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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?

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    $\begingroup$ If you want to consider wether the student spins or not, then the student is part of the system, thus it is not an external force, and internal forces cannot change angular momentum. $\endgroup$
    – FGSUZ
    Nov 26, 2017 at 21:42
  • $\begingroup$ What is the direction of the axis of the non-angled wheel? $\endgroup$
    – DJohnM
    Nov 26, 2017 at 21:59
  • $\begingroup$ The axis is in the vertical direction. $\endgroup$
    – Ethan
    Nov 26, 2017 at 22:20

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It depends a bit on the axis of rotation of the wheel.

If the wheel is vertical (axis horizontal) and the student is on a platform that is only capable of rotating about a vertical axis, then slowing the wheel will do nothing* - there will be a torque applied by the student that does not result in a rotation of the platform.

However, if the axis of the wheel and the platform are both vertical, then slowing the wheel will indeed cause the platform (and student) to start rotating - the torque required to slow the wheel results in an equal and opposite torque on the platform. The force is not "external" to the system "wheel plus student plus platform" - if the student is on the platform, the force used to slow the wheel is internal. Thus there is no external force, and angular momentum must be conserved.

  • nothing that you can easily observe: there will of course be a transfer of angular momentum to the earth as @Hotlicks pointed out
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  • $\begingroup$ Wrong! Slowing the wheel when the wheel axis is horizontal transfers it's angular momentum to Earth. $\endgroup$
    – Hot Licks
    Nov 26, 2017 at 22:32
  • $\begingroup$ @HotLicks I chose not to add that detail - it makes things a bit more complicated than I think the question warranted. In all cases angular momentum is conserved. $\endgroup$
    – Floris
    Nov 26, 2017 at 22:34
  • $\begingroup$ Note - I said "doesn't result in rotation of the platform" - NOT "doesn't result in transfer of angular momentum" $\endgroup$
    – Floris
    Nov 26, 2017 at 22:35
  • $\begingroup$ You said "slowing the wheel will do nothing". I think moving the earth is not "nothing". $\endgroup$
    – Hot Licks
    Nov 26, 2017 at 22:37
  • $\begingroup$ I thought I sufficiently clarified what I meant by "nothing" in the bit that followed... $\endgroup$
    – Floris
    Nov 26, 2017 at 22:38

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