A shearing machine requires $150$ kg$-$m of energy to shear a steel sheet, and has a normal speed of $3$ rev$/$sec$,$ slowing down to $2\mathrm{.}8$ rev$/$sec during the shearing process. The flywheel of the machine has a mean diameter of $75$ cm and weighs $0\mathrm{.}0155$ kg$/$cm$3.$ The width of the rim is $30$ cm$.$ If the hub and arms of the flywheel account for $15\%$ of its total weight, find the weight of the flywheel.