I Why does a paper roll unwind in jerks?

[ubergewehr273]

TL;DR Summary

Paper is rolled into a tube and it unwinds in jerks. Why is it so?

I came across a problem regarding a paper being rolled into a tube. When a piece of paper is rolled into a tube and then left to unwind, it is always seen that the unwinding happens in jerks and not smoothly. Why is it so?

What I have thought (and thanks to some discussions on reddit), that when one rolls a paper into a tube, creases form along the surface which in essence prevent the tube from unwinding smoothly. Potential energy gets stored and is released all at once when the force of friction due to the crease is overcome. This happens in intervals.

I would be glad if someone could correct me on this one and provide some further explanation on this phenomenon.

 

[A.T.]

.. then left to unwind,...

How exactly? Left in place, so the winding loosens up? Or rolled along the floor?

When it loosens in place, I suspect static friction is responsible for the non-uniform propagation.

 

[anorlunda]

Nonlinear oscillations are called limit cycles. They can be very difficult to analyze, but at the root there is some kind of dynamic instability.

Are you familiar with differential equations and stability analysis?

 

[ubergewehr273]

How exactly? Left in place, so the winding loosens up? Or rolled along the floor?

I'm sorry for not mentioning but the rolled paper tube is placed vertically on a flat surface and left to unwind.

 

[ubergewehr273]

Are you familiar with differential equations and stability analysis?

I'm not familiar with the latter one.

 

[davenn]

I'm sorry for not mentioning but the rolled paper tube is placed vertically on a flat surface and left to unwind.

OK
then read the second part of @A.T. 's answer

 

[A.T.]

I'm sorry for not mentioning but the rolled paper tube is placed vertically on a flat surface and left to unwind.

This could be quite complex. As the unwinding propagates around and into the roll, it could interfere with itself, creating phases of faster and slower movement.