A flat uniform circular disk (radius = 3.70 m, mass = 320 kg) is initially stationary.

A flat uniform circular disk (radius = 3.70 m, mass = 320 kg) is initially stationary. The disk is free to rotate in the horizontal plane about a frictionless axis perpendicular to the center of the disk. A 47.0-kg person, standing 0.980 m from the axis, begins to run on the disk in a circular path and has a tangential speed of 3.10 m/s relative to the ground. Find the resulting angular speed (in rad/s) of the disk.