Running backwards on a carousel Let's suppose I'm on a carousel rotating with a speed $\omega$ and start running on it in the opposite direction with a speed $v$ such that $\omega r=-v$ where $r$ is the distance between me and the center of the carousel.
What are the forces that act on me? Do I feel Coriolis force?
Intuitively I'm "still" so no force should act on me, but also intuitively this explanation seems too easy to be the real one.
 A: As viewed in an inertial frame, no force acts on you.  This makes sense, because you are at rest in that frame.
As viewed in the rotating reference frame attached to the carousel, two forces are acting on you:  the Coriolis force and the centrifugal force.  The Coriolis force has magnitude $2 m \omega v = 2 m \omega^2 r$ inwards.  The centrifugal force has magnitude $m \omega^2 r$ outwards.  Thus, in the rotating reference frame there is a net force of $m \omega^2 r$ inwards.  This is completely in line with your motion in the rotating reference frame, since in that frame you are executing uniform circular motion about the origin with radius $r$ and angular frequency $\omega$.
A: I assume you mean that you remain stationary while the carousel spins underneath you. This means that the net force acting on you must be zero, or that you would only feel the reaction to your weight from your feet.
If you closed your eyes it would feel like you are running on a straight line, except because your feet are a certain distance apart, and the carousel has different speeds under each foot, it would feel like running on two treadmills, (one per foot) each with a different speed.
