QUESTION: Say you have two spools of thread. Let's assume it's a sturdy, but mass-less thread. You unwrap one spool entirely and gather up the loose thread in your hand in such a way that it doesn't knot, and let it hang from a certain measured height. The other spool you hold from the same height, but it still has all the thread wrapped around it. You then let go of them at the same time. The first one falls straight down, but reaches the end of the length of thread and stops. The second one rolls all the way down. The threads are the same length. My question is, which one reaches the end of the thread first? The one that just fell, or the one that rolls? My attempt at reasoning: Both spools start out with the same GPE. The spool that just falls has all that GPE converted into translational (vertically) KE. The spool that unwinds as it falls has all that GPE converted into translational (vertically) KE AND rotational KE. However, here's where I get confused. When the spool is just falling, thread is being "used." But even when the spool is turning (while falling), thread is also being "used." How do we know if the rates are equal? In essence, although the spool that just straight falls down has more translational KE, the spool that unwinds "uses" thread while rotating AND falling, so while the translational KE may be less, the rotational KE makes up for it (in terms of "spool usage"). So, I'm wondering if I'm completely wrong in my reasoning. Visuals of any sort would be appreciated too!