- #1
hkyriazi
- 175
- 2
Does anyone know of a formula describing the relationship between precession rate, precession angle, and spin rate for a top (or gyroscope, or any hard, non-spherical object) spinning freely, in zero gravity? All the analyses I've been able to find are for tops under constant torque (gravity), or with their tip held in place in some way.
Specifically, I'm trying to analyze what happens to a baton-like object (like the ones that majorettes twirl in marching bands) as it goes from pure twirling (which has, by my definition, an axial spin rate of zero, and 90 deg precession angle), under a series of frictionless taps at opposite ends and sides, to the pure spinning state (zero deg precession angle, zero twirl/precession rate, and much higher spin rate than the initial twirl/precession rate).
I've had this posted for almost a full day, with no takers, so I'll add that the Earth is known to precess once every 26,000 years or so, but the explanations I've found on the web seem to attribute this to the constant force the equatorial bulge feels from the sun and other planets.
In order to prove to myself that an object can indeed precess under weightless and force-free conditions, I spun a smooth surfaced pen off my fingertips into the air (one must spin it very rapidly, with a finger-snap movement) with a slight jerk as I let it go, and could see (with a good spin and flick) that it precessed nicely until it hit the floor. (If one does this with a pencil, which is usually hexagonal in cross-section, the air resistance effect is so great that it causes very bizarre movements through the air, obscuring the precession.)
--Harold Kyriazi
Specifically, I'm trying to analyze what happens to a baton-like object (like the ones that majorettes twirl in marching bands) as it goes from pure twirling (which has, by my definition, an axial spin rate of zero, and 90 deg precession angle), under a series of frictionless taps at opposite ends and sides, to the pure spinning state (zero deg precession angle, zero twirl/precession rate, and much higher spin rate than the initial twirl/precession rate).
I've had this posted for almost a full day, with no takers, so I'll add that the Earth is known to precess once every 26,000 years or so, but the explanations I've found on the web seem to attribute this to the constant force the equatorial bulge feels from the sun and other planets.
In order to prove to myself that an object can indeed precess under weightless and force-free conditions, I spun a smooth surfaced pen off my fingertips into the air (one must spin it very rapidly, with a finger-snap movement) with a slight jerk as I let it go, and could see (with a good spin and flick) that it precessed nicely until it hit the floor. (If one does this with a pencil, which is usually hexagonal in cross-section, the air resistance effect is so great that it causes very bizarre movements through the air, obscuring the precession.)
--Harold Kyriazi
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