A Problem from my book - 3

Due to persistence of vision, human eye is unable to view events happening in less than $(\frac{1}{16})^{th}$ of a second.

So for one blade to be visible the frequency of rotation $(f)$ should satisfy:

$f \leq 16$

$\frac{\omega_1}{2\pi} \leq 16$

For 3 blades, the angular velocity $(\omega_3)$ satisfies the condition:

$\frac{\omega_3}{2\pi} \leq \frac{16}{3}$

$\displaystyle \Rightarrow (\omega_3)_{max} = \frac{32\pi}{3}$

$\displaystyle \Rightarrow \frac{21(\omega_3)_{max}}{22} \simeq \frac{21\cdot 32 \cdot 22}{22\cdot 3\cdot 7} \simeq \boxed{32}$