$($a$)$ Briefly describe, giving an example, the function of a flywheel.

$(4$ marks$)$

$($b$)$ A $5$ kW motor drives a flywheel that provides the energy for a machine press. At the start of a press operation the fy ywheel speed is $300$ rpm $.$ Eagh press takes $0\mathrm{.}5$ seconds and requires $6$ kJ of energy. Determine:

$($i$)$

The maximum number of operations per minute, assuming no energy losses

$(4$ marks$)$

$($ii$)$

The minimum moment of inertia required for the flywheel if the reduction in speed is not to exceed $30$ rpm $.$

$($iii$)$ The average acceleration and deceleration of the flywheel during and after the press operation.

$(8$ marks$)$