Answer
$w=\frac{\pi}{18}$ radians per seconds
Work Step by Step
Step 1: The formula to be used here is $s=rwt$.
Step 2: After substituting the values of $s$,$r$ and $t$ provided by the question into this formula, the equation becomes
$\frac{8\pi}{9}=\frac{4}{3}\times w\times 12$
Step 3: Simplifying, $\frac{8\pi}{9}=16w$
Step 4: Multiplying both sides by $\frac{1}{16}$,
$\frac{8\pi}{9}\times\frac{1}{16}=16w\times\frac{1}{16}$
Step 5: Simplifying, $w=\frac{\pi}{18}$ radians per seconds.