Velocity in circular motion, $v = r × \omega$ or $v = \omega × r$? I know it might sound silly to ask, but is the relation between linear velocity and angular velocity of an object undergoing circular motion $ v = r × \omega$ or $v = \omega × r$? I didn't notice it at first, but now, I could cite any websites using $ r × \omega$ and many using $\omega ×r$ so I'm just confused which one is correct. Also there is same question asked on other websites but is I guess unanswered or ambiguously answer everywhere. Can someone make clear to me the reason and the correct formula even if it means using right hand rule or stuff like that.
 A: If you're seeing web sites disagreeing about something very basic like this, why not just look it up in a reliable source like a textbook? The relation is $v=\omega\times r$. You can verify this using the right-hand rule.
A: To be consistent with the vector notation, when $r$ points to the center of mass from the center of rotation it is $$ v = \omega \, r$$ in scalar form and $$ \vec{v} = \vec{\omega} \times \vec{r} $$ in vector form where $\times$ is the vector cross product.
A: Cross product:
Let's first stablish the rule for the cross product: $ \ \vec{a}=\vec{b}\times\vec{c} \ $ if you rotate from the $\vec{b}$ direction to the $\vec{c}$ direction, the resulting $\vec{a}$ direction of such a product, will point in the direction from which looking down the rotation is positive (anticlockwise), check the white drawings [check image].
Or you can also use the typical righ-hand rule check the orange drawings [check image]



Question:
Now the answer will basically, depend on which direction you take the radius to go:
1) Radius goes from the axis of rotation to the object (mi personal preference, and the most used in the literature I would say) $\longrightarrow \vec{v}=\vec{\omega} \times \vec{r}\ $
2) Radius goes from the object to the axis of rotation $\longrightarrow \vec{v}=\vec{r} \times \vec{\omega}\ $
As we can see from the examples, of the following image:



Update:
All the webs and literature I checked use the 1) (pointing out) direction for the radius, therefore the consensus is:
\begin{equation}
 \vec{v}=\vec{\omega} \times \vec{r}\ \ \text{ and } \ \vec{\omega}= \frac{1}{|r|^2} \vec{r} \times \vec{v}
\end{equation}
