A slender rod of mass Mr has a disk of mass Mo fastened to it at its end. It is pinned at 0 - a "frictionless" pin. The circular frequency in rad/s of the system for small oscillations is what?
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If the system is displaced by small angle 'theta' from the vertical, the torque about the fastened end,
Mr*g*sin(theta)*(l/2) + Mo*g*sin(theta)*l = - (Ir+Mr*(l/2)^2 + Io + ...
This solution is provided in 150 words. It uses torque, angular acceleration and simple harmonic motion to find the angular frequency squared.