Why Might a Rotating Ring in a B-field Ignore Certain Torques?

[phantomvommand]

Summary:: Please see the attached photo.

I have obtained the correct answer, and my solution agrees with the official solution. However, I have some questions about why the solution is correct. (One may have to draw out some diagrams for this problem, it was quite hard to visualise for me.) The solution goes as such:
1. Find the induced current in the ring using Faraday's Law
2. Find the magnetic torque mu x B, where B is the horizontal component of B-field
3. Using average torque = Ia, solve for a, and then perform some integration.

My question at step 2. Notice that there is still a vertical component of B-field that is perpendicular to the Area vector, and thus perpendicular to magnetic dipole moment mu. Wouldn't this component of B-field exert a torque on the ring about another axis, resulting in the ring rotating about 2 axes? Why can this torque be ignored?

All help is appreciated. Thank you!

 

[kuruman]

Is there a picture that comes with this problem? Note the sentence "You may assume that the frictional effects of the supports and air are negligible." I understand "air" but what "supports" are these? It could very well be that there is a fixed vertical axis that goes through the vertical diameter of the ring.

 

[Steve4Physics]

My question at step 2. Notice that there is still a vertical component of B-field that is perpendicular to the Area vector, and thus perpendicular to magnetic dipole moment mu. Wouldn't this component of B-field exert a torque on the ring about another axis, resulting in the ring rotating about 2 axes? Why can this torque be ignored?

Hi. Just to add what @kuruman has said...

The question mentions 'supports'. It is unclear, but suggests that the coil is in a vertical plane with a fixed pivot at the bottom of the coil and another fixed pivot vertically above, at the top of the coil (or perhaps a vertical axle).

If this is the case, the only possible axis of rotation is the vertical diameter.

There will be a (horizontal, rotating) torque arising from the vertical componennt of B. But this will be canceled by the torque produced by horizontal reaction forces at the pivots. So the resutant torque will be the vertical torque you calculated.