Notation in physics - units of measurement of physical quantities

Each measurement is a comparison of the measured quantity with another homogeneous quantity, which is considered unitary. Theoretically, the units for all quantities in physics can be chosen to be independent of each other. But this is extremely inconvenient, since for each value one should enter its own standard. In addition, in all physical equations that reflect the relationship between different quantities, numerical coefficients would arise.

The main feature of the currently used systems of units is that there are certain relationships between units of different quantities. These relationships are established by the physical laws (definitions) that relate the measured quantities to each other. Thus, the unit of speed is chosen in such a way that it is expressed in terms of units of distance and time. When selecting speed units, the speed definition is used. The unit of force, for example, is established using Newton's second law.

When constructing a specific system of units, several physical quantities are selected, the units of which are set independently of each other. Units of such quantities are called basic. The units of other quantities are expressed in terms of the basic ones, they are called derivatives.

Table of units of measurement "Acoustics"

Physical quantity Symbol Unit of measurement of physical quantity Unit change physical led Description Notes
Sound pressure p pascal Pa Variable excess pressure arising in an elastic medium when a sound wave passes through it
Volume velocity c, V cubic meter per second m3/s The ratio of the volume of raw materials supplied to the reactor per hour to the volume of catalyst
Sound speed v, u meter per second m/s Velocity of propagation of elastic waves in a medium
Sound intensity l watt per square meter W/m2 A quantity characterizing the power transferred by a sound wave in the direction of propagation scalar physical quantity
Acoustic impedance Za, Ra pascal second per cubic meter Pa•s/m3 The ratio of the amplitude of sound pressure in a medium to the vibrational speed of its particles when a sound wave passes through the medium
Mechanical resistance Rm newton second per meter N•s/m Indicates the force required to move a body at each frequency

Designation: height, width, length. Width

Constructing drawings is not an easy task, but you can’t do without it in the modern world. After all, in order to make even the most ordinary item (a tiny bolt or nut, a shelf for books, the design of a new dress, etc.), you first need to carry out the appropriate calculations and draw a drawing of the future product. However, often one person draws it up, and another person produces something according to this scheme.

To avoid confusion in understanding the depicted object and its parameters, conventions for length, width, height and other quantities used in design are accepted all over the world. What are they? Let's find out.

Quantities

Area, length, width, height and other designations of a similar nature are not only physical, but also mathematical quantities.

Their single letter designation (used by all countries) was established in the mid-twentieth century by the International System of Units (SI) and is still used to this day. It is for this reason that all such parameters are indicated in Latin, and not in Cyrillic letters or Arabic script. In order not to create certain difficulties, when developing design documentation standards in most modern countries, it was decided to use almost the same conventions that are used in physics or geometry.

Any school graduate remembers that depending on whether a two-dimensional or three-dimensional figure (product) is depicted in the drawing, it has a set of basic parameters. If there are two dimensions, these are width and length, if there are three, height is also added.

So, first, let's find out how to correctly indicate length, width, height in the drawings.

Width

As mentioned above, in mathematics the quantity in question is one of the three spatial dimensions of any object, provided that its measurements are made in the transverse direction. So what is width famous for? It is designated by the letter “B”. This is known all over the world. Moreover, according to GOST, it is permissible to use both capital and lowercase Latin letters. The question often arises as to why this particular letter was chosen. After all, the abbreviation is usually made according to the first letter of the Latin, Greek or English name of the quantity. In this case, the width in English will look like “width”.

Probably the point here is that this parameter was initially most widely used in geometry. In this science, when describing figures, length, width, height are often denoted by the letters “a”, “b”, “c”. According to this tradition, when choosing, the letter "B" (or "b") was borrowed from the SI system (although symbols other than geometric ones began to be used for the other two dimensions).

