A friend of mine, regarding point 3, set up a different procedure.
"The weight force acting on the center of mass ##O## forms the angle ##\alpha## with its projection on the plane ##AOB##, ##AB## being the instantaneous axis of rotation. Therefore the component of the weight force acting along the inclined plane, rib of the guide, results ##F_P = Mg \sin \alpha##. The other component ##F_H = Mg \cos \alpha## has two components, one on ##AO## and one on ##BO##, perpendicular to the tracks of ##A## and ##B## on the guides. Their value is ##N = Mg \frac{\sqrt{2}}{2} \cos \alpha##. We determine the minimum value of ##\mu##, i.e., ##\mu_m##, by imposing constancy of ##v##, i.e., that twice the friction force ##F_{friction}## (because it develops in ##A## and ##B##) is equal to the force ##F_P##. Meanwhile, it is ##F_{friction} \le \mu N##, whence ##\mu \ge \frac{F_{friction}}{N}##. Since it must be, for the constancy of ##v##, ##2F_{friction} = 2 Mg \sin \alpha##, it follows that ##\mu## must be at least equal to ##\mu = \sqrt{2} \tan \alpha##".
All this is different from the procedure carried out together a few days ago. What is wrong with this?