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1 December 2024 20:37
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Question |
| Asked by: |
Jesse |
| Subject: |
conservation of energy in a gyroscope |
| Question: |
I am trying to understand the workings of a gyroscope and I'm having trouble with this thought experiment. Can someone help me out?
a gyroscope is set up with one end in a fixed position, yet the whole apparatus is able rotate about that point in any direction(up,down,clockwise, couter-clockwise).
at start the gyroscope is brought up to speed and set with some angle to the ground, lets say 45 deg. above level and held so that it will not precess...
so the starting state has energy equal to the potential energy of the apparatus due to it's height above the ground plus the rotational energy in the flywheel.
When the gyroscope is released, gravity will cause it to precess, presumably without lowering the apparatus below it's angle of 45deg.(?)
in this state the height of the apparatus stays the same, so there is no change in potential energy. I assume then that the total rotational energy stays the same as well, though this time it is divided between the energy in the flywheel and the rotational energy of the entire apparatus.(?)
Finally a force is applied to the apparatus to rotate it in the direction opposite to that caused by procession. This causes the gyroscope to rotate down toward the ground. lets say the force is applied until the apparatus is at 15deg. relative to the ground, and then the force is removed. When this happens the gyroscope will go back to precessing and the system will be in most respects similar to state 2. however, some unknown quantity of energy has been added by the application of force, and the apparatus is now lower than it was, so some of the potential energy also has to be accounted for.
Where does this energy go?
The only thing I can think of is that the flywheel would have the gain some energy, but everything I've read assures me that that is impossible.
hope this is clear, and thanks in advance to anyone who can shed some light on it.
-Jesse |
| Date: |
23 November 2004
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