Use the formula $s=r \omega t$ to find the value of the missing variable. \[ s=\frac{4 \pi}{5} k m, r=1 k m, t=5 \mathrm{sec} \] \[ \omega= \] radians per sec (Type an exact answer, using $\pi$.)

Step 1 ：The question is asking for the value of $\omega$ in the formula $s=r \omega t$. We know the values of $s$, $r$, and $t$, so we can rearrange the formula to solve for $\omega$ as follows: $\omega = \frac{s}{r \cdot t}$.

Step 2 ：Substitute the given values into the formula: $s = \frac{4 \pi}{5}$, $r = 1$, and $t = 5$.

Step 3 ：Solve for $\omega$ to get $\omega = \frac{4 \pi}{25}$.

Step 4 ：Final Answer: $\boxed{\frac{4 \pi}{25}}$ radians per sec.