Answer
(a) increase
(b) $2v$
Work Step by Step
(a) We know that the angular momentum of the puck does not change but the moment of inertia changes because the radius decreases. We know that $L=mvr$; this equation shows us that when the angular momentum L is constant and the radius decreases, then the linear speed v should increase to maintain constant angular momentum.
(b) We can find the final speed as follows:
$L_i=L_f$
$\implies mvr=mv_f r_f$
This can be rearranged as:
$v_f=v(\frac{r}{r_f})$
$\implies v_f=v(\frac{r}{\frac{1}{2}r})$
$v_f=2v$
