Sunday, April 24, 2016

homework and exercises - Shape of a rotating rope with one free-end



One end of a uniform rope (with total mass $M$) is fixed on the edge of a cylinder. The cylinder has a radius $R$ and rotates with angular velocity $\omega$. The axis is vertical in a gravitational field. Air drag is neglected. What is the shape of the rope?


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I tried to use the Euler-Lagrange equation to solve this problem but I don't know how to handle free-end boundary condition. Maybe some other method?





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