Physics Help Forum Cylinder rotating on a horizontal surface with friction

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 Jul 15th 2017, 07:55 AM #1 Junior Member   Join Date: Jul 2017 Posts: 8 Cylinder rotating on a horizontal surface with friction A hollow cylinder with mass m and radius R stands on a horizontal surface with its smooth flat end in contact the surface everywhere. A thread has been wound around it and its free end is pulled with velocity v in parallel to the thread. Find the speed of the cylinder. Consider two cases: (a) the coefficient of friction between the surface and the cylinder is zero everywhere except for a thin straight band (much thinner than the radius of the cylinder) with a coefficient of friction of μ, the band is parallel to the thread and its distance to the thread $\displaystyle a < 2R$(the figure shows a top-down view); (b) the coefficient of friction is μ everywhere. Hint: any planar motion of a rigid body can be viewed as rotation around an instant centre of rotation, i.e. the velocity vector of any point of the body is the same as if the instant centre were the real axis of rotation. Any suggestion about the set up of the solution? I must write the two torque equations? (One for the pulling thread and the other for the friction force)
 Jul 16th 2017, 05:37 AM #2 Junior Member   Join Date: Jul 2017 Posts: 8 I put an image of the situation Attached Thumbnails
Jul 16th 2017, 06:08 AM   #3
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 Originally Posted by Berker Any suggestion about the set up of the solution? I must write the two torque equations? (One for the pulling thread and the other for the friction force)
Forum rules require that you must post your attempt to solve the problem before we can help you. Otherwise we'd be doing peoples homework.

Is this a calculus based text that you're using? We can give hints as to how to start. If you know calculus then I'd suggest portioning the cylinder into infinitesimal pieces as a first step.

Jul 30th 2017, 09:23 AM   #4
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 Originally Posted by Pmb Forum rules require that you must post your attempt to solve the problem before we can help you. Otherwise we'd be doing peoples homework. Is this a calculus based text that you're using? We can give hints as to how to start. If you know calculus then I'd suggest portioning the cylinder into infinitesimal pieces as a first step.
No, i don't want the solution, only some hints. :-)
If $\displaystyle L$ is the length and $\displaystyle \rho$ is the density of the cylinder, then $\displaystyle dm= \rho \cdot 2 \pi r dL$. (I used the formula of perimeter because it is a hollow cylinder, am I right?)
But how can it help me?

EDIT: I am wrong, it would be dimensionally wrong, so:
$dm= \rho \pi dr^2 dL$

Last edited by Berker; Jul 30th 2017 at 01:55 PM.

 Aug 2nd 2017, 09:43 AM #5 Junior Member   Join Date: Jul 2017 Posts: 8 No hints?

 Tags cylinder, friction, horizontal, rotating, surface

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