I am trying to find out the force needed to rotate a 5LB flat plate along a tubular track. The track is circular and runs 10 feet in a straight line (looking much like a pipe), and it is assumed to be perpendicular to gravity. The plate is a perfcet circle within the (pipe) except for two teeth which run along grooves situated in the sides. Over the course of the 10 feet the grooves rotate 360 degrees. I'm trying to find the force necessary (or possibly angular momentum?) to push the plate 10 feet. And lets assume minimal friction.

How fast do you want the plate to go, and how quickly do you want it to accelerate up to this speed? Also, you say the tube is "perpendicular to gravity" - that means it's horizontal, correct?

That's correct, horizontal. I would like for the tube to complet the full rotation in 10 seconds, so averagng 1 ft per second. Not sure about the acceleration, anything as long as it completes the cirlcle in 10 sconds

The problem is that the amount of force to be applied is proportoinal to the acceleration that you want, NOT the velocity. So we need to come up with a way to estimate the acceleration. Does this plate start from a standing start at time t = 0, move down the tube, and come to a stop again after 10 feet? Or is this track actually quite a bit longer and so you don't care how far it has to travel before it gets up to speed? Also - what is the diameter of the plate (need that to calculate its moment of inertia)?

The diameter is 1 foot. I believe we could say the start time is t=0 and that the track moves down the trck and stops after 10 feet. That being said he stoppage of the plate does not matter.