[Physics] tangential acceleration for uniform circular motion

Question

I understand that circular motion is defined by 2 components of acceleration, one tangential and one radial and their resultant is what causes circular motion.

I am confused though as to why it is said that in uniform circular motion (constant angular velocity) there is no tangential acceleration. How can the radial vector be always pointing towards the centre? Is there is no tangential vector component to it?

So is there still a vectorial tangential acceleration (since the vector points to a different point at each time)?

And is centripetal acceleration the resultant of the tangential and radial accelerations?

Answer 1

Radial acceleration $\vec a_{rad}$ takes care of turning (when pulling perpendicular to the velocity vector $\vec v$, it can only turn it, not increase it), and tangential acceleration $\vec a_{tan}$ takes care of speeding up (when pulling parallel to $\vec v$, it can only increase it, not turn it).

1. A car speeding up while driving straight, has a $\vec a_{tan}$ but no $\vec a_{rad}$.
2. A car turning but not speeding up has a $\vec a_{rad}$ only and no $\vec a_{tan}$.
3. A car speeding up while turning has both a $\vec a_{rad}$ and a $\vec a_{tan}$.

A uniform circular motion is case 2. The word "uniform" means constant speed.