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angular velocity average angular velocity

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кутова швидкість середня кутова швидкість

right-hand rule instantaneous angular velocity

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правило правої руки миттєва кутова швидкість

An angular velocity characterizes the rate of change of the angular displacement. There is an average (mean) angular velocity and an instantaneous angular velocity.

The average angular velocity equals the ratio between the vector of the angular displacement and the corresponding time interval D t:

A unit of measurement of an angular velocity is rad/s¹.

The modulus of average angular velocity equals the ratio between the angle of rotation and the corresponding time interval D t:

The instantaneous angular velocity is the limit of the average angular velocity as Δ t is made to approach zero. Thus:

The instantaneous angular velocity equals
the first derivative of the angle of rotation with respect to time

Fig. 1.15

The vector of angular velocity has the same direction as vector of the angular displacement that is along the axis of rotation according to right-hand rule (Curl your right hand about the axis of rotation, your fingers pointing in the direction of rotation. Your extended thumb will then point in the direction of the angular velocity vector (Fig. 1.15.)).

If a particle moves in translation along an x axis, its linear velocity u can be either positive or negative, depending on whether the particle is moving in the direction of increasing x or decreasing x. Similarly, the angular velocity ω of a rotating rigid body can be either positive or negative, depending on whether the body is rotating in the direction of increasing (counterclockwise) or of decreasing (clockwise). The magnitude of an angular velocity is called the angular speed, which is also represented with .

Angular velocity can be calculated, if equation of rotational motion is known.

It is possible to solve a reverse task: if angular velocity and time of rotation dependence is known, the angular distance can be calculated as:

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