All letters in physics. Designations in physics are units of measurement of physical quantities. Refractive index problems
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Paul Adrien Maurice Dirac Paul Adrien Maurice Dirac Date of birth: 8 &… Wikipedia
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The construction of drawings is not an easy task, but in the modern world there is nothing without it. Indeed, in order to make even the most ordinary object (a tiny bolt or nut, a shelf for books, a design for a new dress, etc.), you first need to carry out the appropriate calculations and draw a drawing of the future product. However, it is often made up by one person, and another person is engaged in the manufacture of something according to this scheme.
To avoid confusion in understanding the depicted object and its parameters, the symbols of length, width, height and other quantities used in design are accepted all over the world. What are they? Let's find out.
The quantities
Area, 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 middle of the twentieth century by the International System of Units (SI) and is used to this day. It is for this reason that all such parameters are indicated in Latin, not Cyrillic letters or Arabic script. In order not to create individual difficulties, when developing standards for design documentation 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 shown in the drawing, it has a set of basic parameters. If there are two dimensions - these are the width and the length, if there are three of them - the height is also added.
So, first, let's find out how to correctly designate the length, width, height in the drawings.
Width
As mentioned above, in mathematics, the value under consideration 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 has the designation of the letter "B". This is known all over the world. Moreover, according to GOST, it is permissible to use both uppercase and lowercase Latin letters. The question often arises as to why such a letter was chosen. After all, usually the abbreviation is made according to the first 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, often the length, width, height are denoted by the letters "a", "b", "c". According to this tradition, when choosing the letter "B" (or "b") was borrowed by the SI system (although for the other two dimensions they began to use symbols other than geometric).
Most assume this was done so as not to confuse width (indicated by the letter "B" / "b") with weight. The fact is that the latter is sometimes referred to as "W" (an abbreviation for the English name weight), although it is permissible to use other letters ("G" and "P"). According to international standards of the SI system, the width is measured in meters or multiples (sub-multiples) of their units. It is worth noting that in geometry it is sometimes also permissible to use "w" to denote width, but in physics and other exact sciences, this designation, as a rule, is not used.
Length
As already mentioned, in mathematics, length, height, width are three spatial dimensions. Moreover, if the width is a linear dimension in the transverse direction, then the length is in the longitudinal direction. Considering it as the magnitude of physics, one can understand that this word means a numerical characteristic of the length of the lines.
In English, this term is referred to as length. It is because of this that this value is designated by the uppercase or lowercase initial letter of this word - "L". Like width, length is measured in meters or their multiples (sub-multiples) units.
Height
The presence of this value indicates that one has 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 spelled as "height". Therefore, according to international standards, it is designated by the Latin letter "H" / "h". In addition to height, in drawings sometimes this letter also acts as a depth designation. Height, width and length - all these parameters are measured in meters and their multiples and sub-multiples (kilometers, centimeters, millimeters, etc.).
Radius and diameter
In addition to the parameters considered, when drawing up drawings, one has to deal with others.
For example, when working with circles, it becomes necessary to determine their radius. This is the name of the line that connects two points. The first one is the center. The second is located directly on the circle itself. In Latin, this word looks like "radius". Hence the lowercase or uppercase "R" / "r".
When drawing circles, in addition to the radius, one often has to deal with a phenomenon close to it - the diameter. It is also a line segment connecting two points on a circle. Moreover, it necessarily passes through the center.
Numerically, the diameter is equal to two radii. In English this word is spelled like this: "diameter". Hence the abbreviation - large or small Latin letter "D" / "d". Often the diameter in the drawings is indicated by the crossed out circle - "Ø".
Although this is a common abbreviation, it should be borne in mind that GOST provides for the use of only the Latin "D" / "d".
Thickness
Most of us remember our school math lessons. Even then, teachers said that the Latin letter "s" is customary to denote such a value as area. However, according to generally accepted standards, a completely different parameter is recorded in the drawings in this way - thickness.
