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## Homework Statement

Cylinder with mass of 2 kg can be rotated around fixed horizontal geometrical axis. Around cylinder's circumference there is wounded rope, end of which is pulled by force equal 2,5 N in a horizontal direction, so that cylinder's rotation is accelerated. In what time does end of the rope move for 1,2 m in horizontal direction?

http://img113.imageshack.us/img113/613/cylinder.png [Broken]

## Homework Equations

- [itex]m=2kg[/itex]
- [itex]F=2,5N[/itex]
- [itex]x=1,2m[/itex]

[itex]\phi=\omega_0t+\frac{1}{2}\alpha t^2[/itex]

## The Attempt at a Solution

- First and unsuccessful attempt (solution is [itex]1,0s[/itex]):

[itex]\frac{F}{m}=a_{tangential}=r\alpha=r\frac{2\phi}{t^2}=r\frac{2\frac{x}{r}}{t^2}=\frac{2x}{t^2}\Rightarrow t=\sqrt\frac{2mx}{F}=1,4s[/itex]

- While writing this thread, I gave it another shot, this time including inertia [itex]I[/itex] (and getting, what seems, correct solution):

[itex]\frac{2\phi}{t^2}=\alpha=\frac{\tau}{I}=\frac{Fr}{\frac{1}{2}mr^2}=\frac{F}{\frac{1}{2}m\frac{x}{\phi}}=\frac{2F\phi}{mx}\Rightarrow t=\sqrt\frac{mx}{F}=1,0s[/itex]

What is wrong with first attempt? Ignoring inertia ([itex]I[/itex]) doesn't seem right, but why does (seemingly) rigorous 1. attempt not lead to correct solution (i.e., why is there an extra [itex]\sqrt2[/itex])?

Yours truly,

courteous.

PS.: Quite likely that I've made grammatical mistakes in 'problem statement'. Please correct me.

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