A small puck on an air table revolves in a circle with rotational speed \(\omega\), held at radius \(r\) by a weighted string that passes through a hole in the table. You slowly pull down on the weighted end of the string, decreasing the radius \(r\). Assume that the angular momentum of the puck about the hole remains constant.

(a) What is the rotational speed when half the string has been taken up? 

\((b)\) What has happened to the speed \(v\) during this time interval?