Conservation of Energy in a Gyroscope Thought Experiment

[jamie_sibley]

Conservation of Energy in a Gyroscope Thought Experiment

I have posted a though experiment at the following address. I would appreciate anyone's thoughts on this.


http://sibleysystems.pro/gyro/gyro.html"

Thanks in advance.

Jamie

 

[Cleonis]

I have posted a though experiment at the following address.
http://sibleysystems.pro/gyro/gyro.html"

Let me give labels to the axes.

The outer axis is vertical: swivel axis
The "in between" axis: pitch axis
The inner axis: roll axis

The words "pitch" and "roll" are here used in the same way as in aviation.

As I understand it:
You are starting with only rotation around the roll axis
Then a torque is applied around the swivel axis.
The main visible effect is that the rotor will pitch.

For one thing: as the rotor pitches more and more the roll axis becomes aligned with the swivel axis. Once you have that alignment then the gimbal mounting is pretty much locked up, which is the end of interesting physics taking place.

To prevent the rotor from pitching over completely you need very stiff springs. Since this is a thought experiment we are free to declare our springs as stiff as we need them to be. Also, this being a thought experiment we can declare the rotor velocity as fast as we want.

Assume that the springs are stiff enough. Then applying a torque around the swivel axis will induce swivel. There will be some pitching, and potential energy will be stored in the springs. Other than that the energy inflow will go to kinetic energy of the swiveling motion.

The faster the rotor spins, the stronger the tendency to pitch. So the faster the rotor spins, and the stiffer the springs, the more energy can be stored in the springs.

 

[jamie_sibley]

Lets choose to replace the springs with force gauges that have negligible compression and therefore store negligible energy due to spring compression. I understand how rotational energy can be store while rotating the device around the vertical axis, but this stored energy should be independent of the rotor spin speed.

If we rotated the vertical swivel axis at a fixed speed, ( 10 rad/sec ) then there would be a corresponding force indicated on the force gauges ( proportional to rotor RPM I believe ). In this steady state, the force gauges would have a small and constant amount of stored potential energy. However, to maintain this steady state force on the force gauges, we would have to maintain the input-swivel RPM, and continuously deliver torque to the swivel axis too.

Am I correct to understand, that this continuous input of energy would be constant?? ( input torque and input RPM would remain constant ). Or would it taper off after a while, if the input torque decreases?

I would very much like to have this explained in theory to save me the time and expense of building it into an actual physical experiment. ( most of my experiments don't turn out well :( )

 

[Cleonis]

If we rotated the vertical swivel axis at a fixed speed, ( 10 rad/sec ) then there would be a corresponding force indicated on the force gauges

Yes, there would be a continuous force exerted upon the force gauges.

This force is not doing work. In order for a force to do work there must be displacement in the direction of that force. You have specified that the compression of the force gauges is negligable, hence no work.

You have specified: devoid of gravity, friction, air.
Hence once swiveling motion is started and then left like that it will continue at uniform rate.

Conversely, as long as a torque around the swiveling axis is sustained, rotation rate around the swiveing axis will keep going up.