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Comment by mikeash | Hacker News Reader

Gyros are really simple! Think of the gyro's ring as a series of independent particles flying around really fast in a horizontal circle. Now you push up at one point on that circle. Does the circle move up at that point? No. You're applying a force to each particle only very briefly before it moves past and you're pushing on the next one. But you do impart some upward velocity on the particle during its brief time under your influence. This causes it to follow an upward path away from the point where you're pushing, which will continue until the circular path brings it back down. This will tilt the entire circle along the axis connecting the center of the circle to the point where you're pushing.

The faster the gyro spins, the less important the imparted velocity will be relative to the particle's speed, which is why a gyro is more stable the faster it spins.

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I think the phrase "...which will continue until the circular path brings it back down" requires a bit more explanation. At this point, you seem to be switching from treating the rotating ring as a stream of independent particles to being a rigid body, but if you treat it as a rigid body from the start, the first part is no longer obvious.

I think that once you establish that angular momentum is a vector quantity that is entirely consistent with Newton's laws, then the particular case of the gyroscope becomes straightforward.

You can imagine each particle being somehow tethered to the center, without any need for the particles to be connected otherwise.

You’re totally right that gyroscopes are straightforward if you understand angular velocity as a vector quantity, but it’s not quite so intuitive.

If each particle is only tethered to the center, how does the circle bring it down again? If the tethers are all fixed to one another, we're back to rigidity.

Edit: I'm trying to think of a way to bring in angular momentum without having to derive it in full generality...

You could imagine that they’re connected to the center of rotation with a string or something. You just need centripetal force, not a rigid connection to anything. Although that may still be more than what you’re after....

string held taught by centripetal force is rigid. effect is the same.

a spinning disk 'averages' its mass distribution. Consider a gyroscope spinning fast. so if all of a sudden you try a push its top northward then that instantaneous force pushes down on the north edge of the disk and up on the south edge.Those specific parts of the disk acquire momentum. However because the disk is spinning, the part of the disk that was north soon becomes south. and the southern piece that was moving up is now north.now the momenta of the influenced disk segments act to right the gyroscope.

The same effect can occur during the acceleration of a gyroscope in a missile in space. Even tho there is no gravity. The effect of acceleration on the gyroscope is the same, causing it to maintain its orientation in space.

The faster a gyroscope spins, the more quickly it rights itself. and thus appears more stable. as it slows down, the righting effect fails.

Yes, though I think you can avoid the question of why just "those specific parts of the disk" by considering a dumbbell (two joined, point masses spinning around an axis perpendicular to the center of the rod joining them) rather than a disk or ring, and a continuous torque. If you are pushing northwards on the axis, the maximum rate of change of the instantaneous velocities of the point masses is when they are aligned north-south, and when they are aligned east-west, there is no change in their instantaneous velocity from the applied torque. Integrate this over one revolution, and you get the axis tipping in the east-west plane. A picture would really help, maybe I can find one on the web...

indeed it tips perpendicular to the direction of applied force. and this is what happens in reality. try spinning a bicycle wheel holding its axle on both ends. now try to twist the axle and it curiously wants to move the wheel in a perpendicular direction.

This is a description of rotational stability, gyroscopic stability is: http://www.real-world-physics-problems.com/gyroscope-physics...

Key point

Gyroscopic stability also explains why a spinning axisymmetric projectile, such as a football, can have its symmetric (long) axis stay aligned with its flight trajectory, without tumbling end over end when in flight. The spin imparts a gyroscopic response to the aerodynamic forces acting on the projectile, which results in the projectile long axis aligning itself with the flight trajectory. The physics involved here is a combination of gyroscopic analysis and aerodynamic force analysis due to drag and (potentially) the Magnus effect. This is quite complicated and will not be discussed here. However, there is a lot of literature available online on gyroscope physics, as related to projectile spin and gyroscopic stability, if one wishes to study this topic further.

Inertia is not a property intrinsic to an object but depends upon all the mass in the universe.

That quote from the article really crystallized Mach's Principle for me. So continuing mikeash's great explanation... basically the rest of the universe is pushing the gyroscope into its stable position?

But if so, we don't know how the universe does that, and relativity has failed to settle the matter so far. That's what I got from the article.

Don't rely much on Mach's Principle. It's a philosophical statement with exactly zero experimental evidence.

General Relativity would say somewhat the same thing, but in a very different form, with different results. GR would say that it depends on the geometry of the local spacetime, which, yes, does depend on all the mass in the universe, but not in the way that Mach's Principle would lead you to expect.

Note that GR, in contrast with Mach's Principle, does have experimental evidence.

I once built a simple mass-spring physics engine, and this exact effect what was causing the wheels of my car-like mass-spring blob to bend "funny". It was only after I slowly debugged it (by removing friction, then gravity, softer springs, slower timescale etc) that I felt I really got how these forces come about.

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