You measure its length as it passes. by how many millimeters do you determine the rod has contracted?

It sounds like a special relativity question but I need more info for a total answer. But remember it's length in the lab frame is

L•sqrt (1 - (v/c) ^2) where L is the rest length, v is its velocity magnitude and c is the speed of light. Sqrt is the square root (I'm on a phone so I can't see the math equation editor)