Question

a person sits on a freely spinning lab stool that has no friction in its axle. when this person extends her arms,

Answer 1

Hi there!

$\boxed{\text{Her angular velocity decreases.}}$

Recall the conservation of angular momentum:

$L_i = L_f\\\\I_iw_i = I_fw_f$

When this person extends her arms, her moment of inertia increases.

According to the conservation of angular momentum, if the moment of inertia increases, the angular velocity must DECREASE.