The setup to this question is a variation on the popular demo where a student on a stool holds a bicycle wheel and by angling the axis, the student spins in order to conserve angular momentum.
However, in this question, the student does not angle the spinning wheel, but instead applies a force to slow down the wheel to half its original rotational velocity.
The question is whether or not the student on stool rotates.
I think angular momentum is not conserved in this instance. My rationale is that the student, by applying an external force (and thus a torque) throws conservation of angular momentum out the window. However, I'm not entirely sure if the force applied by the student counts as external. That being said, I can't find any demos on youtube to show the experiment either way.
Is this rationale correct?