Most believe that this was done so as not to confuse width (designated with the letter "B"/"b") with weight. The fact is that the latter is sometimes referred to as “W” (short for the English name weight), although the use of other letters (“G” and “P”) is also acceptable. According to international standards of the SI system, width is measured in meters or multiples (multiples) of their units. It is worth noting that in geometry it is sometimes also acceptable to use “w” to denote width, but in physics and other exact sciences such a designation is usually not used.

Length

As already mentioned, in mathematics, length, height, width are three spatial dimensions. Moreover, if width is a linear dimension in the transverse direction, then length is in the longitudinal direction. Considering it as a quantity of physics, one can understand that this word means a numerical characteristic of the length of lines.

In English this term is called length. It is because of this that this value is denoted by the capital or lowercase initial letter of the word - “L”. Like width, length is measured in meters or their multiples (multiples).

Height

The presence of this value indicates that we have to deal with a more complex - three-dimensional space. Unlike length and width, height numerically characterizes the size of an object in the vertical direction.

In English it is written as "height". Therefore, according to international standards, it is denoted by the Latin letter “H” / “h”. In addition to height, in drawings sometimes this letter also acts as a designation for depth. Height, width and length - all these parameters are measured in meters and their multiples and submultiples (kilometers, centimeters, millimeters, etc.).

Radius and diameter

In addition to the parameters discussed, when drawing up drawings you have to deal with others.

For example, when working with circles, it becomes necessary to determine their radius. This is the name of the segment that connects two points. The first of them is the center. The second is located directly on the circle itself. In Latin this word looks like "radius". Hence the generally accepted abbreviation: lowercase or capital “R”/“r”.

When drawing circles, in addition to the radius, you often have to deal with a phenomenon close to it - diameter. It is also a line segment connecting two points on a circle. In this case, it necessarily passes through the center.

Numerically, the diameter is equal to two radii. In English this word is written like this: “diameter”. Hence the abbreviation - large or small Latin letter “D” / “d”. Often the diameter in the drawings is indicated using a crossed out circle - “Ø”.

Although this is a common abbreviation, it is worth keeping in mind that GOST provides for the use of only the Latin “D” / “d”.

Thickness

Most of us remember school mathematics lessons. Even then, teachers told us that it is customary to use the Latin letter “s” to denote a quantity such as area. However, according to generally accepted standards, a completely different parameter is written in drawings in this way - thickness.

Why is that? It is known that in the case of height, width, length, the designation by letters could be explained by their writing or tradition. It’s just that thickness in English looks like “thickness”, and in Latin it looks like “crassities”. It is also not clear why, unlike other quantities, thickness can only be indicated in lowercase letters. The notation "s" is also used to describe the thickness of pages, walls, ribs, etc.

Perimeter and area

Unlike all the quantities listed above, the word “perimeter” does not come from Latin or English, but from Greek. It is derived from “περιμετρέο” (“to measure the circumference”). And today this term has retained its meaning (the total length of the boundaries of the figure). Subsequently, the word entered the English language (“perimeter”) and was fixed in the SI system in the form of an abbreviation with the letter “P”.

Area is a quantity that shows the quantitative characteristics of a geometric figure that has two dimensions (length and width). Unlike everything listed earlier, it is measured in square meters (as well as in submultiples and multiples thereof). As for the letter designation of the area, it differs in different areas. For example, in mathematics this is the Latin letter “S”, familiar to everyone since childhood. Why this is so - no information.


Some people unknowingly think that this is due to the English spelling of the word "square". However, in it the mathematical area is “area”, and “square” is the area in the architectural sense. By the way, it is worth remembering that “square” is the name of the geometric figure “square”. So you should be careful when studying drawings in English. Due to the translation of “area” in some disciplines, the letter “A” is used as a designation. In rare cases, “F” is also used, but in physics this letter means a quantity called “force” (“fortis”).

Other common abbreviations

The designations for height, width, length, thickness, radius, and diameter are the most commonly used when drawing up drawings. However, there are other quantities that are also often present in them. For example, lowercase "t". In physics, this means “temperature”, however, according to GOST of the Unified System of Design Documentation, this letter is the pitch (of helical springs, rivet joints, etc.). However, it is not used when it comes to gears and threads.

