Since 1963, in the USSR (GOST 9867-61 “International System of Units”), in order to unify units of measurement in all fields of science and technology, the international (international) system of units (SI, SI) has been recommended for practical use - this is a system of units of measurement of physical quantities , adopted by the XI General Conference on Weights and Measures in 1960. It is based on 6 basic units (length, mass, time, electric current, thermodynamic temperature and luminous intensity), as well as 2 additional units (plane angle, solid angle) ; all other units given in the table are their derivatives. The adoption of a unified international system of units for all countries is intended to eliminate the difficulties associated with the transfer of numerical values ​​of physical quantities, as well as various constants from any one currently operating system (GHS, MKGSS, ISS A, etc.) into another.

Note. Multiple and submultiple units of measurement, with the exception of units of time and angle, are formed by multiplying them by the appropriate power of 10, and their names are added to the names of the units of measurement. It is not allowed to use two prefixes to the name of the unit. For example, you cannot write millimicrowatt (mmkW) or micromicrofarad (mmf), but you must write nanowatt (nw) or picofarad (pf). You should not use prefixes to the names of such units that indicate a multiple or submultiple unit of measurement (for example, micron). To express the duration of processes and designate calendar dates of events, the use of multiple units of time is allowed.

The most important units of the International System of Units (SI)

Basic units
(length, mass, temperature, time, electric current, light intensity)

Additional and derived units

This guide has been compiled from various sources. But its creation was prompted by a small book from the Mass Radio Library, published in 1964, as a translation of O. Kroneger’s book in the GDR in 1961. Despite its antiquity, it is my reference book (along with several other reference books). I think time has no power over such books, because the fundamentals of physics, electrical and radio engineering (electronics) are unshakable and eternal.

Units of measurement of mechanical and thermal quantities.

The units of measurement of all other physical quantities can be defined and expressed through basic units of measurement. The units obtained in this way, in contrast to the basic ones, are called derivatives. To obtain a derived unit of measurement of any quantity, it is necessary to choose a formula that would express this quantity through other quantities already known to us, and assume that each of the known quantities included in the formula is equal to one unit of measurement. A number of mechanical quantities are listed below, formulas for their determination are given, and it is shown how the units of measurement of these quantities are determined. Unit of speed v- meter per second (m/sec) . Meter per second is the speed v of such uniform motion in which the body covers a path s equal to 1 m in time t = 1 second: 1v=1m/1sec=1m/sec Acceleration unit A - meters per second squared (m/sec 2). Meter per second squared - acceleration of such uniform motion, in which the speed changes by 1 m!sec in 1 second. Unit of force F - newton (And). Newton - the force that imparts an acceleration a equal to 1 m/sec 2 to a mass t of 1 kg: 1н=1 kg×1m/sec 2 =1(kg×m)/sec 2 Unit of work A and energy- joule (j). Joule -work done by a constant force F, equal to 1 n, on a path s in 1 m, traveled by a body under the influence of this force in a direction coinciding with the direction of the force: 1j=1n×1m=1n*m. Power unit W -watt (Tue). Watt - power at which work A equal to 1 J is performed in time t=-l sec: 1w=1j/1sec=1j/sec. Unit of heat quantity q - joule (j). This unit is determined from the equality: which expresses the equivalence of thermal and mechanical energy. Coefficient k taken equal to one: 1j=1×1j=1j Units of measurement of electromagnetic quantities Unit of electric current A - ampere (A). The force of an unchanging current, which, passing through two parallel straight conductors of infinite length and negligibly small circular cross-section, located at a distance of 1 m from each other in a vacuum, would cause between these conductors a force equal to 2 × 10 -7 newton. Unit of quantity of electricity (unit of electric charge) Q- pendant (To). Pendant - charge transferred through the cross-section of the conductor in 1 second at a current strength of 1 A: 1k=1a×1sec=1a×sec Unit of electrical potential difference (electrical voltage U, electromotive force E) - volt (V). Volt - the potential difference between two points of the electric field, when moving between which a charge Q of 1 K, work of 1 J is performed: 1v=1j/1k=1j/k Unit of electrical power R - watt (Tue): 1w=1v×1a=1v×a This unit is the same as the unit of mechanical power. Capacity unit WITH - farad (f). Farad - the capacitance of a conductor, the potential of which increases by 1 V if a charge of 1 k is applied to this conductor: 1f=1k/1v=1k/v Unit of electrical resistance R - ohm (ohm). - the resistance of a conductor through which a current of 1 A flows with a voltage at the ends of the conductor of 1 V: 1ohm=1v/1a=1v/a Unit of absolute dielectric constant ε- farad per meter (f/m). farad per meter - absolute dielectric constant of the dielectric, when filled with a flat capacitor with plates of area S of 1 m 2 each and a distance between the plates d~ 1 m acquires a capacity of 1 lb. Formula expressing the capacitance of a parallel-plate capacitor: From here 1f\m=(1f×1m)/1m 2 Unit of magnetic flux Ф and flux linkage ψ - volt second or weber (vb). Weber - magnetic flux, when it decreases to zero in 1 second, an e-wave appears in a circuit coupled with this flux. d.s. induction equal to 1 V. Faraday - Maxwell's law: E i =Δψ / Δt Where Ei- e. d.s. induction occurring in a closed loop; ΔW - change in magnetic flux coupled to the circuit during time Δ t : 1vb=1v*1sec=1v*sec Recall that for a single turn of the concept of flow Ф and flux linkage ψ match. For a solenoid with the number of turns ω, through the cross section of which flow Ф flows, in the absence of dissipation the flux linkage Unit of magnetic induction B - tesla (tl). Tesla - the induction of such a uniform magnetic field in which the magnetic flux φ through an area S of 1 m*, perpendicular to the direction of the field, is equal to 1 wb: 1tl = 1vb/1m 2 = 1vb/m 2 Unit of magnetic field strength N - ampere per meter (a!m). Ampere per meter - magnetic field strength created by a rectilinear infinitely long current with a force of 4 pa at a distance r = 2 m from the current-carrying conductor: 1a/m=4π a/2π * 2m Unit of inductance L and mutual inductance M - Henry (gn). - inductance of a circuit with which a magnetic flux of 1 Vb is connected, when a current of 1 A flows through the circuit: 1gn = (1v × 1sec)/1a = 1 (v×sec)/a Unit of magnetic permeability μ (mu) - henry per meter (g/m). Henry per meter - absolute magnetic permeability of a substance in which, at a magnetic field strength of 1 a/m magnetic induction is 1 tl: 1gn/m = 1vb/m 2 / 1a/m = 1vb/(a×m)

