In this recent question which discusses about why it is static friction which acts on a moving car. User Neelim answered this question with an explanation based on the condition of non accelerated rotating and hence there is no actual relative motion between road and the car wheels here
This leads me to my variant of the question: Suppose instead of a car, we had a box set to move in the circular path by action of some forces. Would static friction act still in the centripetal direction?
In other words, does the presence of motion in a tangential direction have any control over the friction which acts in the centripetal direction?
The reason I told box is to have a flat surface w/o rolling.