Minimal rotational kinetic energy for a gyroscope to precess

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Homework Help Overview

The original poster investigates the minimum rotational kinetic energy required for a gyroscope to precess without falling over, focusing on energy loss due to surface friction. The context involves measuring the time it takes for the gyroscope to fall when subjected to torque, with an interest in the relationship between angular velocity and kinetic energy.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relationship between kinetic energy and the gyroscope's stability, questioning the role of friction and the mechanics involved in precession versus falling. Some suggest measuring the gyroscope's behavior on different surfaces to understand energy loss better.

Discussion Status

Participants are exploring various interpretations of the problem, with some offering insights into the complexities of gyroscopic motion and energy loss. There is no explicit consensus, but several lines of inquiry have been proposed, including measuring initial energies and the effects of surface friction.

Contextual Notes

There are discussions about the lack of a clear dividing line between precession and falling, as well as the potential impact of the gyroscope's supporting structure on its behavior during experiments. The original poster has not yet recorded specific data on the structure's rotation, which may be relevant to their investigation.

  • #31
hutchphd said:
Feynman does a good job on precession. In particular fig. 20-6 and its environs.
Okay, I understand how the equations for new Torques are derived. Does moment of inertia (I) work analogously, because τ = Iα, so
Iz′=Iz
Ix′=Ixcosθ+Iycosθ
Iy'=Iycosθ-Ixsinθ?
 
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  • #32
The moment of inertia is fixed (in the frame of reference attached to the body). It is a matrix that is diagonal in the coordinate system that recognizes the symmetry of the body. Those are the body coordinates usually chosen. Your question is rather general.....I do not know what you need here, please be specific.
 
  • #33
Generally, I want to calculate the energy loss in the gyroscope overtime. To do that I did the evaluation of the dependency of KE on ωp as haruspex sugested in #14. Now I realized that there might be a problem with the formulas, as I think the spin axis and precession axis are not parallel, but perpendicular at the end point (when the gyroscope tipped to the horizontal). Now I'm looking for a way to incorporate this into the formula for KE associated with precession, but I do not know how.

Basically, I am looking for a formula relating KE with ωp.
 
  • #34
Oh! Nevermind! I misunderstood what the parallel axis theorem refered to. It is not the spin and precession axes that are parallel, but spin about the side of the disc and the spin about the centroid of the disc. The formulas work then, thank you.

My new idea is to put the gyroscope at the horizontal initially and since I found a function expressing KE as a function of ωp, I can calculate KE at different times by measuring ωp.
 
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