Why is that? It is known that in the case of height, width, length, the designation with letters could be explained by their writing or tradition. But the thickness in English looks like "thickness", and in the Latin version - "crassities". It is also not clear why, unlike other values, thickness can only be indicated by lowercase letters. The notation "s" is also used to describe the thickness of pages, sides, edges, and so on.
Perimeter and area
Unlike all of the above values, the word "perimeter" did not come from Latin or English, but from the Greek language. It is derived from "περιμετρέο" (to measure the circumference). And today this term has retained its meaning (the total length of the borders of the figure). Subsequently, the word got into the English language ("perimeter") and was fixed in the SI system in the form of abbreviation with the letter "P".
Area is a quantity that shows the quantitative characteristics of a geometric figure with two dimensions (length and width). Unlike everything listed earlier, it is measured in square meters (as well as in sub-multiples and multiples of their units). 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 from childhood. Why 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 shape "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
Designations of height, width, length, thickness, radius, diameter are the most used in drawing up drawings. However, there are other quantities that are also often present in them. For example, the lowercase "t". In physics, this means "temperature", however, according to GOST of the Unified System for Design Documentation, this letter is a step (of helical springs, and the like). However, it is not used when it comes to gearing and threads.
The capital and small letter "A" / "a" (according to all 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 the different values, angles of different sizes are often indicated in the drawings. For this, it is customary to use lowercase letters of the Greek alphabet. The most commonly used are "α", "β", "γ" and "δ". However, it is permissible to use others as well.
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 peoples have adopted common standards for letter designation. In other words, if you are in doubt about the interpretation of a particular abbreviation, take a look at GOSTs. Thus, you will find out how the height, width, length, diameter, radius, and so on are correctly indicated.
The study of physics at school lasts for several years. At the same time, students are faced with the problem that the same letters mean completely different values. Most often, this fact applies to Latin letters. How, then, do you solve problems?
You should not be afraid of such a repetition. Scientists have tried to introduce them into the designation so that the same letters do not meet in the same formula. Most often, students are faced with the Latin n. It can be lowercase or uppercase. Therefore, the question logically arises of what is n in physics, that is, in a certain formula that a student meets.
What does the capital letter N stand for in physics?
Most often in the school course, it is found in the study of mechanics. After all, there it can be immediately in the spirit of the meanings - the power and strength of the normal reaction of the support. Naturally, these concepts do not overlap, because they are used in different sections of mechanics and are measured in different units. Therefore, you always need to determine exactly what n is in physics.
Power is the rate at which the energy of the system changes. It is a scalar, that is, just a number. Its unit is watt (W).
The normal reaction force of the support is the force that acts on the body from the side of the support or suspension. In addition to a numerical value, it has a direction, that is, it is a vector value. Moreover, it is always perpendicular to the surface on which the external influence is made. The unit for this N is Newton (N).
What is N in physics, in addition to the quantities already indicated? This could be:
Avogadro's constant;
magnification of the optical device;
concentration of the substance;
Debye number;
total radiation power.
What can a lowercase letter n stand for in physics?
The list of names that may be hidden behind it is quite extensive. The notation n in physics is used for such concepts:
refractive index, and it can be absolute or relative;
neutron - a neutral elementary particle with a mass slightly greater than that of a proton;
rotation frequency (used to replace the Greek letter "nu", as it is very similar to the Latin "ve") - the number of repetitions of revolutions per unit of time, measured in hertz (Hz).
What does n mean in physics, in addition to the quantities already indicated? It turns out that the main quantum number (quantum physics), concentration and Loschmidt's constant (molecular physics) are hidden behind it. By the way, when calculating the concentration of a substance, you need to know the value, which is also written in the Latin "en". It will be discussed below.
What physical quantity can be designated by n and N?
Its name comes from the Latin word numerus, translated it sounds like "number", "quantity". Therefore, the answer to the question of what n means in physics is quite simple. This is the number of any objects, bodies, particles - everything that is discussed in a particular task.
Moreover, "quantity" is one of the few physical quantities that do not have a unit of measurement. It's just a number with no name. For example, if the problem is about 10 particles, then n will be just 10. But if it turns out that the lowercase "en" is already taken, then you have to use an uppercase letter.
