A boy is pushing his sister on a playground merry-go-round. The angle where the merry-go-round turned is varies with time according to the angular displacement function, ????(????) = ???????? + ???????? ³ where a and b is given as 0.5 rad/s and 0.012 rad/s ³ . 

(a) Determine the angular velocity of the merry-go-round in term of t  and calculate its initial angular velocity.

(b) The given angular acceleration of the merry-go-round is ???? = (0.3????) rad/s ² when it is start at initial angular velocity. Determine the magnitude of the normal and tangential components of acceleration of point P at his sister when ???? =2 rev.