# Conservation of Angular Momentum and a Spinning Bicycle Wheel

• I
A person standing on a stationary friction-less turntable spins a bicycle wheel with the rotation axis of the wheel in the horizontal direction, thus the initial angular momentum is in the horizontal direction (x - axis), say to the right. Now suddenly the person turns the axis of rotation of the wheel by 90 degrees upward (final angular momentum of the wheel is now directed upward along the y- axis).

I understand that the initial angular momentum along the y- axis is zero. Thus we expect the final angular momentum of the system along the y- axis to be zero as well. So the person + platform will spin finally in the opposite direction of the spinning wheel.

But the problem I am having is with the initial x - component of angular momentum. How do we account for a final x- component of angular momentum? If there is no final angular momentum in the x- direction, then this means that angular momentum is not conserved! contradiction! Any help would be appreciated. Thanks.

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Orodruin
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There will be external forces acting on the system and so you should not expect angular momentum to be conserved in general.

Thanks Orodruin. I did think so but I can not figure out what the external torque is in this case.

Orodruin
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The external torque comes from the axis of the turnable. The only direction it cannot provide a torque in is the y-direction (and hence the angular momentum in the y-direction is conserved).

If instead you fixed the entire system to rotate about a single point instead of an axis, then angular momentum with respect to that point would be conserved and the entire system would start spinning in the x-direction as well.

samirgaliz
The external torque comes from the axis of the turnable. The only direction it cannot provide a torque in is the y-direction (and hence the angular momentum in the y-direction is conserved).

If instead you fixed the entire system to rotate about a single point instead of an axis, then angular momentum with respect to that point would be conserved and the entire system would start spinning in the x-direction as well.
The external torque comes from the axis of the turnable. The only direction it cannot provide a torque in is the y-direction (and hence the angular momentum in the y-direction is conserved).

If instead you fixed the entire system to rotate about a single point instead of an axis, then angular momentum with respect to that point would be conserved and the entire system would start spinning in the x-direction as well.
Thank you.

Thank you Orodruin for you response. I am have difficulty visualising how this force is coming from the axis of the turntable. Any clarification would be appreciated.