Hi, firstly, appologies if I'm posting in the wrong forums! Its been along time since I was at school and I have a feeling this may be a simple question for knowledgable people so I have placed it in the high school area and I'm not 100% where this questions lies in type of mathematics.
As for my question -
I'm trying to work out the length of a material of a known thickness whilst it is wound up into a tight sprial.
Imagine a carboard tube with an external diameter of say 300mm, and a material with a thickness of say 1mm which is 100000mm (100 Linear M) in length. The material is attached at one end to the tube and wound up tightly around the tube over and over against itself with no space between each wrap/layer until all 100000mm is wrapped up.
My thoughts are because the circumference of the material on the inside of each single wrap is smaller than on the outside (because the material is 1mm thick), the side of the material on the inside must be travelling less distance than the side of the material on the outside? Does that make sense??
This would lead me to believe that there is some compression of the material somewhere (on the inside) or extension (on the outside) to allow this to happen (the material must be extensible?).
What I want to calculate is the length of the inside of the material and the length of the outside of the material, if it where to be measured whilst wound up on this tube.