A particle has centripetal acceleration whenever it's a making a turn of radius R. If the particle is moving at a constant tangential speed v throughout the turn, then the magnitude of centripetal acceleration is
v²/R
If the particle is following a uniformly circular path, then it moves in a circle of radius R and travels a distance equal to its circumference, 2πR. Let T be the time it takes to complete one such loop. Then the entire circle is traversed with speed v = 2πR/T, so that the centripetal acceleration is also given by
v²/R = (2πR/T)²/R = 4π²R/T²
