The relation between linear velocity and angular velocity of a body moving in a circle is

Explanation

Consider an object moving along a circle of radius r. In a time `Delta t` , the object travels an arc distance `Delta s` as shown in the figure . The corresponding angle subtended is `Delta theta` .
In terms of `Delta theta, Delta s` can written as
`Delta s = r Delta theta`
In a time t ,
`(Delta s)/(Delta t) = r""(Delta theta)/(Delta t)`
In the limit ` Delta t to 0` , the above equation becomes
`(ds)/(dt) = romega" " . . . (1)`
Here `(ds)/(dt)` is linear speed (v) that is tangential to the circle and `omega` is angular speed. So equation (1) becomes
` v = r omega`