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Note on tex2html_wrap_inline748

We derived tex2html_wrap_inline748 and tex2html_wrap_inline792 for a two dimensional continuous object rotating in an axis perpendicular to its plane, but we can apply it to non-pancake-like objects with a few caveats.

First consider some symmetric object that's rotating about a symmetry axis in zero gravity:


there is no torque on the bearing.

Now take off one of the arms


Now the object will not continue to spin around. It is ``off balance". To insure it continues to rotate around as it did before you need to change the construction of the bearing:


Now the bearing provides a torque to hold the object at the right angle. If we apply an external torque to the red ball, it will cause a torque to be applied to the bearing. The bearing torque keeps the objects rotating about in the horizontal direction. In this case we can still write tex2html_wrap_inline748 , but keep in mind that additional torques are being generated to keep the object rotating around like we want it to.

Now what happens to tex2html_wrap_inline778 ? In the first picture, the angular momentum vector points along the axis of rotation. In the second it does not. Our derivation of tex2html_wrap_inline792 assumes the former case. We have to be careful to only use this formula when rotation is along an axis of symmetry.

Joshua Deutsch
Sun Feb 23 15:54:50 PST 1997