As has been, accceleration is always the derivative of velocity. In rotational motion (circular uniform), however, the tangential acceleration is the change in speed rather than velocity. Why is this so? For any points on a uniform circular disc, the tangential velocity is changing because direction is changing but the magnitude of the tangential velocity (AKA speed) is constant. Well, make sense, the quantity remains the same but the direction changes and always in a direction tangent to the centripetal acceleration. Why then is tangential acceleration make in reference to the change in speed rather than with the change in velocity?