Formulas with uppercase N
The first of them determines the power, which is equal to the ratio of work to time:
In molecular physics, there is such a concept as the chemical amount of a substance. It is designated by the Greek letter "nu". To calculate it, divide the number of particles by Avogadro's number:
By the way, the latter value is also denoted by the so popular letter N. Only it always has a subscript - A.
To determine the electric charge, you need the formula:
Another formula with N in physics - vibration frequency. To count it, you need to divide their number by time:
The letter "en" appears in the formula for the circulation period:
Formulas containing lowercase n
In the school physics course, this letter is most often associated with the refractive index of a substance. Therefore, it is important to know the formulas with its application.
So, for the absolute refractive index, the formula is written as follows:
Here c is the speed of light in vacuum, v is its speed in a refractive medium.
The formula for the relative refractive index is a little more complicated:
n 21 = v 1: v 2 = n 2: n 1,
where n 1 and n 2 are the absolute refractive indices of the first and second medium, v 1 and v 2 are the speed of the light wave in these substances.
How to find n in physics? The formula will help us with this, in which it is required to know the angles of incidence and refraction of the ray, that is, n 21 = sin α: sin γ.
What is n in physics if it is the refractive index?
Typically, tables provide values for the absolute refractive indices of various substances. Do not forget that this value depends not only on the properties of the medium, but also on the wavelength. Refractive index tabulated values are for the optical range.
So, it became clear what n is in physics. So that there are no questions left, it is worth considering some examples.
Power challenge
№1. During plowing, the tractor pulls the plow evenly. In doing so, he applies a force of 10 kN. With this movement within 10 minutes, he overcomes 1.2 km. It is required to determine the power developed by it.
Conversion of units to SI. You can start with force, 10 N are equal to 10,000 N. Then the distance: 1.2 × 1000 = 1200 m.Time remains - 10 × 60 = 600 s.
Choice of formulas. As mentioned above, N = A: t. But the task has no meaning for work. To calculate it, another formula is useful: A = F × S. The final form of the formula for the power looks like this: N = (F × S): t.
Solution. Let's calculate the work first, and then the power. Then in the first action it will turn out 10,000 × 1,200 = 12,000,000 J. The second action gives 12,000,000: 600 = 20,000 watts.
Answer. The tractor power is 20,000 watts.
Refractive index problems
№2. Glass has an absolute refractive index of 1.5. The speed of propagation of light in glass is slower than in a vacuum. It is required to determine how many times.
It is not required to translate data into SI.
When choosing formulas, you need to stop at this one: n = c: v.
Solution. It can be seen from this formula that v = c: n. This means that the speed of propagation of light in glass is equal to the speed of light in vacuum divided by the refractive index. That is, it decreases by one and a half times.
Answer. The speed of propagation of light in glass is 1.5 times less than in vacuum.
№3. There are two transparent media. The speed of light in the first of them is equal to 225,000 km / s, in the second - 25,000 km / s less. A ray of light goes from the first environment to the second. The angle of incidence α is equal to 30º. Calculate the value of the angle of refraction.
Do I need to translate into SI? Speeds are given in off-system units. However, when substituted in formulas, they will be reduced. Therefore, there is no need to convert the speed to m / s.
The choice of formulas required to solve the problem. You will need to use the law of refraction of light: n 21 = sin α: sin γ. And also: n = c: v.
Solution. In the first formula, n 21 is the ratio of the two refractive indices of the substances under consideration, that is, n 2 and n 1. If we write down the second indicated formula for the proposed environments, we get the following: n 1 = c: v 1 and n 2 = c: v 2. If we compose the ratio of the last two expressions, it turns out that n 21 = v 1: v 2. Substituting it into the formula for the law of refraction, you can derive the following expression for the sine of the angle of refraction: sin γ = sin α × (v 2: v 1).
Substituting the values of the indicated speeds and sine 30º (equal to 0.5) into the formula, it turns out that the sine of the angle of refraction is equal to 0.44. According to the Bradis table, it turns out that the angle γ is equal to 26º.
