Assignment formulation: An aircraft is flying at a constant tangential speed of $\backslash (707\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )$ in a horizontal circle of radius $3050$ m and turning to the left. The engine rotating parts have a moment of inertia of $\backslash (26,2\backslash$mathrm$\{$kgm$\}^\{2\}\backslash )$ and are rotating at a constant $3200$ RPM in a clockwise direction viewed from aft of the plane.

Do the following:

$($i$)$ Determine the magnitude and direction of the gyroscopic reaction torque $(20$ marks$).$

$($ii$)$ Draw the angular momentum$-$ and moment vector diagramme $(15$ marks$).$