Calculate the total inertia of the system shown in Figure $2$ as seen by the clutch. Then calculate the time required to accelerate the system from rest to motor speed of $550$ rpm if the clutch exerts a torque of $158$ Nm$.$ The moment of inertia I for the armature of the clutch, which must also be accelerated, is $0\mathrm{.}00927$ kgm$2,$ including the $32$ mm shaft.