The time derivative of angular position used when studying rotating objects or systems.

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Calculation of the G-force

I have a formula which is $\text{G-force} = \frac{v\omega}{9.8}$, where $v$ is speed and $\omega$ is the angular velocity. I've seen on the internet that G-force is actually $\text{acceleration}/9.8$. ...
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How is it that angular velocities are vectors, while rotations aren't?

Does anyone have an intuitive explanation of why this is the case?