In that case, it's easy-- but you have define "immovable" relative to what, first!
If you're dealing with
Earth in this Universe, and if you mean the Rod is immovable to center of the earth, then at the equator the Rod zips eastward at 1000mph, and that drops to zero the close to the poles you go, where it would just slowly spin in a circle over one day's time.
If you mean it's Immovable relative to the Sun, then there's that motion, plus another 65000mph that the Rod will move away from you! Measure relative to the center of the galaxy, and you have to consider another 400,000mph or so in some direction...
If you add up all the motions in the universe, and assume the Rod is activated when the stars are aligned just perfectly, then the thing will zip off at something like 2million mph in some direction.
So yeah, not really very Immovable for the guy trying to use them as a ladder. But it probably could do a LOT of damage to whoever it hit (or, more accurately, whoever hit it) if you timed it just right.
