Changing axis of a rotating wheel

[degn]

Homework Statement

Imagine a woman standing on a rotating disc (D) with a rotating wheel in her stretched arms (se picture here: http://image.vandrermodlyset.net/rotation.jpg ). The wheel is oriented in a horizontal plane, with the rotating axis (W) of the wheel parallel to that of the rotating woman (O) – that is vertical. This situation is rather stable as long as the woman doesn’t get nausea or tired arms. In situation A: W = O = D.
Lets say that she would suddenly change the axis of the rotating wheel (W) so that it became horizontal (situation B), and the wheel would now be oriented in the vertical plane intersecting the axis of the woman (O and D). A point on the outer rim of the wheel would form a helix-shape as the woman rotates on the disk.
I know that this task (going from situation A to B) will be difficult, even more when the wheel rotates fast, but how can I prove this using equations from rotational dynamics.

Homework Equations

T (torque) = r X F
L (angular momentum) = r x p

The Attempt at a Solution

The torque of the rotating woman rotates vetor L of the wheel until it becomes parallel to W=O=D

 

[Nate810]

. When the woman then changes the orientation of the wheel, the torque will have to change as well, since there is a moment of inertia connected to it. This means that in order for the woman to change the orientation of the wheel, she has to apply a force F at the point r of the wheel and generate a larger torque T. The angular momentum of the wheel will also have to be changed since it depends on the force applied.

 

[Moetasim]

. In order to change the axis of the rotating wheel from vertical to horizontal, the woman would need to apply a torque in the direction perpendicular to both the original and final axis of rotation. This can be calculated using the equation T = r x F, where r is the distance from the axis of rotation to the point where the force is applied, and F is the force applied. The greater the distance and the force, the greater the torque needed to change the axis of rotation. Additionally, the angular momentum of the wheel would also need to be conserved, meaning the woman would need to exert a force to counteract the change in angular momentum caused by changing the axis of rotation. This would require a significant amount of energy and strength, making it a difficult task as mentioned.