The rotational kinetic energy of a rotating object is
[tex]K= \frac{1}{2}I \omega^2 [/tex]
where
I is the moment of inertia of the body
[tex]\omega[/tex] is its angular speed
Let's convert the angular speed from rpm (revolutons per minutes) into rad/s. Keeping in mind that
[tex]1 rev = 2 \pi rad[/tex]
[tex]1 min = 60 s[/tex]
we have
[tex]\omega=8750 \frac{rev}{min} \cdot \frac{2 \pi rad/rev}{60 s/min}=915.8 rad/s [/tex]
So the final kinetic rotational energy of the rotor is
[tex]K= \frac{1}{2} I \omega^2 = \frac{1}{2}(3.25 \cdot 10^{-2} kg m^2)(915.8 rad/s)^2=1.36 \cdot 10^4 J [/tex]
And since its initial energy is zero (it starts from rest), this is equal to the amount of energy needed to bring it at speed 8750 rpm.
