I am looking at the following problem.
A large flat horizontal platform rotates at a constant angular speed $\omega$. A person on the platform walks in a circular path of radius $R_0$ centered on the axis of the platform with a constant linear speed $v$ relative to the platform’s surface. The coefficient of friction between the person and the platform’s surface is $\mu$ and the mass of the person is $m$. How fast can the person walk if (a) they move in the direction of rotation? (b) if they move opposite the direction of rotation?
For part a I found that when walking in the direction of motion, the Coriolis and centrifugal forces both point away from the center of the platform. So I set $$m\omega^2 R_0 +2m\omega v -\mu N=0$$ Setting $N=mg$ and solving for the required speed $v$ is then straight forward.
For part b however, I found that when opposing the direction of the platform, the centrifugal force points away from the center and the Coriolis force points towards the center. In this case, I don't understand which direction to set the frictional force as the centrifugal and coriolis forces are in opposite directions. How can the direction of friction be determined when the two forces can balance with or without it?