A $55\mathrm{.}0kg$ runner runs around the edge of a horizontal turntable mounted on a vertical, frictionless axis through its center. The runner's velocity relative to the earth has magnitude $2\mathrm{.}70\frac{m}{s}.$ The turntable is rotating in the opposite direction with an angular velocity of magnitude $0\mathrm{.}250ra\frac{d}{s}$ relative to the earth. The radius of the turntable is $3\mathrm{.}50m,$ and its moment of inertia about the axis of rotation is $75\mathrm{.}0kg*m^2.$

Part A

Find the magnitude of the final angular velocity of the system if the runner comes to rest relative to the turntable. $($You can model the runner as a particle.$)$

Express your answer in radians per second.