Answer
Her angular speed stays the same.
Work Step by Step
When she lets go of the weights, they have a tangential velocity, and do not immediately fall straight down toward the floor. The angular momentum they have right after she lets go of them is the same that they had right before she let go of them.
The sum of the student’s angular momentum and of the weights’ angular momentum is conserved. Since the latter quantity did not change, neither did the former.
The students’ angular momentum right after she drops the weights is the same as it was before, i.e., her angular speed stays the same.