Relationships between units of magnetic quantities
in SGSM and SI systems

Non-system units

Some mathematical and physical concepts
used in radio engineering

Just like the concept of speed of movement, in mechanics and radio engineering there are similar concepts, such as the rate of change of current and voltage. They can be either averaged over the course of the process or instantaneous.

i= (I 1 -I 0)/(t 2 -t 1)=ΔI/Δt

When Δt -> 0, we obtain instantaneous values ​​of the rate of change of current. It most accurately characterizes the nature of the change in value and can be written as:

i=lim ΔI/Δt =dI/dt Δt->0

Moreover, you should pay attention - average values ​​and instantaneous values ​​can differ tens of times. This is especially clearly seen when a changing current flows through circuits with a sufficiently large inductance.

decibel

To evaluate the ratio of two quantities of the same dimension in radio engineering, a special unit is used - the decibel.

K u = U 2 / U 1 Voltage gain; K u[db] = 20 log U 2 / U 1 Voltage gain in decibels. Ki[db] = 20 log I 2 / I 1 Current gain in decibels. Kp[db] = 10 log P 2 / P 1 Power gain in decibels.

The logarithmic scale also allows you to depict functions with a dynamic range of parameter changes of several orders of magnitude on a graph of normal sizes.

To determine the signal strength in the reception area, another logarithmic unit of the DBM is used - dicibels per meter. Signal power at the receiving point in dbm:

P [dbm] = 10 log U 2 / R +30 = 10 log P + 30. [dbm];

The effective voltage across the load at a known P[dBm] can be determined by the formula:

Dimensional coefficients of basic physical quantities

Length and distance converter Mass converter Bulk and food volume converter Area converter Volume and unit converter in culinary recipes Temperature converter Pressure, mechanical stress, Young's modulus converter Energy and work converter Power converter Force converter Time converter Linear speed converter Flat angle Converter of thermal efficiency and fuel efficiency Converter of numbers in different number systems Converter of units of measurement of quantity of information Currency rates Sizes of women's clothing and shoes Sizes men's clothing and footwear Angular velocity and rotational speed converter Acceleration converter Angular acceleration converter Density converter Specific volume converter Moment of inertia converter Moment of force converter Torque converter Specific heat of combustion converter (by mass) Converter of energy density and specific heat of combustion of fuel (by volume) Converter Temperature difference Thermal expansion coefficient converter Thermal resistance converter Thermal conductivity converter Specific heat capacity converter Energy exposure and thermal radiation power converter Heat flux density converter Heat transfer coefficient converter Volume flow rate converter Mass flow rate converter Molar flow rate converter Mass flow density converter Molar concentration converter Mass concentration in solution converter Dynamic (absolute) viscosity converter Kinematic viscosity converter Surface tension converter Vapor permeability converter Vapor permeability and vapor transfer rate converter Sound level converter Microphone sensitivity converter Sound pressure level (SPL) converter Sound pressure level converter with selectable reference pressure Brightness converter Luminous intensity converter Illuminance converter Converter Resolutions in Computer Graphics Frequency and Wavelength Converter Diopter Power and Focal Length Diopter Power and Lens Magnification (×) Electric Charge Converter Linear Charge Density Converter Surface Charge Density Converter Volume Charge Density Converter Electric Current Converter Linear Current Density Converter Surface Converter current density Electric field strength converter Electrostatic potential and voltage converter Electrical resistance converter Electrical resistivity converter Electrical conductivity converter Electrical conductivity converter Electrical capacitance Inductance converter American wire gauge converter Levels in dBm (dBm or dBmW), dBV (dBV), watts, etc. . units Magnetomotive force converter Magnetic field strength converter Magnetic flux converter Magnetic induction converter Radiation. Ionizing radiation absorbed dose rate converter Radioactivity. Radioactive decay converter Radiation. Exposure dose converter Radiation. Absorbed Dose Converter Decimal Prefix Converter Data Transfer Typography and Imaging Unit Converter Timber Volume Unit Converter Molar Mass Calculation Periodic Table chemical elements D. I. Mendeleev

1 meter per second [m/s] = 3600 meter per hour [m/h]

Initial value

Converted value

meter per second meter per hour meter per minute kilometer per hour kilometer per minute kilometer per second centimeter per hour centimeter per minute centimeter per second millimeter per hour millimeter per minute millimeter per second foot per hour foot per minute foot per second yard per hour yard per minute yard per second mile per hour mile per minute miles per second knot knot (UK) speed of light in vacuum first escape velocity second escape velocity third escape velocity speed of rotation of the Earth speed of sound in fresh water speed of sound in sea ​​water(20°C, depth 10 meters) Mach number (20°C, 1 atm) Mach number (SI standard)

More about speed

General information

Speed ​​is a measure of the distance traveled in a certain time. Speed ​​can be a scalar quantity or a vector quantity - the direction of movement is taken into account. The speed of movement in a straight line is called linear, and in a circle - angular.

Speed ​​measurement

Average speed v found by dividing the total distance traveled ∆ x for total time ∆ t: v = ∆x/∆t.

In the SI system, speed is measured in meters per second. Kilometers per hour in the metric system and miles per hour in the US and UK are also widely used. When, in addition to the magnitude, the direction is also indicated, for example, 10 meters per second to the north, then we're talking about about vector speed.

The speed of bodies moving with acceleration can be found using the formulas:

• a, with initial speed u during the period ∆ t, has a finite speed v = u + a×∆ t.
• A body moving with constant acceleration a, with initial speed u and final speed v, has average speed ∆v = (u + v)/2.

Average speeds

Speed ​​of light and sound

According to the theory of relativity, the speed of light in a vacuum is the highest speed at which energy and information can travel. It is denoted by the constant c and is equal to c= 299,792,458 meters per second. Matter cannot move at the speed of light because it would require an infinite amount of energy, which is impossible.

The speed of sound is usually measured in an elastic medium, and is equal to 343.2 meters per second in dry air at a temperature of 20 °C. The speed of sound is lowest in gases and highest in solids X. It depends on the density, elasticity, and shear modulus of the substance (which shows the degree of deformation of the substance under shear load). Mach number M is the ratio of the speed of a body in a liquid or gas medium to the speed of sound in this medium. It can be calculated using the formula:

M = v/a,

Where a is the speed of sound in the medium, and v- body speed. Mach number is commonly used in determining speeds close to the speed of sound, such as airplane speeds. This value is not constant; it depends on the state of the medium, which, in turn, depends on pressure and temperature. Supersonic speed is a speed exceeding Mach 1.

