It's always good to be able to break down old electronic devices to find useful parts, and one example of this is old CDROM drives. Expensive in the 1990s, but now almost a dead format - which you can make use of one more time by extracting the motors for fun and other projects. This has been documented by Instructables user m-shams who explans how to use the small brushless DC motor with an Arduino and L293D motor control IC.
The L293D is required as brushless motors require a change in current direction for rotation, however the hardware and Arduino sketch to get them moving is explained in detail, plus the background theory of operation for these tiny motors.
If you're looking to learn how to use motors and much more with Arduino, you can't go past "Arduino Workshop - A Hands-On Introduction with 65 Projects” by John Boxall.
Arduino Workshop takes the reader from having zero knowledge about the Arduino platform, electronics and programming and leaves them with the know-how and instructions on everything from blinking an LED, to robotics, wireless data, cellular communications, motor control, sensors, Internet connected systems and more. For more information including a sample chapter and table of contents, visit the book page.