What letter denotes quantity in physics. School curriculum: what is n in physics

Studying physics at school lasts several years. At the same time, students are faced with the problem that the same letters represent completely different quantities. Most often this fact concerns Latin letters. How then to solve problems?

There is no need to be afraid of such a repetition. Scientists tried to introduce them into the notation so that identical letters would not appear in the same formula. Most often, students encounter the Latin n. It can be lowercase or uppercase. Therefore, the question logically arises about what n is in physics, that is, in a certain formula encountered by the student.

What does the capital letter N stand for in physics?

Most often in school courses it occurs when studying mechanics. After all, there it can be immediately in spirit meanings - the power and strength of a normal support reaction. 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 define exactly what n is in physics.

Power is the rate of change of energy in a system. This is a scalar quantity, that is, just a number. Its unit of measurement is the watt (W).

The normal ground reaction force is the force exerted on the body by the support or suspension. In addition to the numerical value, it has a direction, that is, it is a vector quantity. Moreover, it is always perpendicular to the surface on which the external influence is made. The unit of this N is newton (N).

What is N in physics, in addition to the quantities already indicated? It could be:

Avogadro's constant;

magnification of the optical device;

substance concentration;

Debye number;

total radiation power.

What does the 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 the following 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", since 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, besides the quantities already indicated? It turns out that it hides the fundamental quantum number (quantum physics), concentration and Loschmidt constant (molecular physics). By the way, when calculating the concentration of a substance, you need to know the value, which is also written with the Latin “en”. It will be discussed below.

What physical quantity can be denoted by n and N?

Its name comes from the Latin word numerus, translated as “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 certain task.

Moreover, “quantity” is one of the few physical quantities that do not have a unit of measurement. It's just a number, without a name. For example, if the problem involves 10 particles, then n will simply be equal to 10. But if it turns out that the lowercase “en” is already taken, then you have to use a capital letter.

Formulas containing capital N

The first of them determines power, which is equal to the ratio of work to time:

In molecular physics there is such a thing as the chemical amount of a substance. Denoted by the Greek letter "nu". To count it, you should divide the number of particles by Avogadro's number:

By the way, the last value is also denoted by the so popular letter N. Only it always has a subscript - A.

To determine the electric charge, you will need the formula:

Another formula with N in physics - oscillation 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 a 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 a vacuum, v is its speed in a refractive medium.

The formula for the relative refractive index is somewhat 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 speeds of the light wave in these substances.

How to find n in physics? A formula will help us with this, which requires knowing the angles of incidence and refraction of the beam, that is, n 21 = sin α: sin γ.

What is n equal to in physics if it is the refractive index?

Typically, tables give 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. Table values ​​of the refractive index are given for the optical range.

So, it became clear what n is in physics. To avoid any questions, it is worth considering some examples.

Power task

№1. During plowing, the tractor pulls the plow evenly. At the same time, he applies a force of 10 kN. With this movement, it covers 1.2 km within 10 minutes. It is necessary to determine the power it develops.

Converting units to SI. You can start with force, 10 N equals 10,000 N. Then the distance: 1.2 × 1000 = 1200 m. Time left - 10 × 60 = 600 s.

Selection of formulas. As mentioned above, N = A: t. But the task has no meaning for the work. To calculate it, another formula is useful: A = F × S. The final form of the formula for power looks like this: N = (F × S) : t.

Solution. Let's first calculate the work and then the power. Then the first action gives 10,000 × 1,200 = 12,000,000 J. The second action gives 12,000,000: 600 = 20,000 W.

Answer. The tractor power is 20,000 W.

Refractive index problems

№2. The absolute refractive index of glass is 1.5. The speed of light propagation in glass is less than in vacuum. You need to determine how many times.

There is no need to convert data to SI.

When choosing formulas, you need to focus on this one: n = c: v.

Solution. From this formula it is clear that v = c: n. This means that the speed of light in glass is equal to the speed of light in a vacuum divided by the refractive index. That is, it decreases by one and a half times.

Answer. The speed of light propagation in glass is 1.5 times less than in vacuum.

№3. There are two transparent media available. The speed of light in the first of them is 225,000 km/s, in the second it is 25,000 km/s less. A ray of light goes from the first medium to the second. The angle of incidence α is 30º. Calculate the value of the angle of refraction.

