A uniform solid disk of mass \(M\) and radius \(R\) is mounted on a fixed, frictionless central axle. When a constant net torque \(\tau_0\) is applied, the disk experiences an angular acceleration \(\alpha_D\). An identical net torque \(\tau_0\) is applied to a thin circular hoop of the same mass \(M\) and radius \(R\) mounted on a similar axle, producing an angular acceleration \(\alpha_H\). If the solid disk is replaced by a larger uniform solid disk of the same mass \(M\) but radius \(2R\), how does the new angular acceleration of the disk, \(\alpha_D'\), compare to \(\alpha_H\) under the same torque \(\tau_0\), and what justifies this comparison?