Active vocabulary

rotational (rotational) motion Rotation axis

—   —

обертальний рух   вісь обертання

angle of rotation (angular position) Angular path (distance) Angular displacement

— — —

кут повороту   кутовий шлях кутове переміщення

Fig. 1.13

In this section, we deal with the rotation of a rigidbody about afixedaxis.

Let us consider a rigid body of arbitrary shape in pure rotation around a fixed axis(fig. 1.13), called the axis of rotation or the rotation axis. Every point of the body moves in a circle whose center lies on the axis of rotation, and every point moves through the same angle during a particular time interval. (In pure translation, every point of the body moves in a straight line, and every point moves through the same linear distanceduring a particular time interval.)

The points of the body, lying in different distances from the axis of rotation, move along different circles, therefore all linear kinematics characteristics of different points of a rigid body will be different:

, , .

However there is a characteristic which remains identical for all points of a rigid body. It is angle of rotation (angular position) φ:

Fig. 1.14

Now we deal with the angular equivalents of the linear quantities of position, displacement, velocity, and acceleration.

The vector of displacement and the vector of the angular displacement are different vectors. Vector , as well as and are polar vectors. The angular displacement is axial vector (fig. 1.14).

Axial vectors are used for consideration of a rotating body.
They always have direction along rotation axis

Similarly, the angular displacement of a rotating body can be either positive or negative, depending on whether the body is rotating in the direction of increasing (counterclockwise), or decreasing (clockwise).

Equation of motion is a vector of the angular displacement and the time dependence:

.

Дата добавления: 2015-11-16