Time required for the cylinder to stop?

Figure shows a uniform rigid rod of \(‘L\)’ shape whose mass is ‘\(m\)’ and is lying in a vertical plane. It is hinged at one end and the other end is rubbing with a rotating solid cylinder of mass \(m\) and radius \(R = 1 \text { m}\). If the initial angular velocity of the cylinder is \(\omega_0 = 30 \text{ rad/sec}\). Co-efficient of friction between the rod and the cylinder is \(\mu = 0.5\).

After how much time (in second) will the cylinder stop rotating?

Take \(g = 10 \text{ m/s}^2\).

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