dawn of human civilization. Just as to determine the number of sets, people compared different sets, different homogeneous quantities, determining first of all which of the compared quantities is larger, which is smaller. These comparisons were not measurements yet. Subsequently, the procedure for comparing values ​​was improved. One quantity was taken as the standard, and other quantities of the same kind were compared with the standard. When people mastered the knowledge about numbers and their properties, the number 1 was attributed to the value - the standard, and this standard became known as the unit of measurement. The purpose of measurement has become more specific – to evaluate. How many units are in the measurand. the result of the measurement began to be expressed as a number.

The essence of measurement is the quantitative fragmentation of the measured objects and the establishment of the value of this object in relation to the accepted measure. By means of the measurement operation, the numerical ratio of the object between the measured value and a pre-selected unit of measure, scale or standard is established.

The measurement includes two logical operations:

the first is the process of separation, which allows the child to understand that the whole can be divided into parts;

the second is the replacement operation, which consists in connecting separate parts (represented by the number of measures).

The measurement activity is quite complex. It requires certain knowledge, specific skills, knowledge of the generally accepted system of measures, the use of measuring instruments.

In the process of forming measuring activity among preschoolers by means of conditional measurements, children must understand that:

§ measurement gives an accurate quantitative characteristic of the value;

§ for measurement, it is necessary to choose an adequate measure;

§ the number of measures depends on the measured value (the larger the value, the greater its numerical value and vice versa);

§ the measurement result depends on the chosen measure (the larger the measure, the smaller the numerical value and vice versa);

§ To compare quantities, it is necessary to measure them with the same standards.

3. From the history of the development of the system of units of quantities

Man has long realized the need to measure different quantities, and to measure as accurately as possible. The basis of accurate measurements are convenient, well-defined units of quantities and accurately reproducible standards (samples) of these units. In turn, the accuracy of standards reflects the level of development of science, technology and industry of the country, speaks of its scientific and technical potential.

In the history of the development of units of quantities, several periods can be distinguished.

The most ancient is the period when units of length were identified with the name of the parts of the human body. So, the palm (the width of four fingers without the thumb), the elbow (the length of the elbow), the foot (the length of the foot), the inch (the length of the knuckle of the thumb), etc. were used as units of length. The units of area during this period were: , which can be watered from one well), plow or plow (average area cultivated per day with a plow or plow), etc.

In the XIV-XVI centuries. appear in connection with the development of trade so-called objective units of measurement. In England, for example, an inch (the length of three barley grains placed side by side), a foot (the width of 64 barley grains laid side by side).

Grains (grain mass) and carats (seed mass of one of the bean species) were introduced as units of mass.

The next period in the development of units of quantities is the introduction of units interconnected with each other. In Russia, for example, such units were mile, verst, sazhen and arshin; 3 arshins made up a sazhen, 500 sazhens - a verst, 7 versts - a mile.

However, the connections between units of quantities were arbitrary, their measures of length, area, mass were used not only by individual states, but also by separate regions within the same state. Particular discord was observed in France, where each feudal lord had the right to establish his own measures within the limits of his possessions. Such a variety of units of quantities hindered the development of production, hindered scientific progress and the development of trade relations.

The new system of units, which later became the basis for the international system, was created in France at the end of the 18th century, during the era of the French Revolution. The basic unit of length in this system was meter- one forty-millionth part of the length of the earth's meridian passing through Paris.

In addition to the meter, the following units were also installed:

§ ar is the area of ​​a square whose side length is 10 m;

§ liter- volume and capacity of liquids and loose bodies, equal to the volume of a cube with an edge length of 0.1 m;

§ gram is the mass of pure water occupying the volume of a cube with an edge length of 0.01 m.

Decimal multiples and submultiples were also introduced, formed with the help of prefixes: myria (104), kilo (103), hecto (102), deca (101), deci, centi, milli

The kilogram mass unit was defined as the mass of 1 dm3 of water at a temperature of 4 °C.

Since all units of quantities turned out to be closely related to the unit of length, the meter, the new system of quantities was called metric system.

