Answer
a) The woman's angular velocity decreases.
b) The woman's angular momentum remains the same.
Work Step by Step
According to the conservation of angular momentum, $$ I_0\omega_0=I_f\omega_f$$
a) When the woman extends her arms outward, she increases the distance $R$ of mass $M$ from the axis of rotation. And because $I=\sum MR^2$, by doing so, she increases her moment of inertia, too.
Because angular momentum is conserved before and after the action, since $I$ increases, the woman's angular velocity $\omega$ will decrease.
b) Because angular momentum is conserved before and after the action, it remains the same.
