Conservation of Energy in a Gyroscope Thought Experiment

In summary, the thought experiment involves a gyroscope with three axes: swivel, pitch, and roll. By applying a torque around the swivel axis, the rotor will pitch and potential energy will be stored in the springs. The faster the rotor spins and the stiffer the springs, the more energy can be stored. It is possible to replace the springs with force gauges to store negligible energy due to spring compression. However, in this steady state, a continuous input of energy in the form of torque and RPM is required to maintain the force on the gauges. Without gravity, friction, or air, the swiveling motion will continue at a uniform rate.
  • #1
jamie_sibley
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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
 
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  • #2
jamie_sibley said:
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.
 
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  • #3
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 :( )
 
  • #4
jamie_sibley said:
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.
 
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  • #5


I find this thought experiment on conservation of energy in a gyroscope to be quite interesting. The concept of conservation of energy is a fundamental principle in physics, stating that energy cannot be created or destroyed, only transferred from one form to another. In this thought experiment, the author discusses how a gyroscope can seemingly defy gravity and maintain its angular momentum without any external energy input.

Upon reading through the experiment, I can see how the author's initial assumption that the gyroscope would slow down due to friction and eventually stop, is incorrect. This is because the gyroscope's angular momentum is conserved, meaning that any external forces acting on it must be counteracted by an equal and opposite internal force. In this case, the internal forces are provided by the gyroscope's spinning motion, which creates a torque that keeps it stable and prevents it from falling.

Furthermore, the author's suggestion of using a frictionless environment to eliminate any external forces is a valid approach to demonstrate the conservation of energy in a gyroscope. In this scenario, the gyroscope would continue to spin indefinitely, as there are no external forces acting on it to slow it down. This thought experiment highlights the importance of understanding the laws of physics and how they govern the behavior of objects in our world.

In conclusion, this thought experiment on conservation of energy in a gyroscope is a great example of how fundamental principles in physics can be observed and understood through simple yet intriguing experiments. It also serves as a reminder of the importance of considering all factors and variables when conducting experiments and drawing conclusions. Thank you for sharing this thought experiment, Jamie. I hope to see more discussions and experiments on this topic in the future.
 

What is a gyroscope?

A gyroscope is a spinning wheel or disc that is mounted on an axis, allowing it to rotate freely in any direction. It is used to maintain orientation and stability in objects such as airplanes, ships, and smartphones.

What is a thought experiment?

A thought experiment is a mental exercise that explores a particular idea or concept without the need for physical experimentation. It allows scientists to test theories or hypotheses in their mind before conducting actual experiments.

How does a gyroscope demonstrate conservation of energy?

In a gyroscope, the spinning wheel has a rotational kinetic energy. When the axis of the gyroscope is tilted, the force of gravity acts on the wheel, causing it to precess (rotate). This precession is due to the conservation of energy, as the potential energy from the tilt is converted into kinetic energy of precession.

What is the significance of conservation of energy in a gyroscope thought experiment?

The conservation of energy in a gyroscope thought experiment demonstrates the fundamental principle of energy conservation in physics. It shows that energy cannot be created or destroyed, only transformed from one form to another.

What real-world applications does the conservation of energy in a gyroscope thought experiment have?

Gyroscopes are used in various real-world applications, such as navigation systems, spacecraft attitude control, and stabilizing devices for cameras and drones. The understanding of conservation of energy in a gyroscope thought experiment is crucial for the development and improvement of these technologies.

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