In accordance with the accepted definitions, platinum standards of the meter and kilogram were made:

§ the meter was represented by a ruler with strokes applied at its ends;

§ kilogram - a cylindrical weight.

These standards were transferred to the National Archives of France for storage, in connection with which they received the names "archival meter" and "archival kilogram".

The creation of the metric system of measures was a great scientific achievement - for the first time in history, measures appeared that form a harmonious system, based on a model taken from nature, and closely related to the decimal number system.

But soon this system had to be changed.

It turned out that the length of the meridian was not determined accurately enough. Moreover, it became clear that with the development of science and technology, the value of this quantity will be refined. Therefore, the unit of length, taken from nature, had to be abandoned. The meter began to be considered the distance between the strokes applied at the ends of the archival meter, and the kilogram - the mass of the standard of the archive kilogram.

In Russia, the metric system of measures began to be used on a par with Russian national measures starting in 1899, when a special law was adopted, the draft of which was developed by an outstanding Russian scientist. By special decrees of the Soviet state, the transition to the metric system of measures was legalized, first by the RSFSR (1918), and then completely by the USSR (1925).

4. International system of units

International System of Units (SI)- this is a single universal practical system of units for all branches of science, technology, the national economy and teaching. Since the need for such a system of units, which is uniform for the whole world, was great, in a short time it received wide international recognition and distribution throughout the world.

This system has seven basic units (meter, kilogram, second, ampere, kelvin, mole and candela) and two additional units (radian and steradian).

As you know, the unit of length, the meter, and the unit of mass, the kilogram, were also included in the metric system of measures. What changes did they undergo when they entered the new system? A new definition of the meter has been introduced - it is considered as the distance that a plane electromagnetic wave travels in vacuum in a fraction of a second. The transition to this definition of the meter is caused by an increase in the requirements for measurement accuracy, as well as the desire to have a unit of magnitude that exists in nature and remains unchanged under any conditions.

The definition of the unit of mass of the kilogram has not changed, as before, the kilogram is the mass of a cylinder made of platinum-iridium alloy, made in 1889. This standard is stored at the International Bureau of Weights and Measures in Sevres (France).

The third basic unit of the International System is the second unit of time. She is much older than a meter.

Prior to 1960, a second was defined as 0 " style="border-collapse:collapse;border:none">

Prefix names

Prefix designation

Factor

Prefix names

Prefix designation

Factor

For example, a kilometer is a multiple of a unit, 1 km = 103×1 m = 1000 m;

millimeter is a submultiple, 1 mm=10-3×1m = 0.001 m.

In general, for length, a multiple unit is a kilometer (km), and longitude units are centimeter (cm), millimeter (mm), micrometer (µm), nanometer (nm). For mass, the multiple unit is the megagram (Mg), and the submultiples are the gram (g), milligram (mg), microgram (mcg). For time, the multiple unit is the kilosecond (ks), and the submultiples are the millisecond (ms), microsecond (µs), nanosecond (not).

5. The quantities that preschoolers get acquainted with and their characteristics

The purpose of preschool education is to acquaint children with the properties of objects, to teach them to differentiate them, highlighting those properties that are commonly called quantities, to introduce the very idea of ​​​​measurement through intermediate measures and the principle of measuring quantities.

Length is a characteristic of the linear dimensions of an object. In the preschool methodology for the formation of elementary mathematical representations, it is customary to consider “length” and “width” as two different qualities of an object. However, in school, both linear dimensions of a flat figure are more often called "side length", the same name is used when working with a three-dimensional body that has three dimensions.

The lengths of any objects can be compared:

§ approximately;

§ application or overlay (combination).

In this case, it is always possible either approximately or precisely to determine "by how much one length is greater (less) than the other."

