Will a gyroscope spin by itself at the equator?
I know a foucault pendulum will “spin” by itself at the poles. Actually, the pendulum is steady and the observer is the one who spins.
This seems to be the same thing, only sideways.
The inertia factor would make the gyroscope want to go in a straight line, tangent to the earth. Since the observer is in a curved path with the earth, he would think he was steady and the gyroscope was spinning.
No, it wouldn’t. That would make it a perpetual motion machine, which is impossible.
Au contraire. It simply steals some of the Earth’s rotational energy, slowing it down an all-but-unnoticeable amount.
A gyroscope on a perfectly frictionless mount, situated anywhere on earth, would start to spin on its own provided it is aligned properly. For best results, on the equator, you would want the axis to be horizontal north-south; at say 40 degrees of north latitude, you would want to tip it sixty degrees from vertical, leaning northward.
The result of such an orientation is that the point on the gyroscope that is farthest from the earth’s axis of rotation is going around a larger circle than the point that is closest, so it has slightly more angular momentum. This will cause the gyroscope to start spinning (veeeeeeery slowly). The bigger around the gyroscope, the faster it will spin. The other consequence is that the Earth itself will slow down ever-so-slightly. (Some things that humans have done have measurably affected the length of Earth’s day, namely the creation of large reservoirs in high latitudes that have caused the Earth’s rotation to speed up a tiny bit. Of course, the day is still getting longer, but it’s slightly shorter than it would have been without the reservoirs.)
In real life, the force of acceleration on the gyroscope is dwarfed by bearing friction and air resistance.
Wrong, it wouldn’t be a perpetual motion machine any more than the earth is a perpetual motion machine (it will slow down and stop rotating eventually)
If you lay the gyroscope on it’s side on the equator so that the axis is in parallel to the earth’s axis of rotation, it should spin on it’s own, but the bearings would have to be perfect, so in practice, it won’t.
MrDeath and Mangetout, in your descriptions, is the gyroscope rotating once per day (cancelling the earth’s rotation so that the side nearest, say, Orion, is always nearest Orion), or is there more to it than that?
Yes, that’s all I had in mind
I think you used spin where you meant precession of axis. If that is the case, yes, a gyro in gimballs will try to stay in a stable axis, independant of the earth revolving benath it. This is factor in any navigation system that uses gyros. They have to be reset periodically in aircraft because the horizon has changed and no longer matches the gyro’s “artificial” horizon.
I used to work on inertial navigation systems in aircraft. Tht ASN-92 system in the F-14 had sufficient programming built in and a good enough clock that if you just turned one on and didn’t bother to set coordinates it would “figure out” where it was by sensing the earth revolving and rotating beneath it.
I can see how the inertia of the gyro’s wheel would tend to keep it aligned with the stars and it would therefore revolve with respect to an observer on Earth. But I’m having trouble visualizing MrDeath’s explanation. Could someone elaborate on the mechanism of the angular momentum thingy?