A question about why gyroscopes fall slowly

In summary: I was about to ask this question myself.If you place a gyroscope on the equator of the Earth, it will take less than 6 hours for it to fall over.
  • #36
cmb said:
A perfectly friction-free gyroscope that is fixed with a pivot along its axis does not so much 'resist' gravity as transfer any forces that act on it to the pivot.
The torque provided by gravity is tangential to the rotation of the centre of mass of the spinning wheel. Since the direction of "tangential" is constantly changing, the net change in angular momentum over a single revolution of 2π is zero IF there is no friction. But if there is even the slightest amount of friction, there is a net gravitational torque that will cause the gyroscope axis to tilt more (which will change the direction of the angular momentum spin vector which will lead to an increase the angular momentum precession vector to compensate). And eventually the spinning wheel/frame/top will touch the ground and stop.

AM
 
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  • #37
Ibix said:
If the gyroscope is initially pointing at the Sun, directly overhead, and we wait six hours and it's still pointing at the Sun, which way is it pointing relative to the Earth's surface?

Baluncore said:
The gyroscope (mounted in gimbals), was named that by Foucault because it could show (scope) the rotation (gyro) of the Earth.
There is a famous incident involving the shutdown of an early SOYUZ launch in 1966 and subsequent gyro-triggered abort:
https://en.wikipedia.org/wiki/Soyuz_7K-OK_No.1
.
 
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  • #38
cmb said:
A perfectly friction-free gyroscope that is fixed with a pivot along its axis does not so much 'resist' gravity as transfer any forces that act on it to the pivot.

So the answer is that a truly friction-free gyroscope will no more drop than would any stationary object resting on the pivot that such a gyroscope was attached to.

The table in my room has not dropped a mm in the last week, despite gravity acting on it all the time. The same for a 'perfect gyroscope', by translating its load to the pivot, the pivot provides the reaction force that keeps the gyroscope pointing in the same direction (which might look different to your moving frame, but it remains the same), just like the floor keeps my table at the same height (in this local gravity field) where it is now.
what happens with non-perfectly friction-free gyros, How is friction make the gyros fall?
 
  • #39
AHaHaCiK said:
what happens with non-perfectly friction-free gyros, How is friction make the gyros fall?
If you are asking me; AFAIU a torque from the bearing shaft of a gyroscope when combined with a straight-vector force on that shaft will cause a cross-product force and the gyroscope will precess around the pivot. As the gyroscope slows down from that torque, the precession would actually speed up (if the pivot itself was friction free) or reach some 'terminal presessional rotational speed' (friction at the pivot). That 'terminal rotation speed' will be a function of the strength of the cross-product force, which diminishes as the gyroscope slows down.

i.e. if the gyroscope is spinning on a friction axis, the axis will precess horizontally around the pivot due to the downward gravitational force, and both the gyroscope and precession will gradually slow down, whilst the angle of its axis drops downwards. The faster the gyropscope spins at the start of all this slowing-down, the faster the precession rate, and the longer it will take for the axis to dip downwards.

(AFAIU)
 
  • #40
cmb said:
The faster the gyropscope spins at the start of all this slowing-down, the faster the precession rate
You should check this.
 
  • #41
hutchphd said:
You should check this.
Yeah, not sure about that now you mention it. I was just assuming "a x b" would always be bigger, but it'd be translated back to the pivot point, so it might be the pivot point bears a higher load rather than a faster precession.

Sorry, I am not clear on the mechanics of that, happy to say I am not sure about that comment.
 
  • #42
Would a compass needle also resist toppling over and insist on precessing instead?
Remember, the aligned spins and orbital angular momenta of electrons confer on the compass needle an angular momentum even though the solid arrangement of iron nuclei is not rotating.
 
  • #43
AHaHaCiK said:
what happens with non-perfectly friction-free gyros, How is friction make the gyros fall?
See my post #36. Gravity provides a torque if the axis is not completely vertical. The torque vector is tangential to the direction of rotation of the centre of mass of the gyroscope.