Weight is a physical property of an object, measured by weighing. Distinguish between mass and weight of an object. With a concept item weight children get acquainted in the 7th grade in a physics course, since weight is the product of mass and acceleration of free fall. The terminological incorrectness that adults allow themselves in everyday life often confuses the child, because we sometimes say without hesitation: "The weight of an object is 4 kg." The very word "weighing" encourages the use of the word "weight" in speech. However, in physics, these quantities differ: the mass of an object is always constant - this is a property of the object itself, and its weight changes if the force of attraction (free fall acceleration) changes.

In order for the child not to learn the wrong terminology, which will confuse him later in elementary school, you should always say: mass of the object.

In addition to weighing, mass can be approximately determined by an estimate on the arm (“baric feeling”). Mass is a category that is difficult from a methodological point of view for organizing classes with preschoolers: it cannot be compared by eye, application, or measured by an intermediate measure. However, any person has a “baric feeling”, and using it, you can build a number of tasks that are useful for the child, leading him to an understanding of the meaning of the concept of mass.

The basic unit of mass is kilogram. From this basic unit, other units of mass are formed: grams, tons, etc.

Square- this is a quantitative characteristic of a figure, indicating its dimensions on a plane. The area is usually determined for flat closed figures. To measure the area as an intermediate measure, you can use any flat shape that fits snugly into this figure (without gaps). In elementary school, children are introduced to palette - a piece of transparent plastic coated with a grid of squares of equal size (usually 1 cm2 in size). Overlaying a palette on a flat figure makes it possible to calculate the approximate number of squares that fit in it to determine its area.

At preschool age, children compare the areas of objects without naming this term, using the imposition of objects or visually, by comparing the space they occupy on the table, on the ground. The area is a convenient value from a methodological point of view, since it allows the organization of various productive exercises for comparing and equalizing areas, determining the area by laying down intermediate measures and through a system of tasks for equal composition. For example:

1) comparison of the areas of figures by the overlay method:

The area of ​​a triangle is less than the area of ​​a circle, and the area of ​​a circle is greater than the area of ​​a triangle;

2) comparison of the areas of figures by the number of equal squares (or any other measurements);

The areas of all figures are equal, since the figures consist of 4 equal squares.

When performing such tasks, children indirectly get acquainted with some area properties:

§ The area of ​​a figure does not change when its position on the plane changes.

§ A part of an object is always less than the whole.

§ The area of ​​the whole is equal to the sum of the areas of its constituent parts.

These tasks also form in children the concept of area as a number of measures contained in a geometric figure.

Capacity is a characteristic of liquid measures. At school, capacity is considered sporadically in one lesson in grade 1. They introduce children to a measure of capacity - a liter in order to use the name of this measure in the future when solving problems. The tradition is such that capacity is not associated with the concept of volume in elementary school.

Time is the duration of the process. The concept of time is more complex than the concept of length and mass. In everyday life, time is what separates one event from another. In mathematics and physics, time is considered as a scalar quantity, because time intervals have properties similar to those of length, area, mass:

§ Time spans can be compared. For example, a pedestrian will spend more time on the same path than a cyclist.

§ Time intervals can be added. Thus, a lecture in college lasts the same amount of time as two lessons in high school.

§ Time intervals are measured. But the process of measuring time is different from measuring length. You can repeatedly use a ruler to measure length by moving it from point to point. The time interval taken as a unit can be used only once. Therefore, the unit of time must be a regularly repeating process. Such a unit in the International System of Units is called second. Along with the second, other units of time: minute, hour, day, year, week, month, century .. Such units as year and day were taken from nature, and hour, minute, second were invented by man.

A year is the time it takes for the Earth to revolve around the Sun. A day is the time it takes the Earth to rotate around its axis. A year consists of approximately 365 days. But a year of human life consists of a whole number of days. Therefore, instead of adding 6 hours to each year, they add a whole day to every fourth year. This year consists of 366 days and is called a leap year.

A calendar with such an alternation of years was introduced in 46 BC. e. Roman emperor Julius Caesar in order to streamline the very confusing calendar that existed at that time. Therefore, the new calendar is called the Julian. According to him, the new year begins on January 1 and consists of 12 months. It also preserved such a measure of time as a week, invented by the Babylonian astronomers.

