What happens if we cut this rope off?

Main Question or Discussion Point

If we spun such a wheel up to speeds close to the speed of light, what would happen if we cut the rope off?

After some pondering, using my little knowledge of classical physics, I came to the conclusion that it wouldn't fall with the same G as an apple would, right? And the higher the speed, the slower the acceleration toward earth.

Correct me please if I am wrong.

P.S.
My background is not physics, but mechanical engineering.

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Nabeshin
Why wouldn't it fall with g? There is nothing attempting to change the angular momentum, so one expects no resistance in this case. The reason we get weird motion with the string is because it's attempting to torque the spinning wheel as it attempts to fall. Without the string, there is no such torque.

Why wouldn't it fall with g?.
Well I was comparing this gyroscopic wheel to a similar hypothetical situation in which one was riding a bicycle on a horizontal surface at higher speeds (close to the speed of light) and all of a sudden the road ended at a cliff. The rider+bicycle would continue to maintain their horizontal speed/momentum (both translational and rotational) off the cliff since the gravitational pull (here g=9.81) on them would exert a relatively small force downward and as a result the fall of the object would be slower and proportionate to its initial speed/velocity. i.e. the higher the speed, the slower free fall!!!

So if the physical laws are true for the bike in this example, so should they be for the gyroscope here.

I may be wrong but please enlighten me.

Dale
Mentor
The bicycle would be moving faster than escape velocity, so it would escape. But during the brief time that it was near the surface of the earth it would be accelerated like any other object. The gyroscope is not at all analogous since it is not moving at escape velocity prior to cutting the string. All that will happen is that it will fall like normal.

The bicycle would be moving faster than escape velocity,
I should have clarified, the bicycle was moving on a flat surface/planet (not spherical like Earth)with a known small g i.e. g=9.81 or 12 N/kg. And when off the cliff, still under the same gravitational pull.

Dale
Mentor
Then it would fall.

Then it would fall.
...Not entirely unlike those poor fools who try homemade stunts (at less Relativistic speeds lol) with ramps! I think cartoons for all of their fun and whimsy, have done a number on the general notion of a "trajectory".

From the psychological and physiological perspective, now in all seriousness, I wonder why this notion of, "gravity is constantly 'ON'" is not as intuitive as you'd think for a terrestrial species. I find that odd.

...Not entirely unlike those poor fools who try homemade stunts (at less Relativistic speeds lol) with ramps! I think cartoons for all of their fun and whimsy, have done a number on the general notion of a "trajectory".

From the psychological and physiological perspective, now in all seriousness, I wonder why this notion of, "gravity is constantly 'ON'" is not as intuitive as you'd think for a terrestrial species. I find that odd.
It is well known "fact" documented in cartoons that you do not fall when you go off the end of a cliff until you look down.

More seriously, here is a link to an actual experiment that compared the fall rate of high velocity gyroscopes to non spinning gyroscops and found no difference.

http://arxiv.org/PS_cache/gr-qc/pdf/0111/0111069v1.pdf

Dale
Mentor
Wow kev, we need to make a "citation of the month" award so that you can win it.

Wow kev, we need to make a "citation of the month" award so that you can win it.
Thanks :tongue2:

I guess your saying they should never have carried out this experiment (and I should never have cited it) because the outcome was obvious, but there were some claims from earlier experiments that there was some anomally in the fall rate of gyroscopes and that had to be countered. It does answer the OP though.

Dale
Mentor
Yes, exactly. It seems so obvious that I would not have thought to even look for the experiment let alone thought that someone would have actually performed it to such an impressive 2 ppm precision! That is why I think the citation is impressive.

More seriously, here is a link to an actual experiment that compared the fall rate of high velocity gyroscopes to non spinning gyroscops and found no difference.
Good example, but the gyroscope in their experiment is spun at relatively low speeds: 17000-18000 RPM. But what if the gyroscope/disk is spinning at 50-99% of speed of light? My understanding is that, at those speeds an object would have immense momentum or inertia, so that any small force(=like gravity) would make no difference in moving the object(here gyroscope) in a different direction or from its rest position, correct? So it's free-fall rate would be 'zero' or close to zero depending on how fast it is rotating? Correct me please if I am wrong.

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Good example, but the gyroscope in their experiment is spun at relatively low speeds: 17000-18000 RPM. But what if the gyroscope/disk is spinning at 50-99% of speed of light? My understanding is that, at those speeds an object would have immense momentum or inertia, so that any small force(=like gravity) would make no difference in moving the object(here gyroscope) in a different direction or from its rest position, correct? So it's free-fall rate would be 'zero' or close to zero depending on how fast it is rotating? Correct me please if I am wrong.
I just did a quick calculation and estimate that any relativistic effect that is a function of the gamma factor at the rim velocity of the gyroscope would be of the order of 1*10^(-15) and while the accuracy of the experiment to 2*10^(-6) is impressive, it is not enough to detect any relativistic effect. A practical problem is that trying to get gyroscopes to spin significantly faster tends to make them explode. However as Dalespam points out, it is fairly certain from other considerations such as the equivalence principle that even at very high relativistic spin velocities no difference in fall rate would occur.