Vehicle speed

Below are some vehicle speeds.

• Passenger aircraft with turbofan engines: The cruising speed of passenger aircraft is from 244 to 257 meters per second, which corresponds to 878–926 kilometers per hour or M = 0.83–0.87.
• High-speed trains (like the Shinkansen in Japan): such trains reach maximum speeds of 36 to 122 meters per second, that is, from 130 to 440 kilometers per hour.

Animal speed

The maximum speeds of some animals are approximately equal to:

Human speed

• People walk at speeds of about 1.4 meters per second, or 5 kilometers per hour, and run at speeds of up to about 8.3 meters per second, or 30 kilometers per hour.

Examples of different speeds

Four-dimensional speed

In classical mechanics, vector velocity is measured in three-dimensional space. According to special theory relativity, space is four-dimensional, and the measurement of speed also takes into account the fourth dimension - space-time. This speed is called four-dimensional speed. Its direction may change, but its magnitude is constant and equal to c, that is, the speed of light. Four-dimensional speed is defined as

U = ∂x/∂τ,

Where x represents a world line - a curve in space-time along which a body moves, and τ is the "proper time" equal to the interval along the world line.

Group speed

Group velocity is the speed of wave propagation, describing the speed of propagation of a group of waves and determining the speed of wave energy transfer. It can be calculated as ∂ ω /∂k, Where k is the wave number, and ω - angular frequency. K measured in radians/meter, and the scalar frequency of wave oscillation ω - in radians per second.

Hypersonic speed

Hypersonic speed is a speed exceeding 3000 meters per second, that is, many times faster than the speed of sound. Solid bodies moving at such speeds acquire the properties of liquids, since, thanks to inertia, the loads in this state are stronger than the forces that hold the molecules of a substance together during collisions with other bodies. At ultrahigh hypersonic speeds, two colliding solids turn into gas. In space, bodies move at exactly this speed, and engineers designing spacecraft, orbital stations and spacesuits must consider the possibility of a station or astronaut colliding with space debris and other objects when working in outer space. In such a collision, the casing suffers spaceship and a spacesuit. Hardware developers conduct hypersonic collision experiments in special laboratories to determine how intense impacts the suits can withstand, as well as the skin and other parts of the spacecraft, such as fuel tanks and solar panels, testing their strength. To do this, spacesuits and skin are exposed to impacts from various objects from a special installation at supersonic speeds exceeding 7500 meters per second.

Of the many angular characteristics and dynamometer indicators, the most obvious is the curve of changes in the axial forces acting on the stick when pushing off with the hands in the OBD. Strain gauges mounted under the handle were pre-calibrated with standard weights from 5 to 50 kg. The resistance to direct electric current changing under load was recorded at a frequency of 2000 times per second.

In the speed range from 21 km/h up to 30 km/h the total time of push-off with hands was from 0.34 sec up to 0.26 sec, total cycle time 1.2 - 0.9 sec. Peak maximum effort values ​​from 230 to 270 newton were achieved in 0.12 - 0.08 sec from the moment the pins are inserted.

At first it appears that the maximum axial force on each stick is 250 n fantastically great. However, in terms of application to two sticks, it means approximately 50 kg the weight with which the riders pressed on the support. In other words, with a good overhang of their feet, elite athletes lean on the poles approximately two thirds of its weight.

It is interesting to compare the graph of the change in axial force on each stick with the frames of P. Northug’s filmograms taken for example. Such a compilation allows us to approximately estimate the effectiveness of the athlete’s efforts depending on the angles of inclination of the poles in terms of his horizontal advancement.

When the racer leans on the sticks, hand pushing force Ffell applied to the handles and then to the pins. The force of the reaction of leaning on the sticks is transmitted from the hands to the shoulder joints. It also affects them rider weight, directed vertically downwards. Summed up in magnitude and direction, these forces give the skier a horizontal component of repulsion with poles - acceleration forcePAzg, which, then transmitted to the foot, ensures that the skis with the rider on them move forward:

Unfold =cosa . Ffell

As the skier pushes off and moves away from the pins, the angle of inclination of the poles decreases - from 85 degrees to the horizon when setting to 25 degrees at the moment of separation. During the entire repulsion time, the proportion of force transferred on sticks to horizontal movement increases by 10 times.

