Moment of Inertia:
[tex]I = 0.33 \; \text{J} \cdot \text{kg} \cdot \text{m}^{2}[/tex].
The angular velocity is in rpm or rotations per minutes. In SI units, the unit should reads radians per second. Each rotation is [tex]2\pi[/tex] radians and there are sixty seconds in one minute. Convert to SI units:
[tex]\omega = 1200 \; \text{RPM} \times 2\pi \times \dfrac{1\;\text{minute}}{60\;\text{s}} = 125.7 \;\text{s}^{-1}[/tex].
"Radian" is implied and isn't shown in the unit.
[tex]KE_\text{rotational} = \dfrac{1}{2} \;I \cdot \omega^{2}[/tex].
[tex]I = \dfrac{KE_\text{rotational}}{\dfrac{1}{2} \;\omega^{2}} = \dfrac{2\;KE_\text{rotational}}{\omega} = \dfrac{2 \times 2600}{125.7^{2}} = 0.33 \;\text{kg}\cdot\text{m}^{2}[/tex].
