Halliday, Resnick & Walker — Rotation: Problem 11

11 Two identical disks A and B can spin around vertical axes. Disk A is spinning with an initial angular speed of 40 rev/s when its rim touches initially stationary disk B, causing that disk to begin to spin. The rubbing at the contact point slows A while speeding up B. The rate at which both disks change their angular speeds is $2.0 \text{ rev/s}^2$. Find the time required for the two disks to reach the same angular speed.