but the answer does not match up with the answers possible.
What you didn't include from that post was:ωf = 2ωavg = 2(2π)/30 .
Angular acceleration, α = (ωf-0)/30 . That's 1/4 of the former answer.
i do not know how to find theWhat you didn't include from that post was:Base the angular acceleration on one complete lap.All I did in the above QUOTE'ed text was to repeat what we had previously done, but used a complete lap since for a complete lap, we know the elapsed time. Once you have this value, you will need to find the velocity at the 1/4 lap point so that you can recalculate the radial component of acceleration, since that is also wrong.
Do you know the kinematic equations for constant angular acceleration?
If you work everything out, you would find that using our previous answer for angular acceleration, π/7.5/7.5, one lap would take only 15 seconds.