Time sweeps away both physical and philosophical meaning. Since the sense of time is subjective, it is difficult to rely on feelings in its evaluation and comparison, as can be done to some extent with other quantities. In this regard, at school, almost immediately, children begin to get acquainted with devices that measure time objectively, that is, regardless of human sensations.

When getting acquainted with the concept of "time" at first, it is much more useful to use an hourglass than a watch with arrows or an electronic one, since the child sees how the sand is pouring and can observe the "flow of time." An hourglass is also convenient to use as an intermediate measure when measuring time (in fact, this is precisely what they were invented for).

Working with the value of "time" is complicated by the fact that time is a process that is not directly perceived by the child's sensory system: unlike mass or length, it cannot be touched or seen. This process is perceived by a person indirectly, in comparison with the duration of other processes. At the same time, the usual stereotypes of comparisons: the course of the sun across the sky, the movement of the hands in a clock, etc. - as a rule, are too long for a child of this age to really be able to trace them.

In this regard, "Time" is one of the most difficult topics in both preschool mathematics and elementary school.

The first ideas about time are formed at preschool age: the change of seasons, the change of day and night, children get acquainted with the sequence of concepts: yesterday, today, tomorrow, the day after tomorrow.

By the beginning of schooling, children form ideas about time as a result of practical activities related to the duration of processes: performing routine moments of the day, keeping a weather calendar, getting to know the days of the week, their sequence, children get acquainted with the clock and orientate themselves in connection with visiting kindergarten. It is quite possible to introduce children to such units of time as a year, month, week, day, to clarify the idea of ​​the hour and minute and their duration in comparison with other processes. The instruments for measuring time are the calendar and the clock.

Speed is the path traveled by the body per unit of time.

Speed ​​is a physical quantity, its names contain two quantities - units of length and units of time: 3 km / h, 45 m / min, 20 cm / s, 8 m / s, etc.

It is very difficult to give a visual representation of speed to a child, since this is the ratio of path to time, and it is impossible to depict or see it. Therefore, when getting acquainted with speed, one usually refers to a comparison of the time it takes objects to travel an equal distance or the distances they cover in the same time.

Named numbers are numbers with the names of units of measurement. When solving problems at school, you have to perform arithmetic operations with them. The acquaintance of preschoolers with named numbers is provided in the programs "School 2000" ("One - a step, two - a step ...") and "Rainbow". In the School 2000 program, these are tasks of the form: "Find and correct errors: 5 cm + 2 cm - 4 cm = 1 cm, 7 kg + 1 kg - 5 kg = 4 kg." In the Rainbow program, these are tasks of the same type, but by “names” there is meant any name with numerical values, and not just the names of measures of quantities, for example: 2 cows + 3 dogs + + 4 horses \u003d 9 animals.

Mathematically, you can perform an action with named numbers in the following way: perform actions with the numerical components of named numbers, and add a name when writing the answer. This method requires compliance with the rule of a single name in the components of the action. This method is universal. In elementary school, this method is also used when performing actions with composite named numbers. For example, to add 2 m 30 cm + 4 m 5 cm, children replace the composite named numbers with numbers of the same name and perform the action: 230 cm + 405 cm = 635 cm = 6 m 35 cm or add the numerical components of the same names: 2 m + 4 m = 6 m, 30 cm + 5 cm = 35 cm, 6 m + 35 cm = 6 m 35 cm.

These methods are used when performing arithmetic operations with numbers of any names.

