Question #42439

This question tests the student's ability to couple rotational and translational dynamics under the constraint of static friction.

A common trap is assuming that the system is in quasi-static equilibrium or ignoring the inertial torque, leading to the incorrect torque balance $\kappa \theta = f R$ and the erroneous answer $\theta_{\text{max}} = \mu M g R / \kappa$.

Students must realize that the torsional spring drives both angular and linear acceleration.

By correctly applying Newton's second law for translation ($f = M a$) and rotation ($-\kappa \theta - f R = I \alpha$) along with the rolling constraint ($a = R \alpha$), the true inertial resistance of the disk is accounted for, revealing that friction only provides a fraction of the total restoring torque.