# [time-nuts] Toilet paper speed

WB6BNQ wb6bnq at cox.net
Sun Feb 22 03:00:23 UTC 2009

```Tom,

Don't forget to save a few squares !

Bill....WB6BNQ

Tom Van Baak wrote:

> This is an interesting T&F problem, actually. It depends what
> you mean by "it". If "it goes" means the paper itself -- if you
> pull at a constant linear rate then it goes neither slower nor
> faster. It's constant and then suddenly ends, that's all.
>
> If "it goes" means the rotation (frequency) of the roll -- if you
> pull the paper at a constant linear rate then, yes, a predictable
> drift in frequency occurs as the radius of the roll decreases.
>
> For an interesting mental exercise (perhaps while you're sitting
> down near said roll of TP) see if the frequency drift is linear or
> log or exponential. For extra credit, when the roll is slightly bent
> (as often happens) rather than perfectly circular see what effect
> that modulation has on the short-term ADEV of the frequency.
>
> Alternatively, if you unroll the TP by attaching a stone to the end
> and letting it drop over a cliff then you have a really interesting
> physics problem considering the acceleration of gravity, varying
> mass, inertia, and radius of the roll, nonlinear friction in both air
> and roller, etc.
>
> /tvb
>
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```