Problem

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

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 rod 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 E. Disk C has a negligible mass and is rigidly attached to E; i.e., C and E form a single rigid body. Disk A can rotate about the axis ℓA, disk B can rotate about the axis ℓB,and the arm E along with C can rotate about the fixed axis ℓC. While keeping both B and C stationary, disk A is initially spun with ωA = 1200 rpm. Disk A is then brought in contact with C (contact is maintained via a spring), and at the same time, both B and C (and the arm E) are free to rotate. Due to friction between A and C, C along with E and disk B start spinning. Eventually A and C will stop slipping relative to one another. Disk B always rotates without slip over C .Let d = 0.27 m and w = 0.95 m. Assuming that the only elements of the system that have mass are A, B,and E and that = 0.3 kg, and assuming that all friction in the system can be neglected except for that between A and C and between C and B, determine theangular speeds of A, B ,and C (the angular velocity of C is the same as that of E since they form a single rigid body), when A and C stop slipping relative to one another.