A meteorological mast, used for measuring wind speed and atmospheric data, has a mass of 120 kg and stands 25 m tall. This mast is supported by three guy-wires, each attached at 120° intervals around the mast's base. To assess the failure modes, an analysis is conducted on the scenario where one of the guy-wires breaks. The mast would then rotate about its base opposite the broken wire. Determine the tip speed of the mast as a function of its tilt angle θ relative to the vertical by applying the rotational dynamics equation $\frac{d\vec{L}}{dt}=\vec{τ}_{ext}$. Hint: Approximate the tower as a tall thin rod.