JBA,
This issue is a fixed direction force due to a belt running around a rod as you state in your first example. Just to clarify, rotational inertia would have no affect on decreasing the deflection of the rotating rod compared to the deflection on a stationary rod?
I am curious how the deflection of a shaft changes due to rotation. In the force diagram image the green arrows show the rotational fixture locations and the purple arrow show the location of the applied force. The second image shows the deflection during a static test. If the force is applied...