I want to ask about angular motion. Suppose a circle of radius $r$ rotating with angular acceleration $\alpha$. I know that the polar coordinates of a point in the perimeter of the circle is $(r,\theta)$. Transforming this to cartesian, it becomes $(r\cos\theta, r\sin \theta)$.
I know that the angular position can be calculated using below formula:
$$ \theta = 0.5\,\alpha t^2 $$
I can convert it using polar to cartesian formula to get $(x,y)$ position of the point.
How do I calculate the x-axis and y-axis acceleration and velocity of that point every time point? I assume this is related to tangential acceleration and velocity but I am not sure how to calculate this.