On the hoop / disc question, I could figure out that there is more work involved in rotating the hoop so the disc would go faster. However, what if the incline

On the hoop / disc question, I could figure out that there is more work involved in rotating the hoop so the disc would go faster. However, what if the incline of the surface is so extreme that both of them are falling? Surely in that case they should fall with equal speed, so alpha would seem to matter.