Units of some quantities

Units of length 1 km = 1,000 m 1 m = 10 dm = 100 m 1 dm = 10 cm 1cm=10mm	Mass units 1 t = 1,000 kg 1 kg = 1,000 g 1 g = 1,000 mg	Ancient measures of length 1 verst = 500 fathoms = 1,500 arshins = = 3,500 feet = 1,066.8 m 1 sazhen = 3 arshins = 48 vershoks = 84 inches = 2.1336 m 1 yard = 91.44cm 1 arshin \u003d 16 inches \u003d 71.12 cm 1 inch = 4.450 cm 1 inch = 2.540 cm 1 weave = 2.13 cm
area units 1 m2 = 100 dm2 = cm2 1 ha = 100 a = m2 1 a (ar) = 100m2	Volume units 1 m3 = 1,000 dm3 = 1,000,000 cm3 1 dm3 = 1,000 cm3 1 bbl (barrel) = 158.987 dm3 (l)	Mass measures 1 pood = 40 pounds = 16.38 kg 1 lb = 0.40951 kg 1 carat = 2×10-4 kg

Physical quantity- this is such a physical quantity, which, by agreement, is assigned a numerical value equal to one.

The tables show the 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

Value	Symbol	SI unit	Description
Length	l	meter (m)	The length of an object in one dimension.
Weight	m	kilogram (kg)	The value that determines the inertial and gravitational properties of bodies.
Time	t	second (s)	Event duration.
The strength of the electric current	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.
Amount of substance	ν	mole (mol)	The number of particles referred to the number of atoms in 0.012 kg 12 C

Derived quantities

Value	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	The product of mass and velocity of a body.
Force		kg m / s 2 (newton, N)	The external cause of acceleration acting on the object.
mechanical work	A	kg m 2 / s 2 (joule, J)	The scalar 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 energy change.
Pressure	p	kg / (m s 2) (Pascal, Pa)	Force per unit area.
Density	ρ	kg / m 3	Mass per unit volume.
Surface density	ρ A	kg/m2	Mass per unit area.
Line 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, C)
Voltage	U	m 2 kg / (s 3 A) (volt, V)	The change in potential energy per unit of 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 (radian 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.
angular 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 times the length of the perpendicular from a point to the line of action of the force.
Solid angle	Ω	steradian (sr)

Value is something that can be measured. Concepts such as length, area, volume, mass, time, speed, etc. are called quantities. The value is measurement result, it is determined by a number expressed in certain units. The units in which a quantity is measured are called units of measurement.

To designate a quantity, a number is written, and next to it is the name of the unit in which it was measured. For example, 5 cm, 10 kg, 12 km, 5 min. Each value has an infinite number of values, for example, the length can be equal to: 1 cm, 2 cm, 3 cm, etc.

The same value can be expressed in different units, for example, kilogram, gram and ton are units of weight. The same value in different units is expressed by different numbers. For example, 5 cm = 50 mm (length), 1 hour = 60 minutes (time), 2 kg = 2000 g (weight).

To measure a quantity means to find out how many times it contains another quantity of the same kind, taken as a unit of measurement.

For example, we want to know the exact length of a room. So we need to measure this length using another length that is well known to us, for example, using a meter. To do this, set aside a meter along the length of the room as many times as possible. If he fits exactly 7 times along the length of the room, then its length is 7 meters.

As a result of measuring the quantity, one obtains or named number, for example 12 meters, or several named numbers, for example 5 meters 7 centimeters, the totality of which is called composite named number.

Measures

In each state, the government has established certain units of measurement for various quantities. A precisely calculated unit of measurement, taken as a model, is called standard or exemplary unit. Model units of the meter, kilogram, centimeter, etc., were made, according to which units for everyday use are made. Units that have come into use and approved by the state are called measures.

The measures are called homogeneous if they serve to measure quantities of the same kind. So, grams and kilograms are homogeneous measures, since they serve to measure weight.

Units

The following are units of measurement for various quantities that are often found in math problems:

Measures of weight/mass

• 1 ton = 10 centners
• 1 centner = 100 kilograms
• 1 kilogram = 1000 grams
• 1 gram = 1000 milligrams

• 1 kilometer = 1000 meters
• 1 meter = 10 decimeters
• 1 decimeter = 10 centimeters
• 1 centimeter = 10 millimeters

• 1 sq. kilometer = 100 hectares
• 1 hectare = 10000 sq. meters
• 1 sq. meter = 10000 sq. centimeters
• 1 sq. centimeter = 100 sq. millimeters

• 1 cu. meter = 1000 cubic meters decimeters
• 1 cu. decimeter = 1000 cu. centimeters
• 1 cu. centimeter = 1000 cu. millimeters

Let's consider another value like liter. A liter is used to measure the capacity of vessels. A liter is a volume that is equal to one cubic decimeter (1 liter = 1 cubic decimeter).