Answer. The value of the angle of refraction is 26º.
Tasks for the period of treatment
№4. The blades of the windmill rotate with a period of 5 seconds. Calculate the number of revolutions of these blades for 1 hour.
It is only necessary to convert to SI units the time of 1 hour. It will be equal to 3,600 seconds.
Selection of formulas... The period of rotation and the number of revolutions are related by the formula T = t: N.
Solution. From this formula, the number of revolutions is determined by the ratio of time to period. Thus, N = 3600: 5 = 720.
Answer. The number of revolutions of the blades of the mill is 720.
№5. The aircraft propeller rotates at a frequency of 25 Hz. How long does it take for the propeller to complete 3,000 revolutions?
All data are given in SI, so there is no need to translate anything.
Required formula: frequency ν = N: t. It is only necessary to derive a formula for an unknown time from it. It is a divisor, so it is supposed to be found by dividing N by ν.
Solution. As a result of dividing 3000 by 25, the number 120 is obtained. It will be measured in seconds.
Answer. The propeller of the aircraft makes 3000 revolutions in 120 s.
Let's summarize
When a student in a physics problem encounters a formula containing n or N, he needs deal with two points. The first is from which branch of physics the equality is given. This may be clear from the title in the textbook, reference book, or the teacher's words. Then you should decide what is hidden behind the many-sided "en". Moreover, the name of the units of measurement helps in this, if, of course, its value is given. Another option is also allowed: take a close look at the rest of the letters in the formula. Perhaps they will turn out to be familiar and give a hint in the issue to be resolved.
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Books
- Hydraulics. Textbook and workshop for an academic bachelor's degree, Kudinov V.A.
- Hydraulics 4th ed., Trans. and add. Textbook and workshop for academic bachelor's degree, Eduard Mikhailovich Kartashov. The textbook describes the basic physical and mechanical properties of liquids, issues of hydrostatics and hydrodynamics, gives the foundations of the theory of hydrodynamic similarity and mathematical modeling ...
Cheat sheet with formulas in physics for the exam
and not only (may need 7, 8, 9, 10 and 11 grades).
First, a picture that can be printed in a compact form.
Mechanics
- Pressure P = F / S
- Density ρ = m / V
- Pressure at the depth of the liquid P = ρ ∙ g ∙ h
- Gravity Fт = mg
- 5. Archimedean force Fa = ρ w ∙ g ∙ Vт
- Equation of motion for uniformly accelerated motion
X = X 0 + υ 0 ∙ t + (a ∙ t 2) / 2 S = ( υ 2 -υ 0 2) / 2а S = ( υ +υ 0) ∙ t / 2
- Equation of speed for uniformly accelerated motion υ =υ 0 + a ∙ t
- Acceleration a = ( υ -υ 0) / t
- Circular speed υ = 2πR / T
- Centripetal acceleration a = υ 2 / R
- Relationship between the period and the frequency ν = 1 / T = ω / 2π
- II Newton's law F = ma
- Hooke's law Fy = -kx
- The law of gravitation F = G ∙ M ∙ m / R 2
- Weight of a body moving with acceleration a P = m (g + a)
- Weight of a body moving with acceleration a ↓ P = m (g-a)
- Friction force Ffr = µN
- Body momentum p = m υ
- Force impulse Ft = ∆p
- Moment of force M = F ∙ ℓ
- Potential energy of a body raised above the ground Ep = mgh
- Potential energy of an elastically deformed body Ep = kx 2/2
