[Physics] Centripetal Acceleration as a Cross Product

Question

Is it fine to express the centripetal acceleration as a cross product?
a=v X w (where a is centripetal acceleration, v is magnitude of velocity, w is angular velocity)

And is it v X w or w X v?

What I think:
Since centripetal acceleration requires tangential (perpendicular) velocity, I start thinking about cross products, and was able to express the acceleration vector as 2 other vectors.
Fiddling around with my right hand, I think that a=v X w and not a=w X v.
Where the convention is
-angular velocity towards me implies positive anticlockwise movement
-centripetal acceleration upwards is taken as positive
-velocity has to move in a way to cause anticlockwise movement

Thing is, I've been searching this up on the Internet but couldn't find any resources for confirmation.

Is it true that centripetal acceleration can be represented as the cross product of velocity and angular velocity? v X w

Answer 1

$$\vec{a}=\vec{\omega} \times \vec{v}$$ This delivers the goods for a point moving at speed $v$ in a circular path with angular velocity $\vec\omega$ about the centre of the circle. Because the circle lies in one plane, the direction of $\vec\omega,$ as well as its magnitude, is constant.

We can indeed derive the centripetal acceleration formula rather neatly starting with $$\vec{v}=\vec{\omega} \times \vec{r}$$ So$$\frac{d\vec{v}}{dt}=\frac{d\vec{\omega}}{dt} \times r + \vec\omega \times \frac{d\vec r}{dt}$$ The first term on the right disappears because $\vec\omega$ is a constant for a body moving in a circle at constant speed, so you're left with$$\vec a=\vec\omega \times \vec v$$