Step 1 :Given the formula $v=r \omega$, where $v$ is the velocity, $r$ is the radius and $\omega$ is the angular velocity.
Step 2 :We are given the values of $v$ and $r$ and asked to find $\omega$.
Step 3 :We can rearrange the formula to solve for $\omega$ as follows: $\omega = \frac{v}{r}$.
Step 4 :Substitute the given values into the formula: $v = 9$ and $r = 10$.
Step 5 :Calculate $\omega = \frac{9}{10} = 0.9$.
Step 6 :Final Answer: The angular velocity $\omega$ is \(\boxed{0.9}\) radians per second.