- Kinetic energy of the body Ek = m υ 2 /2
- Work A = F ∙ S ∙ cosα
- Power N = A / t = F ∙ υ
- Efficiency η = Ap / Az
- The oscillation period of the mathematical pendulum T = 2π√ℓ / g
- The period of oscillation of a spring pendulum T = 2 π √m / k
- Equation of harmonic vibrations X = Xmax ∙ cos ωt
- Relationship between wavelength, its speed and period λ = υ T
Molecular physics and thermodynamics
- Amount of substance ν = N / Na
- Molar mass М = m / ν
- Wed kin. energy of molecules of a monatomic gas Ek = 3/2 ∙ kT
- Basic equation of MKT P = nkT = 1 / 3nm 0 υ 2
- Gay - Lussac's law (isobaric process) V / T = const
- Charles's law (isochoric process) P / T = const
- Relative humidity φ = P / P 0 ∙ 100%
- Int. energy is ideal. monatomic gas U = 3/2 ∙ M / µ ∙ RT
- Gas work A = P ∙ ΔV
- Boyle's law - Mariotte (isothermal process) PV = const
- The amount of heat during heating Q = Cm (T 2 -T 1)
- The amount of heat during melting Q = λm
- The amount of heat during vaporization Q = Lm
- The amount of heat during fuel combustion Q = qm
- Ideal gas equation of state PV = m / M ∙ RT
- The first law of thermodynamics ΔU = A + Q
- Efficiency of heat engines η = (Q 1 - Q 2) / Q 1
- Efficiency is ideal. engines (Carnot cycle) η = (T 1 - T 2) / T 1
Electrostatics and electrodynamics - physics formulas
- Coulomb's law F = k ∙ q 1 ∙ q 2 / R 2
- Electric field strength E = F / q
- The tension of the email field of a point charge E = k ∙ q / R 2
- Surface charge density σ = q / S
- The tension of the email field of the infinite plane E = 2πkσ
- Dielectric constant ε = E 0 / E
- Potential energy interaction. charges W = k ∙ q 1 q 2 / R
- Potential φ = W / q
- Point charge potential φ = k ∙ q / R
- Voltage U = A / q
- For a uniform electric field U = E ∙ d
- Electric capacity C = q / U
- Electric capacity of a flat capacitor C = S ∙ ε ∙ε 0 / d
- Energy of a charged capacitor W = qU / 2 = q² / 2С = CU² / 2
- Current I = q / t
- Conductor resistance R = ρ ∙ ℓ / S
- Ohm's law for a section of a circuit I = U / R
- The laws of the last. compounds I 1 = I 2 = I, U 1 + U 2 = U, R 1 + R 2 = R
- Parallel laws conn. U 1 = U 2 = U, I 1 + I 2 = I, 1 / R 1 + 1 / R 2 = 1 / R
- Electric current power P = I ∙ U
- Joule-Lenz law Q = I 2 Rt
- Ohm's law for the complete circuit I = ε / (R + r)
- Short-circuit current (R = 0) I = ε / r
- Magnetic induction vector B = Fmax / ℓ ∙ I
- Ampere force Fa = IBℓsin α
- Lorentz force Fl = Bqυsin α
- Magnetic flux Ф = BSсos α Ф = LI
- The law of electromagnetic induction Ei = ΔФ / Δt
- EMF of induction in the motion conductor Ei = Bℓ υ sinα
- EMF of self-induction Esi = -L ∙ ΔI / Δt
- The magnetic field energy of the coil Wm = LI 2/2
- Oscillation period qty. contour T = 2π ∙ √LC
- Inductive resistance X L = ωL = 2πLν
- Capacitive resistance Xc = 1 / ωC
- The effective value of the current Id = Imax / √2,
- RMS voltage value Uд = Umax / √2
- Impedance Z = √ (Xc-X L) 2 + R 2
Optics
- The law of refraction of light n 21 = n 2 / n 1 = υ 1 / υ 2
- Refractive index n 21 = sin α / sin γ
- Thin lens formula 1 / F = 1 / d + 1 / f
- Optical power of the lens D = 1 / F
- max interference: Δd = kλ,
- min interference: Δd = (2k + 1) λ / 2
- Differential lattice d ∙ sin φ = k λ
The quantum physics
- F-la Einstein for the photoeffect hν = Aout + Ek, Ek = U s e
- Red border of the photoelectric effect ν к = Aout / h
- Photon momentum P = mc = h / λ = E / s
Atomic Nuclear Physics
