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.

 

[PJC01]

A: Thank you for your question about the spinning spool and its relation to the distance traveled by the circumference and the center of the circle. This is a common question in physics, and it is important to understand the concept of rotational motion in order to answer it correctly.

In short, the answer is yes, the distance traveled by the circumference is the same as the distance traveled by the center of the circle. This is because both the circumference and the center are rotating at the same angular velocity, so they cover the same distance in the same amount of time.

To better understand this concept, let's look at the diagram attached. In rotational motion, the distance traveled is related to the angle rotated and the radius of the circle. In this case, the circumference and the center are both rotating at the same angle and have the same radius, so they cover the same distance.

It is also important to note that the distance traveled by the circumference and the center will be the same regardless of the size of the spool or the speed at which it is spinning. This is because the ratio of the circumference to the radius (or the circumference to the diameter) is always constant for a circle.

I hope this explanation helps to clarify the concept of rotational motion and the relationship between the distance traveled by the circumference and the center of a spinning spool. Keep exploring and asking questions, and good luck with your physics olympiad!