Walker, Halliday & Resnick — Rotation: Problem 6

6 A horizontal pottery wheel (a horizontal disk) with a radius of 30.0 cm can rotate about a vertical axis with negligible friction but is initially stationary. A horizontal rubber wheel of radius 2.00 cm is placed against its rim. That wheel is mounted on a motor. When the motor is switched on at time $t = 0$, the rubber wheel undergoes a constant angular acceleration of $5.00 \text{ rad/s}^2$. Its contact with the pottery wheel causes the pottery wheel to undergo an angular acceleration. When the pottery wheel reaches an angular speed of $5.00 \text{ rev/s}$, the rubber wheel is pulled away from contact and thereafter the pottery wheel rotates at $5.00 \text{ rev/s}$. From $t = 0$ to $t = 2.00 \text{ min}$, how many full rotations does the pottery wheel make?