# What is the accurate description of the following rotating system?

A man, standing on a rotating disc with angular frequency w starting from the center, moves radially outwards with a velocity of 6 meters per second. If an inertial frame of reference is placed at the center of the disc is it correct to say that the person has a velocity of 6m/s in direction of i' or that the displacement is 6m/s*time in direction of i' . Where i' is a unit vector pointing radially outwards in the rotating frame of reference and is a function of time in the inertial frame of reference.

Both descriptions seem the same to me but if we use the second description and the fact that velocity is derivative of the displacement wrt time, there is an other component for the velocity in direction of j', the unit vector perpendicular to i'. I can't get why that exists.