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Deriving the centripetal acceleration formula. A body that moves in a circular motion (of radius r) at constant speed (v) is always being accelerated. The acceleration is at right angles to the direction of motion (towards the center of the circle) and of magnitude v2 / r. The direction of acceleration is deduced by symmetry arguments.
Figure 1: Tangential acceleration (at) can be explained as the linear acceleration of a particle at any point on the curved path. The acceleration can consist of two components one is the radial acceleration vector represented by ar and other is tangential component of acceleration at. Acceleration at any point in the curved point is equal to vector sum of tangential and radial acceleration.