We have a rod, 1m long and negligible height compared to the length, mass 10Kg uniformly distributed (center of gravity in the center). It is tilted theta degrees to the horizontal, and rests on two supports at two extreme ends, with one support higher than the other. What is the weight distribution (forces) on both supports?
If calculating, we find that although tilted, the lines of action of the upward reaction forces from both supports are equidistant from the center of gravity, so the forces on both supports should be equal, so that there is no net rotational moment. So, both supports should bear 50% of the weight, regardless of angle of incline.
However, from experience we know that the lower support bears greater weight than the upper support, and as the angle of incline increases to 90 degrees, all of the weight shifts to the lower support, with none on the upper support. This seems to defy logic because if the weight on both supports is unequal and their lines of action are equidistant from the center while tilted, then there should be a rotational moment and the object should rotate.
So what is the correct method of calculation of distribution of weight depending on the angle of incline? Note that I am considering the case where the height is negligible, so the supports are at equal distance from the center, regardless of the angle of incline.