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In a uniform circular motion,
   v = linear tangential speed (or velocity) - constant speed
   omega = w = angular velocity = angle in radians per unit time
   a = linear acceleration = dv/dt
   r = radius of circle the body is moving in
  Ф = angle made by moving body

dФ/dt = w, So r w = r dФ/dt = d s /dt  = v      (s is the arc length traveled in dt time)
v = r w

dv/dt = acceleration = a

dv = Vector difference between velocity at t =t+dt and t = t
    = 2 v cos (π/2 - dФ/2) = 2 v sin dФ/2 = (approximately) v
                directed radially inwards

dv/dt = v dФ/dt = v w

So a = v w = r w² = v²/r  directed radially inwards