Answer Happy

A solid disk with radius R, is spinning about a horizontal axle / at an angular velocity w (it rotates freely: friction is ignored). The axle is perpendicular to the disk; it goes through the center S of the disk. The circumference of this disk (#1) is pushed against the circumference of another disk which is in all respects identical to #1 except that its radius is R2, and it is at rest. It can rotate freely about a horizontal axle, m, through P: m and I are parallel. The friction coefficient between the two touching surfaces (disk circumferences) is . We wait until an equilibrium situation is reached. At that time disk #1 is spinning with angular velocity wi, and disk #2 with angular velocity w R R P IN a) Is kinetic energy of rotation conserved? Give your reasons. Now imagine that you are doing this "experiment" and that you hold one axle m in your left hand and axle / in your right hand; you keep them parallel. b) Do you have to apply a torque while you are pushing the disks against each other? c) Is the total angular momentum of the two disks conserved? d) Calculate wi and wy in terms of Ri, Ry, and w. It is quite remarkable that wi and we are independent of ji and independent of the time it takes for the equilibrium to be reached; i.e., independent of how hard one pushes the disks against each other.