During an earthquake, a tall cylindrical brick chimney begins to topple but doesn't immediately fall. Instead, it wobbles back and forth with its base remaining fixed to the ground. A seismologist models the chimney as a uniform solid cylinder of height L=45m, radius R=1.5m, and mass M=120tons. At the moment of interest, the chimney's axis makes an angle θ0=8° with the vertical, and its angular velocity is zero.
Assuming the chimney remains rigid and its base stays anchored to the ground, find the maximum angular velocity ωmax that the chimney will achieve during its subsequent wobbling motion.