2. Read and sum up the text simplifying and compressing the difficult sentences.

Kinematics. Vectors and Scalars

A) The equations of mechanics are typically writ­ten in terms of Cartesian coordinates. At a certain time t, the position of a particle may be specified by giving its coordinates x(t), y(t), and z(t) in a particular Cartesian frame of reference. However, a different observer of the same particle might choose a differently oriented set of mutually perpendicular axes, say, x', y', and z'. The mo­tion of the particle is then described by the first observer in terms of the rate of change of x(t), y(t), and z(t), while the second observer would discuss the rates of change of x'(t), y'(t), and z'(t). That is, both observers see the same particle executing the same motion and obeying the same laws, but they describe the situation with different equa­tions. This awkward situation may be avoided by means of a mathematical construction called a vector.

B) A vector is a quantity that has both magnitude and direc­tion. It is typically represented symbolically by an arrow in the proper direction, whose length is proportional to the magnitude of the vector. Although a vector has mag­nitude and direction, it does not have position. A vector is not altered if it is displaced parallel to itself as long as its length is not changed.

C) By contrast to a vector, an ordinary quantity having mag­nitude but not direction is known as a scalar. In printed works vectors are often represented by boldface letters such as A or X, and scalars are represented by lightface letters, A or X. The magnitude of a vector, denoted |A|, is itself a scalar i.e., |A| = A.

D) Mathematical operations: addition, subtraction, three kinds of multiplication, and differentiation can be performed with vectors. If vector A is added to vector B, the result is another vector, C, written A + B ─ C. The operation is performed by displacing B so that it begins where A ends, as shown in Figure 6 by arrows. C is then the vector that starts where A begins and ends where B ends.

E) Fig. 7. The right-hand rule used to find the direction of A x B and (right)

the right-hand rule used to find the direction of B x A. By the right- hand rule:

if the fingers of the right hand are made to rotate from A through ǿ to B. the thumb points in the direction of A x B. as shown in the figure.

Vocabulary

in terms в термінах

awkward незграбний

avoid запобігати

by means of засобом

obey to the law підкорятися закону

magnitude величина

axes вісь

observe спостерігати

alter змінювати

displace зміщувати

finger палець

the thumb points великий палець вказує

the right-hand rule правило правої руки

rotate обертатися

arrow стріла

Test