When a particle undergoes uniform circular motion, it has both linear and angular velocity.

The linear velocity is the velocity of particle at any instant (represented by u or v). It's direction at any point on the circle is along the tangent to that point.

The angular velocity is the rate of change of angle swept by the particle from centre with time (represented by ) .

Angular velocity = ,

where is the angle swept in 1 complete rotation (in radians) and T is the time taken for one complete rotation (Also called as Time period)

now the relationship between linear and angular velocity is

where r is the radius of the circular path

substituting the value of in above relation.

v = r