I have two problems dealing with angular displacement. The first is to find the angular displacement of a record (standard 33 1/3 rpm) in .5 seconds. I'm pretty sure I understand this part. The next question asks you to find the angular displacement of the same record if the diameter is 30.48 centimeters. How does this question differ from the last one? What's the significance of giving the diameter?
Answer The record rotates 33.333(2pi)/60 = 3.49 radians/second so in 0.5 seconds, the displacement would be 1.745 radians. The angular displacement is independent of the diameter. However, knowing the diameter you can calculate how far the edge of record travels as a function of time.