Do I need to convert to SI? Speeds are given in non-system units. However, when substituted into formulas, they will be reduced. Therefore, there is no need to convert speeds to m/s.

Selecting the formulas necessary to solve the problem. You will need to use the law of light refraction: n 21 = sin α: sin γ. And also: n = с: v.

Solution. In the first formula, n 21 is the ratio of the two refractive indices of the substances in question, that is, n 2 and n 1. If we write down the second indicated formula for the proposed media, we get the following: n 1 = c: v 1 and n 2 = c: v 2. If we make 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, we can derive the following expression for the sine of the refraction angle: sin γ = sin α × (v 2: v 1).

We substitute the values ​​of the indicated speeds and the sine of 30º (equal to 0.5) into the formula, it turns out that the sine of the refraction angle is equal to 0.44. According to the Bradis table, it turns out that the angle γ is equal to 26º.

Answer. The refraction angle is 26º.

Tasks for the circulation period

№4. The blades of a windmill rotate with a period of 5 seconds. Calculate the number of revolutions of these blades in 1 hour.

You only need to convert time to SI units for 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 the above 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 mill blades is 720.

№5. An airplane propeller rotates at a frequency of 25 Hz. How long will it take the propeller to make 3,000 revolutions?

All data is given in SI, so there is no need to translate anything.

Required formula: frequency ν = N: t. From it you only need to derive the formula for the unknown time. It is a divisor, so it is supposed to be found by dividing N by ν.

Solution. Dividing 3,000 by 25 gives the number 120. It will be measured in seconds.

Answer. An airplane propeller makes 3000 revolutions in 120 s.

Let's sum it up

When a student encounters a formula containing n or N in a physics problem, he needs deal with two points. The first is from what branch of physics the equality is given. This may be clear from the title in the textbook, reference book, or the words of the teacher. Then you should decide what is hidden behind the many-sided “en”. Moreover, the name of the units of measurement helps with this, if, of course, its value is given. Another option is also allowed: look carefully at the remaining letters in the formula. Perhaps they will turn out to be familiar and will give a hint on the issue at hand.

Moving on to physical applications of the derivative, we will use slightly different notations than those accepted in physics.

Firstly, the designation of functions changes. Really, what features are we going to differentiate? These functions are physical quantities that depend on time. For example, the coordinate of a body x(t) and its speed v(t) can be given by the formulas:

(read ¾ix with a dot¿).

There is another notation for derivatives, very common in both mathematics and physics:

(read ¾de x by de te¿).

Let us dwell in more detail on the meaning of notation (1.16). The mathematician understands it in two ways, either as a limit:

or as a fraction, the denominator of which is the time increment dt, and the numerator is the so-called differential dx of the function x(t). The concept of differential is not complicated, but we won't discuss it now; it awaits you in your first year.

A physicist, not constrained by the requirements of mathematical rigor, understands the notation (1.16) more informally. Let dx be the change in coordinate over time dt. Let's take the interval dt so small that the ratio dx=dt is close to its limit (1.17) with an accuracy that suits us.

And then, the physicist will say, the derivative of the coordinate with respect to time is simply a fraction, the numerator of which contains a sufficiently small change in the coordinate dx, and the denominator a sufficiently small period of time dt during which this change in coordinate occurred.

Such a loose understanding of the derivative is typical for reasoning in physics. Further we will adhere to this physical level of rigor.

The derivative x(t) of the physical quantity x(t) is again a function of time, and this function can again be differentiated to find the derivative of the derivative, or the second derivative of the function x(t). Here is one notation for the second derivative:

the second derivative of the function x(t) is denoted by x (t)

(read ¾ix with two dots¿), but here’s another:

the second derivative of the function x(t) is denoted dt 2

(read ¾de two x by de te square¿ or ¾de two x by de te twice¿).

Let's return to the original example (1.13) and calculate the derivative of the coordinate, and at the same time look at the joint use of notation (1.15) and (1.16):

x(t) = 1 + 12t 3t2 )

x(t) = dt d (1 + 12t 3t2 ) = 12 6t:

(The differentiation symbol dt d before the bracket is the same as the prime behind the bracket in the previous notation.)

Please note that the derivative of the coordinate turned out to be equal to the speed (1.14). This is not a coincidence. The connection between the derivative of the coordinate and the speed of the body will be clarified in the next section “Mechanical motion”.

