Angular Velocity of Ice Skater

An ice skater spins at \(4\pi \)rad/s with her arms extended. If her moment of inertia with arms folded is \(80\%\) of that with her arms extended, what is her angular velocity when she folded her arms?


Conservation of angular momentum gives $$ I_1\omega_1=I_2 \omega_2$$
$$ (I_1) (4\pi)=0.8 I_1 \omega_2
Hence, \(\omega_2=5\pi\)


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