If there is NO friction, then in one complete precession period, T, ##\int_0^T \tau dt = 0## so there is no change in angular momentum (##\tau = dL/dt##).

If there IS friction, then in one complete period of precession of the axis ##\int_0^T \tau dt \ne 0## (ie. the torque on the second half of the revolution is going to be applied for a slightly longer time than the torque on the first half of the revolution). This means that there is a change in angular momentum each precession period and it is cumulative.

AM
 
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<h2>1. Why do gyroscopes fall slowly?</h2><p>Gyroscopes fall slowly due to a phenomenon known as precession. When a gyroscope is spinning, it creates a force called angular momentum, which keeps it upright. This force causes the gyroscope to resist any changes in its orientation, including falling over. As a result, the gyroscope appears to fall slowly as it precesses around its axis of rotation.</p><h2>2. What factors affect the speed at which a gyroscope falls?</h2><p>The speed at which a gyroscope falls is affected by its mass, shape, and initial spin rate. A heavier and more massive gyroscope will have a slower fall rate compared to a lighter one. Additionally, a gyroscope with a larger surface area will experience more air resistance, causing it to fall slower. Lastly, a gyroscope with a higher initial spin rate will take longer to precess and fall over.</p><h2>3. Can a gyroscope ever fall completely?</h2><p>Technically, yes, a gyroscope can fall completely. However, it would require a significant amount of external force to overcome its angular momentum and cause it to fall over. In most cases, the gyroscope will continue to precess and fall slowly instead of falling completely.</p><h2>4. How does the Earth's rotation affect a gyroscope's fall?</h2><p>The Earth's rotation does not have a significant impact on a gyroscope's fall. The gyroscope's angular momentum is much stronger than the Earth's gravitational pull, so it will continue to precess and fall slowly in the same direction, regardless of the Earth's rotation.</p><h2>5. Are there any practical applications for understanding why gyroscopes fall slowly?</h2><p>Yes, understanding the principles behind a gyroscope's fall can have practical applications in various fields, including navigation, aviation, and robotics. Gyroscopes are commonly used in these industries to maintain stability and measure orientation, making it crucial to understand their behavior and limitations.</p>

1. Why do gyroscopes fall slowly?

Gyroscopes fall slowly due to a phenomenon known as precession. When a gyroscope is spinning, it creates a force called angular momentum, which keeps it upright. This force causes the gyroscope to resist any changes in its orientation, including falling over. As a result, the gyroscope appears to fall slowly as it precesses around its axis of rotation.

2. What factors affect the speed at which a gyroscope falls?

The speed at which a gyroscope falls is affected by its mass, shape, and initial spin rate. A heavier and more massive gyroscope will have a slower fall rate compared to a lighter one. Additionally, a gyroscope with a larger surface area will experience more air resistance, causing it to fall slower. Lastly, a gyroscope with a higher initial spin rate will take longer to precess and fall over.

3. Can a gyroscope ever fall completely?

Technically, yes, a gyroscope can fall completely. However, it would require a significant amount of external force to overcome its angular momentum and cause it to fall over. In most cases, the gyroscope will continue to precess and fall slowly instead of falling completely.

4. How does the Earth's rotation affect a gyroscope's fall?

The Earth's rotation does not have a significant impact on a gyroscope's fall. The gyroscope's angular momentum is much stronger than the Earth's gravitational pull, so it will continue to precess and fall slowly in the same direction, regardless of the Earth's rotation.

5. Are there any practical applications for understanding why gyroscopes fall slowly?

Yes, understanding the principles behind a gyroscope's fall can have practical applications in various fields, including navigation, aviation, and robotics. Gyroscopes are commonly used in these industries to maintain stability and measure orientation, making it crucial to understand their behavior and limitations.

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