Dear Student
In time T particle travel distance 2πR.
In time T/4 particle travel distance πR/2.
That is from initial position particle cover 1/4th of circle that is 90 degree.
ω = FINAL ANGLE - INITIAL ANGLE/ Time = π/2-0 /T/4=4π/T
Acceleration = ω2R= 16π2 R/T2