User:Msf24

Work to see how fast one must pull on toilet paper to get it to tear:

let $ v $ be how fast you have to pull it

let $ f $ be the force required to tear it (known)

let $ M $ be the Mass of the toilet paper roll (known)

let $ I $ be the rotational inertia of the roll

$ I = \frac{1}{2}MR^2\! $

because it is a solid cylinder (basically known)

let $ R $ be the radius of the roll of toilet paper (known)

And let $ \tau $be the torque

now in order to rip the toilet paper, $ \tau = f \times R $, and we also know that $ \tau = \frac{1}{2} I\omega^2 $

using algebra and the fact that $ \omega = \frac{v}{R} $ we find that $ f = \frac{1}{4} \frac{Mv^2}{R} $ and with a little more algebra out pops:

$ v = \sqrt{\frac{4fR}{M}} $

and there you have it (?). I'm guessing I made a mistake somewhere because I'm rusty, but you can use it if you like. Sorta reminded me of your "when does a bowling ball start to roll rather than slide" problem.

Variations/Modifications:

You could require the students to derive $ I $

You could require the students to calculate $ M $ given information about the dimensions and how heavy some toilet paper is