A circular disk rotates about a fixed axis through its center and slows down with a constant angular acceleration of magnitude \(\alpha\). Point 1 and Point 2 are located at radial distances \(R\) and \(2R\) from the axis, respectively, such that Point 2 traverses twice the linear path length of Point 1 as the disk comes to rest. At the instant when the radial acceleration of Point 1 is equal in magnitude to its tangential acceleration, what is the ratio of the magnitude of the net linear acceleration of Point 2 to that of Point 1, \(\dfrac{a_2}{a_1}\)?