A thin-walled cylindrical pressure vessel of internal diameter 2 m is designed to withstand an internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the cylindrical portion of the vessel is 100 MPa, the minimum thickness of the plate of the vessel (in mm) is _______.

An engine, connected with a flywheel, is designed to operate at an average angular speed of $$800$$ rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to be $$6240$$ J. In order to keep the fluctuation of the angular speed within $$ \pm 1\% $$ of its average value, the moment of inertia (in kg-m²) of the flywheel should be ____________.