As a demonstration of uniform circular motion in class, I often swung my keys from a 52.0 cm string in a horizontal circle over my head. Suppose my keys have a mass of 240. g, and during their motion the string pointed down at a 14.0^o angle (below the horizontal). I then swing the keys harder for 1.50 s, so that they increase to an angular speed of 10.0 rad/s. What is the net angular acceleration of the keys during that 1.50 s?