The capital and lowercase letter “A”/“a” (according to the same standards) in the drawings is used to denote not the area, but the center-to-center and center-to-center distance. In addition to different sizes, in drawings it is often necessary to indicate angles of different sizes. For this purpose, it is customary to use lowercase letters of the Greek alphabet. The most commonly used ones are “α”, “β”, “γ” and “δ”. However, it is acceptable to use others.

What standard defines the letter designation of length, width, height, area and other quantities?

As mentioned above, so that there is no misunderstanding when reading the drawing, representatives of different nations have adopted common standards for letter designation. In other words, if you are in doubt about the interpretation of a particular abbreviation, look at GOSTs. This way you will learn how to correctly indicate height, width, length, diameter, radius, and so on.

For the Russian Federation, such a regulatory document is GOST 2.321-84. It was introduced back in March 1984 (during the times of the USSR), to replace the outdated GOST 3452-59.

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Table of units of measurement “Periodic phenomena, oscillations and waves”

Physical quantity Symbol Unit of measurement of physical quantity Unit change physical led Description Notes
Period T second With The period of time during which the system makes one complete oscillation
Batch frequency v, f hertz Hz =

(s−1)

The number of repetitions of an event per unit of time.
Cyclic (circular) frequency ω radians per second rad/s Cyclic frequency of electromagnetic oscillations in an oscillatory circuit.
Rotation frequency n second to the minus first power s-1 A periodic process equal to the number of complete cycles completed per unit of time.
Wavelength λ meter m The distance between two points in space closest to each other at which the oscillations occur in the same phase.
Wave number k meter to the minus first power m-1 Spatial wave frequency

Table of units of measurement "Mechanics"

Physical quantity Symbol Unit of measurement of physical quantity Unit change physical led Description Notes
Weight m kilogram kg A quantity that determines the inertial and gravitational properties of bodies. extensive quantity
Density ρ kilogram per cubic meter kg/m3 Mass per unit volume. intensive quantity
Surface density ρA Mass per unit area. kg/m2 Ratio of body mass to surface area
Linear density ρl Mass per unit length. kg/m Ratio of body mass to its linear parameter
Specific volume v cubic meter per kilogram m3/kg Volume occupied by a unit mass of a substance
Mass flow Qm kilogram per second kg/s The mass of a substance that passes through a given cross-sectional area of ​​a flow per unit time
Volume flow Qv cubic meter per second m3/s Volume flow of liquid or gas
Pulse P kilogram-meter per second kg•m/s Product of mass and speed of a body. extensive, conserved quantity
Momentum L kilogram-meter squared per second kg•m2/s A measure of the rotation of an object. conserved quantity
Moment of inertia J kilogram meter squared kg•m2 A measure of the inertia of an object during rotation. tensor quantity
Strength, weight F, Q newton N An external cause of acceleration acting on an object. vector
Moment of power M newton meter N•m =

(kg m2/s2)

The product of a force and the length of a perpendicular drawn from a point to the line of action of the force. vector
Impulse force I newton second N•s Product of force and the duration of its action vector
Pressure, mechanical stress p , σ pascal Pa = ( kg/(m s2)) Force per unit area. intensive quantity
Job A joule J = (kg m2/s2) Dot product of force and displacement. scalar
Energy E, U joule J = (kg m2/s2) The ability of a body or system to do work. extensive, conserved quantity, scalar
Power N watt W = (kg m2/s3) Rate of change of energy.

