A student stands on a table rotating with an angular speed w while holding two equal dumbbells at arm's length. Without moving anything else, the two dumbbells are dropped to the floor. What change, if any, is there in the student's angular speed? Is angular momentum conserved? Explain your answers.

The angular speed of the student will increase. When the dumbbells are dropped on the floor, no external torque acts on the student and the turntable, and therefore the angular momentum must be conserved.
When the dumbbells are dropped, the rotational inertia of the student and turntable decreased. To compensate for the decrease in rotational inertia the angular speed of the student and the turntable must increase.