A uniform disk is initially at rest and begins to rotate about its center with a constant angular acceleration \(\alpha\). Let \(a_t\) be the magnitude of the tangential acceleration and \(a_c\) be the magnitude of the centripetal acceleration of a point on the outer rim of the disk. At time \(t = T\), the magnitudes of these two accelerations are equal, such that \(a_c = a_t\). At time \(t = 2T\), what is the ratio \(\dfrac{a_c}{a_t}\) for the same point on the rim?