Table of units of measurement "Molecular physics"

Physical quantity Symbol Unit of measurement of physical quantity Unit change physical led Description Notes
Quantity of substance v, n mole mole The number of similar structural units that make up a substance. Extensive value
Molar mass M , μ kilogram per mole kg/mol The ratio of the mass of a substance to the number of moles of that substance.
Molar energy Hmol joule per mole J/mol Energy of a thermodynamic system.
Molar heat capacity resins joule per mole kelvin J/(mol•K) The heat capacity of one mole of a substance.
Molecular concentration c, n meter to the minus third power m-3 The number of molecules contained in a unit volume.
Mass concentration ρ kilogram per cubic meter kg/m3 The ratio of the mass of a component contained in a mixture to the volume of the mixture.
Molar concentration resins mole per cubic meter mol/m3 The content of the component relative to the entire mixture.
Ion mobility V , μ square meter per volt second m2/(V•s) The proportionality coefficient between the drift velocity of carriers and the applied external electric field.

Table of units of measurement “Optics, electromagnetic radiation”

Physical quantity Symbol Unit of measurement of physical quantity Unit change physical led Description Notes
The power of light J, I candela cd The amount of light energy emitted in a given direction per unit time. Luminous, extensive value
Light flow F lumen lm Physical quantity characterizing the amount of “light” power in the corresponding radiation flux
Light energy Q lumen-second lm•s Physical quantity characterizes the ability of energy transferred by light to cause visual sensations in a person
Illumination E luxury OK The ratio of the luminous flux incident on a small area of ​​a surface to its area.
Luminosity M lumen per square meter lm/m2 Luminous quantity representing luminous flux
Brightness L,B candela per square meter cd/m2 Luminous intensity emitted per unit surface area in a specific direction
Radiation energy E,W joule J = (kg m2/s2) Energy transferred by optical radiation

Table of units of measurement “Space and time”

Physical quantity Symbol Unit of measurement of physical quantity Unit change physical led Description Notes
Length l, s, d meter m The extent of an object in one dimension.
Square S square meter m2 The extent of an object in two dimensions.
Volume, capacity V cubic meter m3 The extent of an object in three dimensions. extensive quantity
Time t second With Duration of the event.
Flat angle α , φ radian glad The amount of change in direction.
Solid angle α , β , γ steradian Wed Part of space
Linear speed v meter per second m/s The speed of changing body coordinates. vector
Linear acceleration a,w meters per second squared m/s2 The rate of change in the speed of an object. vector
Angular velocity ω radians per second rad/s =

(s−1)

Angle change rate.
Angular acceleration ε radian per second squared rad/s2 =

(s−2)

Rate of change of angular velocity

Table of units of measurement “Atomic and nuclear physics. Radioactivity"

Physical quantity Symbol Unit of measurement of physical quantity Unit change physical led Description Notes
Mass (rest mass) m kilogram kg The mass of an object at rest.
Mass defect Δ kilogram kg A quantity expressing the influence of internal interactions on the mass of a composite particle
Elementary electric charge e pendant Cl The minimum portion (quantum) of electric charge observed in nature in free long-lived particles
Communication energy Est joule J = (kg m2/s2) The difference between the energy of a state in which the constituent parts of the system are infinitely distant
Half-life, average lifetime T, τ second With The time during which the system decays in the approximate ratio of 1/2
Effective cross section σ square meter m2 A quantity characterizing the probability of interaction of an elementary particle with an atomic nucleus or another particle
Nuclide activity A becquerel Bk A value equal to the ratio of the total number of decays of radioactive nuclide nuclei in the source to the decay time
Energy of ionizing radiation E,W joule J = (kg m2/s2) Type of energy released by atoms in the form of electromagnetic waves (gamma or x-rays) or particles
Absorbed dose of ionizing radiation D gray Gr The dose at which 1 joule of ionizing radiation energy is transferred to a mass of 1 kg
Equivalent dose of ionizing radiation H , Deck sievert Sv Absorbed dose of any ionizing radiation equal to 100 erg per 1 gram of irradiated substance
Exposure dose of X-ray and gamma radiation X pendant per kilogram C/kg ratio of the total electric charge of ions of the same sign from external gamma radiation

