A technician is testing a circular grinding wheel of radius \(R\) that is rotating about a fixed axis through its center. Initially, a point on the outer rim of the wheel has a tangential speed \(v\) and the wheel has an angular velocity \(\omega\). The technician adjusts the motor so that the tangential speed of the point on the rim increases to \(2v\) while the radius of the wheel remains constant. What is the ratio of the new angular velocity to the original angular velocity \(\omega\)?