NASA uses a centrifuge 8.84 m in diameter for astronaut training to simulate the high gravity conditions that may be experienced during launch and atmospheric re-entry.

Find the relationship between angular velocity and centrifugal acceleration, and plot $\omega$ vs $a_{Cent}$ for values of $a_{Cent}$ from $1g$ to $5g$, where $g$ is gravity. Extend your plot to $20g$ and comment on the shape.