A carousel at a local theme park has eight flying dumbos. Each elephant weighs $100$ kg and is

connected to the center of the carousel via a shaft of $5$ m length. Determine the moment of inertia of the

system $($assume the shafts to be massless$).$ Consider that the system, when spinning, has a friction

coefficient of $b=1000N\frac{m}{s}.$ Calculate the equation of motion of the system when its engine provides a

torque equal to T $.$ Then, determine the value of T assuming that, at steady state, the velocity of the

carousel is $4$ rpm $.$