A helicopter rotor can be modeled as three rectangular blades stretching outward at equal angles around the central rotor shaft. Each blade has a length R$=5$m$,$width W $=0\mathrm{.}2$m$,$and mass m $=50$kg$.$The rotor shaft itself has a mass of $100$kg and a radius of gyration k $=0\mathrm{.}2$m$.$When the gearbox is disengaged, the friction on the rotor shaft is negligible.

Assume a constant local drag coefficient at any point on the blade of C$\_$D $=0\mathrm{.}2($based on the surface area, not the frontal area$).$If the gearbox is disengaged when w$\_0=60$ rpm$,$obtain a solution for the rotational speed w$($t$)$ and plot the rotational speed as a function of time for $0$

solve this equation by hand to get an analytical solution as a differential equation