Think it through this way:
You can calculate the distance around the track from geometry: Circumference = pi times diameter. If it makes one complete revolution in T=12 seconds then its linear velocity is distance traveled divided by time = pi x D/T.
The angular velocity is expressed in radians per second. One revolution = 2 pi radians, so the angular speed is 2 pi radians/12 seconds. The formula that you should remember is w = 2 pi/T, where w = angular velocity in radians/second and T = period of revolution.
The centripetal acceleration is calculated using a = w^2 R, where w = angular velocity in radians/second (which you just calculated) and R = radius. You should memorize this formula.
