circular Motion | Relationship between linear velocity (v) & angular Velocity (w)

Relationship between linear velocity (v) & angular velocity (w) :-

Consider particle of mass 'm' performing circular motion in anticlockwise direction along the circumference of a circle 

Let,

A = initial position of particle 

B = position of particle 

   = Angular displacement

   = Radius vector 

   = Arc length

   = time 

Then instantaneous velocity of a particle is given by,

v = lim     displacement

     -o               time 

  =  lim            8.s  

      -o.              t 

But, 

Angular displacement = Arc length 

                                       Radius

Arc length = Angular displacement ✖️ radius ---(1)

This is the relationship between linear velocity and angular velocity.