# Angular speed

** Abstract**

In this paper, the angular speed formula has been established (proved) on any type of curve. Regarding the importance of the angular speed calculation in most of applied sciences such as dynamic mechanics , aerospace , dynamic systems and lock of a relation established in this connection , the need is felt that in order to design and optimize dynamic systems , a reasonable relation should be presented . This paper tries to prove such a relation in the easiest possible way.

__Key Word: angular speed __

**Introduction**

Angular speed on any curve: In dynamic mechanics literature, “angular speed” has been defined like this: The angle covered by a moving object in time unit.

The unit of angular speed is radiant per second (Rad / sec).

Angular speed formula: V = R.ω

Where V = linear speed on the curve, R = radius of rotation round the rotation axis and ω = the moving object angular speed.

N this paper angular speed is studied in any type of (closed / open) curve. It is initially studied in a closed curve in which there are 2 existing characteristic geometric forms which are common: circle and ellipse.

In the open – type curve, it includes any type of cure both ends of which are not linked to each other.

Now to begin with, a closed curve is studied, firstly a circle.

Angular speed in a circle consists of 2 parts:

An .Angular speed in a circle with constant linear speed linear velocity (V) is constant in a circle and the circle radius R is also constant. Angular speed is thus constant: V = R.ω

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