A thin circular ring of mass \( M \) and radius \( R \) is rotating with a constant angular velocity \( 2 \,\text{rad s}^{-1} \) in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass \( m \) be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in \( \text{rad s}^{-1} \)).
