Part $6$ of $10-$ Angular Speed and Angular Momentum

Darcy asks Wilhelmina why angular speed increases as the skater pulls herself closer to the pole. Which of Wilhelmina's responses is correct?

"Angular momentum can also be written as $I,$ where I is the moment of inertia of the skater. From conservation of angular momentum, $I{}_j=I{}_{},$ and because when the skater

pulls her arm in close to her body, her moment of inertia is increased, so her angular speed is also increased."

"When the skater pulls herself closer to the pole, she changes her moment of inertia, and consequently decreases her angular momentum, which means her angular speed increases."

"For an object with a fixed mass that is rotating about a fixed symmetry axis, angular momentum can also be written as $I,$ where I is the moment of inertia of the skater. From conservation of angular momentum, $I_{}{}_i=I_f{}_f,$ and so when the skater pulls her arm in close to her body, her moment of inertia is reduced and her angular speed is increased."

"When the skater pults herself closer to the pole, she changes her moment of inertia and consequently increases her angular momentum, which means her angular speed increases as well."