Acentrifuge rotor has a moment of inertia of 3.25*10-2 kg*m2. how much energy is required to bring it from rest to 8750 rpm

The rotational kinetic energy of a rotating object is

where 
I is the moment of inertia of the body
is its angular speed

Let's convert the angular speed from rpm (revolutons per minutes) into rad/s. Keeping in mind that


we have


So the final kinetic rotational energy of the rotor is


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.

Inelastic is the answer your looking for.