Answer:
C. 4Eki
Explanation:
The kinetic energy due to the rotation is:
[tex]K = \frac{1}{2}\cdot I \cdot \omega^{2}[/tex]
The motion of the ice skater is modelled after the Principle of Angular Momentum Conservation:
[tex]I_{o}\cdot \omega_{o} = I_{f}\cdot \omega_{f}[/tex]
The initial angular speed is:
[tex]\omega_{o} = \sqrt{\frac{2\cdot E_{ki}}{I} }[/tex]
The final angular speed is:
[tex]\omega_{f} = \frac{I_{o}}{I_{f}}\cdot \omega_{o}[/tex]
[tex]\omega_{f} = 4\cdot \sqrt{\frac{2\cdot E_{ki}}{I} }[/tex]
The final kinetic energy is:
[tex]K = \frac{1}{2}\cdot \left(\frac{1}{4}\cdot I \right)\cdot \left(\frac{32\cdot E_{ki}}{I} \right)[/tex]
[tex]K = 4\cdot E_{ki}[/tex]
The correct answer is option C.