Table of units of measurement “Thermal phenomena”

Physical quantity Symbol Unit of measurement of physical quantity Unit change physical led Description Notes
Temperature T kelvin TO The average kinetic energy of the object's particles. Intensive value
Temperature coefficient α kelvin to the minus first power K-1 Dependence of electrical resistance on temperature
Temperature gradient gradT kelvin per meter K/m Change in temperature per unit length in the direction of heat propagation.
Heat (amount of heat) Q joule J = (kg m2/s2) Energy transferred from one body to another by non-mechanical means
Specific heat q joule per kilogram J/kg The amount of heat that must be supplied to a substance taken at its melting point in order to melt it.
Heat capacity C joule per kelvin J/C The amount of heat absorbed (released) by a body during the heating process.
Specific heat c joule per kilogram kelvin J/(kg•K) Heat capacity of a unit mass of a substance.
Entropy S joule per kilogram J/kg A measure of the irreversible dissipation of energy or the uselessness of energy.

Indication of depth in the drawing - how width is indicated in construction

Quantities

Weight
Time
Height
Pressure
Diameter
Length
Path length
Impulse (amount of movement)
Quantity of substance
Stiffness coefficient (stiffness)
Safety factor
Efficiency
Rolling friction coefficient
Sliding friction coefficient
Weight
Atomic mass
Electron mass
Mechanical stress
Modulus of elasticity (Young's modulus)
Moment of power
Power
Volume, capacity
Oscillation period
Density
Square
Surface tension
Constant gravitational
Tensile strength
Job
Radius
Force, gravity
Linear speed
Angular speed
Thickness
Acceleration linear
Acceleration of gravity
Frequency
Rotation frequency
Width
Energy
Kinetic energy
Potential energy
Wavelength
Sound power
Sound energy
Sound intensity
Sound speed
Frequency
Thermal and molecular physics quantities
Absolute humidity
Gas constant (molar)
Quantity of heat
Efficiency
Relative humidity
Relative molecular weight
Avogadro's constant (number)
Boltzmann's constant
Loschmidt's constant (number)
Curie temperature
Temperature on the Celsius scale
Thermodynamic temperature (absolute temperature)
Temperature coefficient of linear expansion
Temperature coefficient of volumetric expansion
Specific heat
Specific heat of vaporization
Specific heat of fusion
Specific heat of combustion of fuel (abbreviated as heat of combustion of fuel)
Number of molecules
Energy internal
Electrical and magnetic quantities
Dielectric constant of vacuum (electric constant)
Inductance
Self-induction coefficient
Transformation ratio
Magnetic induction
Magnetic permeability of vacuum (magnetic constant)
Magnetic flux
Electric circuit power
Magnetic field strength
Electric field strength
Volume density of electric charge
Relative dielectric constant
Relative magnetic permeability
Specific magnetic field energy density
Specific electric field energy density
Surface charge density
Electric current density
Faraday's constant (number)
Dielectric constant
Electron work function
Potential difference
Current strength
Temperature coefficient of electrical resistance
Electrical conductivity
Electrical resistivity
Electric current frequency
Number of winding turns
Electrical capacity
Electrical induction
Electrical conductivity
Electric dipole moment of a molecule
Electric charge (amount of electricity)
Electric potential
Electrical voltage
Electrical resistance
Electromotive force
Electrochemical equivalent
Magnetic field energy
Electric field energy
Energy Electromagnetic
Wavelength
Illumination
Oscillation period
Radiation flux density
Index of refraction
Light flow
Light power lens
The power of light
Speed ​​of light
Magnification linear
Magnification of eyepiece, microscope, magnifying glass
Beam reflection angle
Beam angle
Focal length
Oscillation frequency
Radiation energy
Light energy
Atomic mass relative
Half-life
Mass defect
Electron charge
Atomic mass
Neutron mass
Proton mass
Electron mass
Planck's constant
Electron radius
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