A $12\mathrm{.}2-$kg cylinder rolls without slipping on a rough surface. At an instant when its center of gravity has a speed of $11\mathrm{.}2$ m$/$s$,$ determine the following.

$($a$)$ the translational kinetic energy of its center of gravity

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$($b$)$ the rotational kinetic energy about its center of gravity

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$($c$)$ its total kinetic energy

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