The mechanism that operates the load/unload tray for holding the disk in a tabletop Blu-...

The mechanism that operates the load/unload tray for holding the disk in a tabletop Blu-ray^TM player uses nylon spur gears, a rack, and a belt drive (Figure P8.29). The gear that meshes with the rack has a module of 2.5 mm. The gears have the numbers of teeth indicated, and the two sheaves have diameters of 7 mm and 17 mm. The rack is connected to the tray that holds the disk. For the tray to move at 0.1 m/s, how fast must the motor turn?