The entrance of a science museum features a funnel into which marbles are rolled one at a time. The marbles circle around the wall of the funnel, eventually spiraling down into the neck of the funnel. The internal radius of the funnel at the top is 0.50 m. At the bottom, the funnel’s neck narrows to an internal radius of 0.041 m. A 5.5 × 10−2 kg marble begins rolling in a large circular orbit around the funnel’s rim at 0.27 rev/s. If it continues moving in a roughly circular path, what will the marble’s angular speed be as it passes through the neck of the funnel? (Consider only the effects of conservation of angular momentum.) Answer in units of rad/s.