A bus contains a $\backslash (1500\backslash$mathrm$\{$~kg$\},0\mathrm{.}600\backslash$mathrm$\{$~m$\}\backslash )$ radius flywheel $($a disk$)$ and has a total mass of $\backslash (10,000\backslash$mathrm$\{$~kg$\}\backslash ).$

$($a$)$ Calculate the angular velocity the flywheel must have, in rad$/$s$,$ to contain enough energy to take the bus from rest to a speed of $\backslash (18\mathrm{.}5\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ),$ assuming $\backslash (84\mathrm{.}0\backslash \%\backslash )$ of the rotational kinetic energy can be transformed into translational energy.

rad$/$s

$($b$)$ How high a hill, in meters, can the bus climb with this stored energy and still have a speed of $\backslash (5\mathrm{.}00\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at the top of the hill?

What kind of energy or energies does the bus have at the bottom of the hill? What kind of energy or energies does the bus have at the top of the hill? m