I am having some trouble defining whether a force is conservative or not. In the example that we are working on a mass on a pulley system is used to cause a slender bar to rotate from rest to a certain angle. I know that the tension forces in this case are conservative but I was wondering what force, if any, was non-conservative?
A non conservative force is generally anything that is affected by friction or air resistance. The amount of energy lost is distance dependent because the further the path traveled, the more an object is affected by these forces. Conservative forces are displacement dependent, meaning they depend only on an initial and final position, and that all the different ways to get between those two points are equivalent.
The simplest example for a non-conservative force is frictional force. For example, to move an object from point A to point B on the table we would require say $10$ J of energy, now to put it back to point A, we would need same $10$ J of energy. Practically nothing observable has changed, but we've performed $20$ J of work, which went to overcome frictional force. So, we may conclude that it is non-conservative. (Since we cannot assign points of potential for it)