As a demonstration of uniform circular motion in class, I often swung my keys from a 68.0 cm string in a horizontal circle over my head. Suppose my keys have a mass of 210. g, and during their motion the string pointed down at a 15.0^o angle (below the horizontal). I then swing the keys harder for 1.00 s, so that they increase to an angular speed of 12.7 rad/s. What is the net angular acceleration of the keys during that 1.00 s?