Answer
$w=\frac{3\pi}{32}$ 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
$\frac{3\pi}{4}=2\times w\times 4$
Step 3: Simplifying, $\frac{3\pi}{4}=8w$
Step 4: Multiplying both sides by $\frac{1}{8}$,
$\frac{3\pi}{4}\times\frac{1}{8}=8w\times\frac{1}{8}$
Step 5: Simplifying, $w=\frac{3\pi}{32}$ radians per seconds.