Have an office cube with sliding door I want to control with an Arduino and rack/pinion gear. What motor should I buy?
Scavenge the motor from a battery drill motor and use that. It would still not move freely as you will have to spin the motor while opening or closing the door. Unless you figure some way to disengage the motor when it is off. You also need to make sure it is a reversible motor to close the door, again the drill motor could do this.
You are going to need a gear set to down gear just about any motor as they all spin too fast for this application unless you control the voltage going to the drill motor and limit it so it does't spin so fast. Possibly the PWM output on the Arduino through a solid state relay for speed control. Good luck