The acceleration in the case of uniform circular motion is the change in the direction of the velocity, but not its magnitude. For an object traveling in a circular path, the centripetal acceleration ...The acceleration in the case of uniform circular motion is the change in the direction of the velocity, but not its magnitude. For an object traveling in a circular path, the centripetal acceleration is directly related to the square of the velocity of the object and inversely related to the radius of the circle. We first determine the velocity of the ball using the facts that the circumference of the circle is 2πr and the ball goes around exactly twice per second.