I'm dizzy

Classical Mechanics Level pending

I have a chain of mass m m and l l , as well as a tall cone with half-angle θ \theta that is firmly attached to the ground. I tie my chain so that it forms a loop, and then throw it over the cone so that it's now wrapped around it. I then spin the chain with an angular speed of ω \omega around the axis of the cone. What is the tension in the chain?

Assume that the friction between the chain and cone is negligible, and that the chain cannot be stretched.

Imagine the cone as one of those pylons that construction workers put on the road.

m ω 2 l + 2 π g cot ⁡ α 2 π \frac{m \omega^{2} l+2 \pi g \cot \alpha}{2\pi} m ω 2 l + 2 π g cot ⁡ α 4 π \frac{m \omega^{2} l+2 \pi g \cot \alpha}{4 \pi} m ω 2 l − π g cot ⁡ α 2 π \frac{m \omega^{2} l- \pi g \cot \alpha}{2 \pi} m ω 2 l − π g cot ⁡ α 4 π \frac{m \omega^{2} l- \pi g \cot \alpha}{4 \pi}

Steven Mai by Steven Mai , 20, Canada

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