Notation e in physics. Basic physical quantities, their letter designations in physics

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 sizes... 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 meanings - power and strength normal reaction supports. 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 at which the energy of the system changes. This is a scalar value, that is, just a number. Its unit is watt (W).

The force of the normal reaction of support is the force that acts on the body from the side of the support or suspension. except 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? 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;

rotational speed (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, besides the quantities already mentioned? 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, 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, you must 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 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 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 is 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 value 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 the above 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 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 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 into formulas, they will be reduced. Therefore, there is no need to convert the speed to m / s.

The choice of formulas needed 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 propeller of the aircraft 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. Dividing 3000 by 25 gives the number 120. It will be measured in seconds.

Answer. The propeller of the aircraft makes 3000 revolutions in 120 s.

Let's sum up

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.

Moving on to physical applications derivative, we will use a slightly different designation, those that are accepted in physics.

First, the designation of functions is changing. Indeed, what functions are we going to differentiate? These functions are physical quantities time-dependent. For example, the coordinate of the body x (t) and its velocity v (t) can be given by the formulas:

(read ix with a dot¿).

There is another notation for the derivative, which is very common in both mathematics and physics:

(read ¾de iks on de te¿).

Let us dwell in more detail on the meaning of notation (1.16). A 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). Differential is not difficult, but we will not discuss it now; it is waiting for you in the first year.

A physicist who is not constrained by the requirements of mathematical rigor understands notation (1.16) more informally. Let dx be the change in coordinate during time dt. Let us 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, in the numerator of which there is a rather small change in the coordinate dx, and in the denominator there is a rather small time interval dt, during which this change in the coordinate occurred.

Such a loose understanding of the derivative is characteristic of reasoning in physics. From now on, we will adhere to this particular 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)

(reads ix with two dots¿), but here's another:

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

(it reads de two x in de te square¿ or de two x in de te twice¿).

Let's go back to the original example (1.13) and calculate the derivative of the coordinate, and at the same time look at sharing 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 in front of the parenthesis is the same as the dash above the parenthesis in the previous notation.)

Note that the derivative of the coordinate turned out to be equal to the velocity (1.14). This is no coincidence. The relationship between the derivative of the coordinate and the velocity of the body will be clarified in the next section "Mechanical motion".

1.1.7 Vector 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 talking about the derivative, you need to understand the concept of the limit of a vector quantity.

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

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

lim An = B:

We denote ~ v = OB. We 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” is quite enough, but perhaps you are interested in a more rigorous explanation? Then this is it.

Let it happen on the plane. “Inflow” of sequence A1; A2; A3; ::: to point B means the following: no matter how small a circle with center at point B we take, all points of the sequence, starting with some one, 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.

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

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

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

moreover, 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 value ~ u (t):

t! t0

1.1.8 Differentiating vectors

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

Suppose 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 the usual (scalar) function, the concept of a change (or increment) of a vector is introduced. The change in the vector ~ u during time t is a vector quantity:

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

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

~ u (t) ~ u

Rice. 1.6. Vector change

If the time interval t is small 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 ratio ~ 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 the dot above (since the ~ u_ symbol does not look very good) and will restrict ourselves to the notation (1.18). But for the derivative of a scalar, we naturally use both notation freely.

Recall that d ~ u = dt is the symbol for the derivative. It can also be understood as a fraction, in the numerator of which there is the differential of the vector ~ u, corresponding to the time interval dt. Above, we did not discuss the concept of differential, since it is not passed at school; we will not discuss the differential here either.

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

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

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

The differentiation rules for vector expressions are very similar to those for 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 `` Momentum '' when Newton's second law

2. The constant vector factor is taken out of the sign of the derivative: 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 more than once. 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. Expansion of a vector in basis

As is known, any vector ~ u unique way decomposed on the basis of unit

vectors ~, ~, ~: i j k

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

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

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

We differentiate this equality. First, we use the rule for differentiating the amount:

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 give a more direct derivation of it. At the 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 of the 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, the fractions ux = t, uy = t, uz = t go over to the derivatives ux, uy, uz, respectively, and we again obtain relation (1.20):

Ux i + uy j + uz k.

It's no secret that there are special designations for quantities in any science. Letter designations in physics prove that given science is no exception in terms of identifying quantities using special symbols. There are 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 generality of the object of study - the laws of the Universe, more specifically - how it functions. As you know, in the XVI-XVII centuries the first scientific revolution took place, 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 through the publication of a textbook translated from German - the first textbook on physics in Russia.

So, physics is a section of natural science devoted to the study of the general laws of nature, as well as matter, its movement and structure. There are not so 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 m is chosen for the mass, and the symbol T for the temperature. Also, all quantities have their own unit of measurement: the intensity of light is candela (cd), and the unit of measurement for the amount of substance is the mole.

Derived physical quantities

There are much more derived 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 - also of length, speed - of time, length, and acceleration, in turn, characterizes the rate of change in speed. Momentum is expressed in terms of mass and velocity, 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, angular momentum, moment of force - they all depend on mass. Frequency, angular velocity, angular acceleration is inversely proportional to time, and electric charge has a direct dependence on time. The angle and solid angle are derived from length.

What letter denotes stress in physics? The voltage, which is a scalar quantity, is denoted by the letter U. For speed, the designation is in the form of the letter v, for mechanical work- A, and for energy - E. The electric charge is usually denoted by the letter q, and the 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 the letter designations in physics, as well as their dimensions and units of measurement. For designation, letters of the Latin alphabet are used, in some cases - the Greek. It is also possible to use as a designation special characters.

Conclusion

So, in any scientific discipline there are special designations for various kinds of quantities. Naturally, physics is no exception. There are a lot of letter designations: force, area, mass, acceleration, tension, etc. They have their own designations. 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 the basic ones.

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 new dress design, etc.), you first need to carry out the appropriate calculations and draw a drawing of the future product. However, it is often composed 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, it is accepted all over the world legend length, width, height and other values ​​used in the design. 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 separate difficulties when developing standards design documentation in most modern countries it was decided to use practically 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 magnitudes. 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 believe 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 the use of other letters ("G" and "P") is also permissible. According to international standards of the SI system, the width is measured in meters or multiples (sub-multiples) of their units. It should be noted that in geometry it is sometimes also permissible to use "w" to denote width, however, 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.

V English language this term is called 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 one - 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 - 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 unclear 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 Greek... 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 a quantitative characteristic geometric shape with two dimensions (length and width). Unlike all of the above, it is measured in square meters(as well as in fractional and multiples of their units). As for the letter designation of the area, then in different areas it is different. 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", but according to GOST Unified system design documentation, this letter is a step (coil springs, and the like). However, it is not used when it comes about gearing and threading.

Capital and lowercase 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 various values, angles often have to be indicated in drawings. different sizes... 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 different nations general lettering standards have been adopted. 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.