Answer
$\omega=1.99\times 10^{-7} rad/s=1.9\times10^{-6}~rev/min$
Work Step by Step
To find the angular speed, use the definition $$\omega=\frac{\Delta \theta}{\Delta t}$$ The time for one full revolution is 365.25 days. Convert this to seconds using dimensional analysis. $$365.25 days \times \frac{24hr}{1day} \times \frac{60min}{1hr} \times \frac{60s}{1min}$$ $$=3.15\times 10^{7} s$$ Substituting known values of $\Delta \theta=2\pi rad$ (one full revolution) and $\Delta t=3.15\times 10^7m/s$ yields an angular speed of $$\omega=\frac{2\pi rad}{3.15\times 10^7s}=1.99\times 10^{-7} rad/s$$
We convert to $rev/min$:
$1.99\times10^{-7}~rad/s*\frac{1~rev}{2\pi~rad}*\frac{60~s}{1~min}=1.9\times10^{-6}~rev/min$
