A large airliner with a mass of $300,000$ kg cruises in the troposphere at a velocity of $240$ m$/$s$.$The aircraft maintains the same speed and altitude whilst performing a circular turn with a radius of $12$km$.$ As an approximation the aircraft wing is considered to be the equivalent of a thin, symmetrical aerofoil with an angle of attack to the airflow of $2\mathrm{.}5$ degrees during cruise. Assuming, for low angles of attack, that the lift curve slope of the aerofoil is $2\backslash$pi $,$ calculate the angle of attack required to perform the turn.

ANS $=2\mathrm{.}8$DEG