Galileo demonstrated a long time ago that objects with different masses fall at the same rate and unlike a lot of Newtonian laws, Galileo's discovery still holds even in General relativity. A 1 kg mass falls at the same rate as 100kg mass because even though the larger mass has 100 times the inertia, the force of gravity acting on it is also 100 times greater. In another thread about a bullet travelling horizontally at 0.99c most people agree the bullet would fall at exactly the same rate a ball with zero horizontal velocity, even though the bullet might have a much greater inertia. You can think of the gyroscope as a bullet going in circles.

A practical problem is that trying to get gyroscopes to spin significantly faster tends to make them explode.
:rofl: been there with a flywheel... It's an immediate and arresting lesson about the potential and kinetic energy. *life flashes before eyes again*.

I would hate to see the learning curve on a gyro spun like a particle accelerator; that's a bomb.

I'm not so sure that Desiree is entirely wrong, but for other reasons than stated.

Here's the prescription:

Take a very large spinning ring--larger than the Earth, located over the equator, somewhat above the atmosphere. Spin it up to orbital velocity.

Pretend it's perfectly rigid so we don't have to worry about the impossibility of this in the context of special relativity. It's just at orbital velocity, anyway.

Assume the Earth is uniform and spherical.

Shrink the ring slightly without changing it's height over the Earth. Say it's now passing over Panama moving due west.

Now it will experience some nominal amount of force to the south. But not as great as a falling object.

Shrink the ring to 24 inches in diameter. It's centered over the North Pole. It experiences a pull to the south some immeasurable amount less than that due to gravity alone.

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Well, that settles it, this is not going to be a feasible test for a while.

... it is fairly certain from other considerations such as the equivalence principle that even at very high relativistic spin velocities no difference in fall rate would occur.
... In another thread about a bullet travelling horizontally at 0.99c most people agree the bullet would fall at exactly the same rate a ball with zero horizontal velocity, even though the bullet might have a much greater inertia. You can think of the gyroscope as a bullet going in circles.
Well, I thought considering the relativistic mass>> mass, We would then need a very large force to overcome the inertia of the object and consequently if the force is small (like g=9.8 N/kg) then no significant change in velocity would be observed.

Well, I thought considering the relativistic mass>> mass, We would then need a very large force to overcome the inertia of the object and consequently if the force is small (like g=9.8 N/kg) then no significant change in velocity would be observed.
A million kg mass accelerates towards the Earth at the same rate as a 1kg mass. Actually the larger mass accelerates slighty faster because the Earth is also accelerated towards the large mass but if both objects are dropped at the same time they both hit the ground at the same time. If somehow a gyroscope with 1kg rest mass could be spun up so its effective inertial mass was a million kgs it would still accelerate towards the Earth a 9.8 m/s just like the ordinary large mass. The larger the inertial mass the larger the gravitational force acting on it and the two cancel out.

You can prove to yourself that whatever the mass of the falling object and whatever its spin rate, it must fall at the same rate, by considering the equivalence principle. Consider a non-accelerating rocket far out in flat space far away from any significant gravitational sources. Near the top of the rocket are two unattached masses at rest with the rocket, one with much more mass than the other and both the same distance from the base of the rocket. When the rocket accelerates towards the two masses they both arrive at the base at the same time. The equivalence principle states that the rocket accelerating in flat space is equivalent to a gravitational field (to first order ignoring tidal effects). Now if we repeat the experiment with two test masses with equal mass but one is spinning and other is not, it should be clear that when the rocket accelerates they will both hit the base at the same time. The same will therefore be true in a gravitational field.

It is interesting to look up the logic Galileo used to conclude that objects with different masses must fall at the same rate in a vacuum without using the equivalence principle. His conclusion is still true today hundreds of years later, even after Newtonian physics has been superceded by relativity.

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Al68
Well I was comparing this gyroscopic wheel to a similar hypothetical situation in which one was riding a bicycle on a horizontal surface at higher speeds (close to the speed of light) and all of a sudden the road ended at a cliff. The rider+bicycle would continue to maintain their horizontal speed/momentum (both translational and rotational) off the cliff since the gravitational pull (here g=9.81) on them would exert a relatively small force downward and as a result the fall of the object would be slower and proportionate to its initial speed/velocity. i.e. the higher the speed, the slower free fall!!!

So if the physical laws are true for the bike in this example, so should they be for the gyroscope here.
In the case of the bike, it will accelerate at 1 g after it reaches the cliff, just like a falling gyroscope.

The bike may travel a long way horizontally for each foot it drops just like the gyroscope may spin many revolutions for each foot it drops. The acceleration of each relative to earth's surface is still 1 g due to gravity, if we neglect air resistance, etc.

My quess is that the wheel would fall down due to gravity and then roll off the table because of the energy stored in the spinning wheel. Also someboby might get hurt by this out of control wheel.

Second quess is that the wheel would saw down through the table, floor, and into the earth. Anybody coming in contact with this wheel would be sorry since it is spinning close to the speed of light.