Words to be remembered:

a number of

concept

descriptive

measurable

size

duration

property

elementary particle

angular

precise

precision

In spite of

limitation

meaningfully

ряд, несколько

понятие

описательный

измеримый

размер

продолжительность

свойство

элементарная частица

угловой

точный

точность

несмотря на

ограничение

многозначительно

№5

The geometry of vectors

There are two points of difference between vectors and numbers. The first difference is that vectors are essentially geometric, numbers are not. Numbers may be represented geometrically, either by points on a line, or by distances measured along the line, but they need not be. And even if they are, the line is arbitrary; its direction in physical space is without significance. A vector, on the other hand, has meaning only when its direction in space is specified. For a mathematician, this "space" of vector may be itself an abstraction, such as a space of many dimensions, but it is still basically geometrical. For the physicist, the space of most vectors is the ordinary three-dimensional space of classical physics, the space of human perception. The second difference between vectors and numbers is the fact that the vector has no sign. To call a vector positive or negative has no meaning. A number has magnitude and direction. Direction may be thought as the generalization of the idea of sign. Instead of two possibilities (plus and minus), there are infinitely many possibilities for direction. Of course a vector may be added or subtracted, and it may appear in an equation with a plus sign or a minus sign. Every vector, whether pointing north, south, west, east, up or down has (as it is said) a positive magnitude. The idea of direction replaces the idea of sign.

Words to be remembered:

point

direction

space

significance

meaning

specify

dimension

three-dimensional

sign

magnitude

add

subtract

equation

replace

пункт, точка

направление

пространство

важность, значение

значение

указывать

измерение

трехмерный

знак

величина

складывать, прибавлять

вычитать

уравнение

заменять

№6

Freely falling bodies

A real object can rotate as it moves. Also a body may vibrate as it moves, for example, a falling water drop. These complications can be avoided if we consider the motion of a very small body that is called a particle. Mathematically, a particle is treated as a point, an object without extent, so that rotational and vibrational considerations are not involved.

Actually, there is no such thing in nature as an object without extent. The concept of "particle" is very useful because real objects often behave to a very good approximation as if they were particles. A body need not be small in usual sense of the word in order to be treated as a particle. We can find out a great deal about the motion of the sun and planets without appreciable error if we treat these bodies as particles. Even if the body is too large in order to be considered a particle for a particular problem, we can always think of it as if it is made up of a large number of particles.

The most common example of motion with nearly constant acceleration is the example of a body that falls toward the earth. In the absence of air resistance it is found out that all bodies, regardless of their size, weight, or composition, fall with the same acceleration at the same point of the earth's surface, and if the distance which is covered by them is not too large, the acceleration remains constant throughout the fall. This ideal motion, in which air assistance and the small change in acceleration with altitude are neglected, is called "free fall".

The acceleration of a freely falling body is called the acceleration due to gravity and is denoted by the symbol g. Near the earth's surface its magnitude is approximately 32 ft/sec², or 980 cm/ sec², and it is directed down toward the center of the earth.

Words to be remembered:

object

rotate

complication

motion

extent

consideration

actually

approximation

appreciable

error

treat

particular

resistance

regardless of

composition

surface

altitude

due to

предмет, объект

вращаться

осложнение

движение

протяженность, размер

соображение

действительно, на самом деле

приблизительный подсчет

заметный, ощутимый

ошибка

трактовать, рассматривать

особый

сопротивление

независимо от

состав

поверхность

высота

благодаря, из-за

№7