1.1.7 Vector magnitude limit

Physical quantities are not only scalar, but also vector. Accordingly, we are often interested in the rate of change of a vector quantity, that is, the derivative of the vector. However, before we talk about the derivative, we need to understand the concept of the limit of a vector quantity.

Consider the sequence of vectors ~u1 ; ~u2 ; ~u3 ; : : : Having made, if necessary, a parallel translation, we bring their origins to one point O (Fig. 1.5):

Suppose that the sequence of points is A1 ; A2 ; A3; : : : ¾flows¿2 to point B:

lim An = B:

Let us denote ~v = OB. We will say then that the sequence of blue vectors ~un tends to the red vector ~v, or that the vector ~v is the limit of the sequence of vectors ~un:

~v = lim ~un :

2 An intuitive understanding of this “flowing in” is quite sufficient, but perhaps you are interested in a more rigorous explanation? Then here it is.

Let things happen on a plane. ¾Inflow¿ of sequence A1 ; A2 ; A3; : : : to point B means the following: no matter how small a circle with a center at point B we take, all points of the sequence, starting from some point, will fall inside this circle. In other words, outside any circle with center B there are only a finite number of points in our sequence.

What if it happens in space? The definition of “flowing in” is modified slightly: you just need to replace the word “circle” with the word “ball”.

Let us now assume that the ends of the blue vectors in Fig. 1.5 run not a discrete set of values, but a continuous curve (for example, indicated by a dotted line). Thus, we are not dealing with a sequence of vectors ~un, but with a vector ~u(t), which changes over time. This is exactly what we need in physics!

The further explanation is almost the same. Let t tend to some value t0. If

in this case, the ends of the vectors ~u(t) flow into some point B, then we say that the vector

~v = OB is the limit of the vector quantity ~u(t):

t!t0

1.1.8 Differentiation of vectors

Having established what the limit of a vector quantity is, we are ready to take the next step of introducing the concept of derivative of a vector.

Let us assume that there is some vector ~u(t) depending on time. This means that the length of a given vector and its direction can change over time.

By analogy with an ordinary (scalar) function, the concept of a change (or increment) of a vector is introduced. The change in vector ~u over time t is a vector quantity:

~u = ~u(t + t) ~u(t):

Please note that on the right side of this relation there is a vector difference. The change in vector ~u is shown in Fig. 1.6 (remember that when subtracting vectors, we bring their beginnings to one point, connect the ends and “prick” with an arrow the vector from which the subtraction is performed).

~u(t) ~u

Rice. 1.6. Vector change

If the time interval t is short enough, then the vector ~u changes little during this time (in physics, at least, this is always considered so). Accordingly, if at t ! 0 the relation~u= t tends to a certain limit, then this limit is called the derivative of the vector ~u:

When denoting the derivative of a vector, we will not use a dot on top (since the symbol ~u_ does not look very good) and limit ourselves to the notation (1.18). But for the derivative of a scalar we, of course, freely use both notations.

Recall that d~u=dt is a derivative symbol. It can also be understood as a fraction, the numerator of which contains the differential of the vector ~u, corresponding to the time interval dt. We did not discuss the concept of differential above, since it is not taught in school; We won’t discuss the differential here either.

However, at the physical level of rigor, the derivative d~u=dt can be considered a fraction, the denominator of which is a very small time interval dt, and the numerator is the corresponding small change d~u of the vector ~u. At a sufficiently small dt, the value of this fraction differs from

the limit on the right side of (1.18) is so small that, taking into account the available measurement accuracy, this difference can be neglected.

This (not entirely strict) physical understanding of the derivative will be quite sufficient for us.

The rules for differentiating vector expressions are in many ways similar to the rules for differentiating scalars. We only need the simplest rules.

1. The constant scalar factor is taken out of the sign of the derivative: if c = const, then

d(c~u) = c d~u: dt dt

We use this rule in the section ¾Momentum¿ when Newton's second law

2. The constant vector multiplier is taken out of the derivative sign: if ~c = const, then dt d (x(t)~c) = x(t)~c:

3. The derivative of the sum of vectors is equal to the sum of their derivatives:

dt d (~u + ~v) =d~u dt +d~v dt :

We will use the last two rules repeatedly. Let's see how they work in the most important situation of vector differentiation in the presence of a rectangular coordinate system OXY Z in space (Fig. 1.7).

