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The principle of the conservation of momentum is the law applied in the given figure. If the figure starts to spin with the arms spread wide, they have a large movement of inertia.

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The skater starts off in a standing position and spins about the vertical axis. After few rotations , the skater pulls both arms closer to the body and spins fatser. In physics, we call it conservation of angular momentum.

 

conservation of momentum is used in the following figure she starts spinning with a vertical axis as soon as she starts spinning faster she pulls both arms to reduce friction                                                                                                                                                                                                                                                                                                                                                                                                                                                             

Basically the ice draws her hands and legs in so as to reduce the distance between her axis of rotation and little bit of her mass. This reduces inertia. Then her angular momentum gets conserved her rotational velocity increases. Axis of rotation is the point around which a rigid body rotates. And inertia here is the rotating motion. 

the law is conservation of angular momentum in absence of external torque

as l =iw

as i increases w decreses