Spinning Spool Physics Q: Is Circumference Dist. = Center Dist.?

[zabachi]

I have a question about a spinning spool, there is a spool spinning and is the sistance traveled by the circumference the same as the center of the circle? You can refer to the diagram attached for a question I had trouble with from a physics olympiad. The answer
was (B).
Thanks in advance!

 

[Doc Al]

I have a question about a spinning spool, there is a spool spinning and is the sistance traveled by the circumference the same as the center of the circle?

I assume you are asking: When the rolling spool makes one complete turn, has it traveled a distance equal to the circumference?

What do you think? (Cut out a circle and try it!)

 

[A.T.]

You can refer to the diagram attached for a question I had trouble with from a physics olympiad. The answer was (B).

The top of the spool moves twice as fast as the center. But what happens when you pull it under the center?

https://www.youtube.com/watch?v=dvyii6QBLtw

 

[haruspex]

I think the easiest way to figure it out is to consider a very small movement. The spool as a whole rotates about its point of contact with the ground.