$($a$)$ An automatic stamping machine stamps out components at the rate of one

every half second. The torque required at the motor is $10$Nm for $0\mathrm{.}2$s followed by

$1\mathrm{.}0$ Nm for $0\mathrm{.}3$s and the variation with time is repeated every half second. Given

that the mean operating speed of the motor is $3000$ RPM$,$ determine the mean

power of the motor. $($b$)$ A flywheel is fixed to the motor shaft in order to limit the speed fluctuations

to $1\mathrm{.}0\%.$ Determine the moment of inertia of the flywheel, given that the

moment of inertia of the remainder of the machine is negligible.