# Two falling spools of thread, which hits first?

1. Jul 28, 2012

### turboderp

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!

2. Jul 28, 2012

### phinds

creation of the angular momentum slows down the one that gets it.

It is a common problem in physics 101 to ask how one could distinguish between two coffee cans of identical weight but one of which has the weight uniformly distributed and the other of which has a thick shell and a hollow inside.

The answer of course is to roll them down the same incline. The hollow one gets there last.

3. Jul 28, 2012

### TurtleMeister

A yo-yo would make a good visual.

4. Jul 28, 2012

### pgardn

While the thread is being "used", one is exerting a much larger force up on the spool (actually a torque) so that the linear acceleration is different. Your energy reasoning seems fine. Maybe there is something I a missing as this seems fairly straightfoward?

Ohh, you are talking about the rate at which the thread "unwinds"?

Last edited: Jul 28, 2012
5. Jul 28, 2012

### turboderp

Yes, I was referring to the rate at which the thread unwinds.

6. Jul 28, 2012

### turboderp

But wouldn't that just mean the spool that rolls takes the longer to travel the same vertical distance as the spool that just falls?

Whereas they both reach the end of the thread at the same time?

7. Jul 28, 2012

### qbert

as the rolling spool is descending you have tension pulling up on the
spool. The tension provides the torque to spin the spool. but it is
also providing an upward force decreasing the net acceleration.
so the spinning spool gets to the bottom later.