$($a$)$ An aeroplane flying at $240$ km$/$h turns towards the left and completes a quarter circle of $60$m radius. The mass of the rotary engine and the propeller of the plane is $450$ kg with a radius of gyration of $320$ mm$.$ The engine speed is $2000$ rpm clockwise when viewed from the rear. Determine the gyroscopic couple on the aircraft and state its effect. In what way is the effect changed when the $($i$)$ aeroplane turns towards right $($ii$)$ engine rotates clockwise when viewed from the front $($nose end$)$ and the aeroplane turns $($p$)$ left $($q$)$ right?