Rice. 1.7. Decomposition of a vector into a basis

As is known, any vector ~u can be uniquely expanded in the basis of unit

vectors ~ ,~ ,~ : i j k

~u = ux i + uy j + uz k:

Here ux, uy, uz are projections of the vector ~u onto the coordinate axes. They are also the coordinates of the vector ~u in this basis.

Vector ~u in our case depends on time, which means that its coordinates ux, uy, uz are functions of time:

Let's differentiate this equality. First we use the rule for differentiating the sum:

Thus, if the vector ~u has coordinates (ux; uy; uz), then the coordinates of the derivative d~u=dt are derivatives of the coordinates of the vector ~u, namely (ux; uy; uz).

In view of the special importance of formula (1.20), we will give a more direct derivation. At time t + t according to (1.19) we have:

~u(t + t) = ux (t + t) i + uy (t + t) j + uz (t + t)k:

Let's write the change in vector ~u:

~u = ~u(t + t) ~u(t) =

Ux (t + t) i + uy (t + t) j + uz (t + t)k ux (t) i + uy (t) j + uz (t)k =

In the limit at t! 0 fractions ux = t, uy = t, uz = t are respectively transformed into derivatives ux, uy, uz, and we again obtain relation (1.20):

Ux i + uy j + uz k.

It's no secret that there are special notations for quantities in any science. Letter designations in physics prove that this science is no exception in terms of identifying quantities using special symbols. There are quite a lot of basic quantities, as well as their derivatives, each of which has its own symbol. So, letter designations in physics are discussed in detail in this article.

Physics and basic physical quantities

Thanks to Aristotle, the word physics began to be used, since it was he who first used this term, which at that time was considered synonymous with the term philosophy. This is due to the commonality of the object of study - the laws of the Universe, more specifically - how it functions. As you know, the first scientific revolution took place in the 16th-17th centuries, and it was thanks to it that physics was singled out as an independent science.

Mikhail Vasilyevich Lomonosov introduced the word physics into the Russian language by publishing a textbook translated from German - the first physics textbook in Russia.

So, physics is a branch of natural science devoted to the study of the general laws of nature, as well as matter, its movement and structure. There are not as many basic physical quantities as it might seem at first glance - there are only 7 of them:

• length,
• weight,
• time,
• current strength,
• temperature,
• amount of substance
• the power of light.

Of course, they have their own letter designations in physics. For example, the symbol chosen for mass is m, and for temperature - T. Also, all quantities have their own unit of measurement: the luminous intensity is candela (cd), and the unit of measurement for the amount of substance is mole.

Derived physical quantities

There are much more derivative physical quantities than basic ones. There are 26 of them, and often some of them are attributed to the main ones.

So, area is a derivative of length, volume is also a derivative of length, speed is a derivative of time, length, and acceleration, in turn, characterizes the rate of change in speed. Momentum is expressed through mass and speed, force is the product of mass and acceleration, mechanical work depends on force and length, energy is proportional to mass. Power, pressure, density, surface density, linear density, amount of heat, voltage, electrical resistance, magnetic flux, moment of inertia, moment of impulse, moment of force - they all depend on mass. Frequency, angular velocity, angular acceleration are inversely proportional to time, and electric charge is directly dependent on time. Angle and solid angle are derived quantities from length.

What letter represents voltage in physics? Voltage, which is a scalar quantity, is denoted by the letter U. For speed, the designation is the letter v, for mechanical work - A, and for energy - E. Electric charge is usually denoted by the letter q, and magnetic flux - F.

SI: general information

The International System of Units (SI) is a system of physical units that is based on the International System of Units, including the names and designations of physical quantities. It was adopted by the General Conference on Weights and Measures. It is this system that regulates letter designations in physics, as well as their dimensions and units of measurement. Letters of the Latin alphabet are used for designation, and in some cases - of the Greek alphabet. It is also possible to use special characters as a designation.

Conclusion

So, in any scientific discipline there are special designations for various kinds of quantities. Naturally, physics is no exception. There are quite a lot of letter symbols: force, area, mass, acceleration, voltage, etc. They have their own symbols. There is a special system called the International System of Units. It is believed that basic units cannot be mathematically derived from others. Derivative quantities are obtained by multiplying and dividing from basic ones.

Drawing 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, 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 reduction is usually 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, 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 indicated, 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 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" ("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 stands for 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, 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 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.