A Puck Moves on a Horizontal Air Table $\sqrt { 2 }$

A puck moves on a horizontal air table. It is attached to a string that passes through a hole in the center of the table. As the puck rotates about the hole, the string is pulled downward very slowly and shortens the radius of rotation, so the puck gradually spirals in towards the center. By what factor will the puck's angular speed have changed when the string's length has decreased to one-half of its original length?

A) 2
B) 4
C) $\sqrt { 2 }$
D) 1
E) 1/2