However, the effort itself is applied unevenly by athletes.

SI: 1 newton is equal to the force imparting to a body weighing 1 kg an acceleration of 1 m/s² in the direction of the force

The entire period of hand repulsion can be divided into three characteristic segments, approximately equal in time to 0.1 seconds each:

1. placing poles (85*) - pile (70*) - vertical stop (55*) - the average axial force in this segment is 200 kgf/sec2:

The rider thrusts the pins with a swing, bringing them 25-35 cm from the fastenings;

The force generated on the sticks initially drops as a result of its deformation and the shock absorption of the pose by bent forearms. The athlete drives up to the poles while working out the sagging of the body between the hands.

- “fast” muscle fibers develop maximum tension (their response time is 0.055-0.085 seconds). The skier pulls up the feet that are lagging behind when placing the poles.

2. - acceleration (47*) - stretching of the feet (40*) - the repulsion force increases, but due to the rider gaining inertia of movement, the pressure on the strain gauges begins to decrease, although on average it is the same 200 kgm/sec2 in the second segment:

- “slow” muscle fibers are connected to “fast” ones (reaction time 0.1-0.14 seconds). Skiers at moderate pole angles gain inertia, accelerating in the most efficient segment.

3. - push (33*) - take-off (25*) the angles of inclination of the poles are the most favorable, but the culmination of the push-off has passed and now occurs at increased speed when the push is performed in pursuit. The deformation of the sensors decreases, which indicates a decrease in resistance to muscle repulsion forces. The average axial force is 80 kgm/sec2.

Imp. Discussion 1= cos 70* (0.34) . 200 kg.m/sec2. 0.1 sec. 2 n = 13,6 kg.m/sec

Imp . Razg.2 = cos 47* (0.68) . 200 kg.m/sec2. 0.1 sec. 2p = 27,2 kg.m/sec

Imp. Ramp 3 = cos 33* (0.84) . 80 kg.m/sec2. 0.1 sec. 2p = 13,4 kg.m/sec

On the right top corner The figure shows a table of approximate calculations of the magnitude of the change in the speed of the rider as a result of pushing off with his hands. Based on the total impulse of force acceleration of the skier (Acceleration) along all three take-off segments 50-60 kgm/s, increasing the speed of the racer (change body impulse) is calculated as:

V1- V2 = Imp. Acceleration / Weight = 50-60 kgm/sec / 70-80 kg = 0.6 - 0.9 m/sec

Achieved in 0.3 sec such a change in speed corresponds to acceleration in 2 - 3 m/sec2. Accordingly, braking during free sliding during straightening and backswing 0.7 sec will be 0.9 - 1.2 m/sec2.

What practical conclusions can be drawn from this study?

1. In the classic Simultaneous Stepless Stroke, the end of push-off with poles does not make a significant contribution to increasing the horizontal movement of the riders - the readings of the strain gauges are recorded here descending effort values in the last third of the push-off with your hands.

2. The most “useful” part of the push-off from the point of view of the effectiveness of the application of muscle effort is the segment between the angles of inclination of the sticks from 60 degrees to 35. Before this the poles are too vertical and most of the athletes’ efforts are spent on creating emphasis in pulling their feet forward. After that At increasing speed, the riders do not have time to fully apply themselves to the slipping support.

3. Therefore, with an increase in the frequency of push-offs in OBH, as in KOOH, instead of pushing with the usual full extension of the arms, athletes “put a point” with their hands at the hips and take them forward in preparation for the next push-off.

At speeds of 7-8 m/sec, a full extension extension would help riders extend their push-off with their arms by another 25-30 cm, which, with a stride length of about 6 meters, would add an extra stride for about every 20 strides.

However, the additional movement of the hands and the delay in straightening the body will require extra time. A racer at a speed of 7-8 m/sec rushes 30 cm in 0.04 sec. It will take about the same amount of time to return your hands to the same “hands at the hips” position, i.e. total “back and forth” = 0.07-0.08 sec. Since the athlete will not be able to start the next step earlier, at ten steps the pushing will take up the time of an entire step. Thus, with OBX, the gain of one step for every 20 is per kilometer:

1000m / 120m(20step) . 6 m(1 step) = 50 m