Measures of time

• 1 century (century) = 100 years
• 1 year = 12 months
• 1 month = 30 days
• 1 week = 7 days
• 1 day = 24 hours
• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 second = 1000 milliseconds

In addition, time units such as quarter and decade are used.

• quarter - 3 months
• decade - 10 days

The month is taken as 30 days, unless it is required to specify the day and name of the month. January, March, May, July, August, October and December - 31 days. February in a simple year has 28 days, February in a leap year has 29 days. April, June, September, November - 30 days.

A year is (approximately) the time it takes for the Earth to complete one revolution around the Sun. It is customary to count every three consecutive years for 365 days, and the fourth following them - for 366 days. A year with 366 days is called leap year, and years containing 365 days - simple. One extra day is added to the fourth year for the following reason. The time of revolution of the Earth around the Sun does not contain exactly 365 days, but 365 days and 6 hours (approximately). Thus, a simple year is shorter than a true year by 6 hours, and 4 simple years are shorter than 4 true years by 24 hours, that is, by one day. Therefore, one day (February 29) is added to every fourth year.

You will learn about other types of quantities as you further study various sciences.

Measure abbreviations

Abbreviated names of measures are usually written without a dot:

Kilometer - km Meter - m Decimeter - dm centimeter - cm Millimeter - mm	Measures of weight/mass ton - t centner - c kilogram - kg gram - g milligram - mg
Area measures (square measures) sq. kilometer - km 2 hectare - ha sq. meter - m 2 sq. centimeter - cm 2 sq. millimeter - mm 2	cube meter - m 3 cube decimeter - dm 3 cube centimeter - cm 3 cube millimeter - mm 3
Measures of time century - in year - y month - m or mo week - n or week day - from or d (day) hour - h minute - m second - s millisecond - ms	A measure of the capacity of vessels liter - l

Measuring instruments

To measure various quantities, special measuring instruments are used. Some of them are very simple and are designed for simple measurements. Such devices include a measuring ruler, tape measure, measuring cylinder, etc. Other measuring devices are more complex. Such devices include stopwatches, thermometers, electronic scales, etc.

Measuring instruments, as a rule, have a measuring scale (or short scale). This means that dash divisions are marked on the device, and the corresponding value of the quantity is written next to each dash division. The distance between two strokes, next to which the value of the value is written, can be further divided into several smaller divisions, these divisions are most often not indicated by numbers.

It is not difficult to determine which value of the value corresponds to each smallest division. So, for example, the figure below shows a measuring ruler:

The numbers 1, 2, 3, 4, etc. indicate the distances between the strokes, which are divided into 10 equal divisions. Therefore, each division (the distance between the nearest strokes) corresponds to 1 mm. This value is called scale division measuring instrument.

Before you start measuring a quantity, you should determine the value of the division of the scale of the instrument used.

In order to determine the division price, you must:

1. Find the two nearest strokes of the scale, next to which the magnitude values ​​are written.
2. Subtract the smaller value from the larger value and divide the resulting number by the number of divisions in between.

As an example, let's determine the scale division value of the thermometer shown in the figure on the left.

Let's take two strokes, near which the numerical values ​​of the measured quantity (temperature) are plotted.

For example, strokes with symbols 20 °С and 30 °С. The distance between these strokes is divided into 10 divisions. Thus, the price of each division will be equal to:

(30 °C - 20 °C) : 10 = 1 °C

Therefore, the thermometer shows 47 °C.

Each of us constantly has to measure various quantities in everyday life. For example, to come to school or work on time, you have to measure the time that will be spent on the road. Meteorologists measure temperature, atmospheric pressure, wind speed, etc. to predict the weather.