A circular table is rotating with an angular velocity of \( \omega \, \text{rad/s} \) about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of \( 1 \, \text{m} \) on the groove. All the surfaces are smooth. If the radius of the table is \( 3 \, \text{m} \), the radial velocity of the ball w.r.t., the table at the time ball leaves the table is \( x \sqrt{2} \, \omega \, \text{m/s} \), where the value of \( x \) is __________.
