Problem

The uniform disk A, of mass mA = 1.2 kg and radius rA = 0.25 m, is mounted on a vertical s...

The uniform disk A, of mass mA = 1.2 kg and radius rA = 0.25 m, is mounted on a vertical shaft that can translate along the horizontal arm E. The uniform disk B, of mass mB = 0.85 kg and radius rB = 0.38 m, is mounted on a vertical shaft that is rigidly attached to arm E. Disk A can rotate about axis ℓA, disk B can rotate about axis ℓB,and the arm E, along with disk C, can rotate about the fixed axis ℓC. Disk C has negligible mass and is rigidly attached to E so that they rotate together. While keeping both B and C stationary, disk A is spun to ωA = 1200 rpm. Disk A is then brought in contact with disk C (contact is maintained via a spring), and B and C (and the arm E) are then allowed to freely rotate. Due to friction between A and C,disks C (and arm E) and B start spinning. Eventually A and C stop slipping relative to one another. Disk B always rotates without slip over C. Let d = 0.27 mand w = 0.95 m. If the only elements of the system that have mass are A and B, and if all friction in the system can be neglected except for that between A and C and between C and B, determine the angular speeds of A and C when they stop slipping relative to one another.