Isn't centripetal force a radial force Probably should have said centripetal acceleration to be clearer. I think what you are describing is angular acceleration. But as I said, I'm at least 15 years from my last thoughts about physics.
I am an idiot, I meant tangential force...an object moving in a circle does not have tangential force, as that creates angular acceleration...it does have radial force and acceleration...otherwise it would go straight!