centrifuge rotor

[logistic_guy]

A centrifuge rotor has a moment of inertia of \(\displaystyle 4.25 \times 10^{-2} \ \text{kg} \cdot \text{m}^2\). How much energy is required to bring it from rest to \(\displaystyle 10,000 \ \text{rpm}\)?

 

[khansaheb]

A centrifuge rotor has a moment of inertia of \(\displaystyle 4.25 \times 10^{-2} \ \text{kg} \cdot \text{m}^2\). How much energy is required to bring it from rest to \(\displaystyle 10,000 \ \text{rpm}\)?

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[logistic_guy]

How much energy?

\(\displaystyle \Delta K = \frac{1}{2}I\omega^2 - 0 = \frac{1}{2}0.0425\left(\frac{10000\times 2\pi}{60}\right)^2 = \textcolor{blue}{23303 \ \text{J}}\)