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Old Jul 15th 2017, 07:55 AM   #1
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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)
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Old Jul 16th 2017, 05:37 AM   #2
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I put an image of the situation
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Cylinder rotating on a horizontal surface with friction-fullsizerender-16-07-17-02-26.jpg  
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Old Jul 16th 2017, 06:08 AM   #3
Pmb
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Originally Posted by Berker View Post
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.
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cylinder, friction, horizontal, rotating, surface



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