(Edited question, 07/04/23)
For someone standing on a carousel, there is a frictional force at their feet of magnitude $|F| \leq \mu N = \mu mg$ that is directed towards the centre of the carousel, where $N$ is the normal force, $m$ is the person's mass, and $\mu$ is the coefficient of friction. If $F \geq mr \omega^2$, where $r$ is the distance from the person to the centre and $\omega$ is the angular velocity of the carousel, then the frictional force is large enough that the person undergoes circular motion.
However, what happens if the person is seated facing the centre, leaning forward such that their back is not in contact with the back of the seat? Their feet are in contact with the carousel as before, but now their body is also in contact with the seat (with a different coefficient of friction), since they are sitting down. In this case, how is the frictional force recalculated, if it is no longer possible to simply use $|F| \leq \mu N$?