Why does a paper roll unwind in jerks?

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Discussion Overview

The discussion revolves around the phenomenon of a paper roll unwinding in jerks rather than smoothly. Participants explore the mechanics behind this behavior, considering factors such as friction, creases in the paper, and dynamic instabilities. The scope includes conceptual explanations and potential mathematical modeling.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that creases formed during the rolling process prevent smooth unwinding, causing potential energy to be stored and released in intervals when friction is overcome.
  • Another participant questions the method of unwinding, proposing that static friction may contribute to the non-uniform propagation of the unwinding process.
  • A third participant introduces the concept of nonlinear oscillations and dynamic instability, indicating that these may play a role in the jerky motion observed.
  • Further clarification reveals that the paper roll is placed vertically on a flat surface, which may influence the unwinding dynamics.
  • One participant notes that the unwinding could be complex, suggesting that the propagation of unwinding might interfere with itself, leading to phases of varying speeds.

Areas of Agreement / Disagreement

Participants express various hypotheses regarding the mechanics of the unwinding process, but no consensus is reached. Multiple competing views remain regarding the causes of the jerky motion.

Contextual Notes

Participants mention factors such as static friction and dynamic instability, but the discussion does not resolve the underlying assumptions or mathematical modeling needed to fully understand the phenomenon.

ubergewehr273
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TL;DR
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.
 
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ubergewehr273 said:
.. 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.
 
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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?
 
A.T. said:
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.
 
anorlunda said:
Are you familiar with differential equations and stability analysis?

I'm not familiar with the latter one.
 
ubergewehr273 said:
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 :smile:
 
ubergewehr273 said:
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.
 

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