Angular displacement = wo + 1/2*a*t^2. Since you are talking about first and second rotation , it must be starting from rest. Therefore wo = 0.
Let it take t second to complete first rotation and t + 0.48 s for two rotation. So 2pi = 1/2*a*(t)^2 and 4pi = 1/2*a*(t + 0.48)^2 . Divide these two equations. a gets cancelled out. Solve for t. Put this value in the first equation. You will get the value of a.