Think twice before sketching the diagram

Classical Mechanics Level 3

An end of a light wire rod is bent into a hoop of radius r r . The straight part of the rod has length l l ; a ball of mass M M is attached to the other end of the rod. The pendulum thus formed is hung by the hoop onto a revolving shaft of angular frequency ω \omega . The coefficient of friction between the shaft and the hoop is μ μ . Find the equilibrium angle α \alpha between the rod and the vertical.

α \alpha = = a r c t a n μ r 1 + μ 2 arctan\frac{μr}{\sqrt{1+μ^{2}}} α \alpha = = a r c t a n μ r ( l + r ) arctan\frac{μr}{(l+r)} α \alpha = = a r c t a n ( μ ) arctan(μ) α \alpha = = a r c s i n μ r ( l + r ) 1 + μ 2 arcsin\frac{μr}{(l+r)\sqrt{1+μ^{2}}}

Richeek Das by Richeek Das , 20, India

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