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Ribbon around the Earth

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cr1t
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cr1t
« Reply #15 on: November 24, 2014, 10:39:27 AM »

But as far as I can work out, such an artificial gravity field, created via acceleration, would be indistinguishable from "real" gravity, and the pencil should drop to the floor. Isn't that what Uncle Albert said?
You’re thinking of Einstein’s “Equivalence Principle” of General Relativity, which pertains to rectilinear acceleration.  (However, it should be noted that rotating gravitational fields are entirely possible, in which case such a field and artificial gravity through rotation would again be indistinguishable, but we are entirely unfamiliar with such fields.)

In a situation where artificial gravity is produced by rotation, the aforesaid “Coriolis effect” comes into play.  Unless the pencil is exactly at the axis of rotation, it would appear to accelerate towards the “floor” — but following an apparently curved path, not the rectilinear path our experience suggests!  The link has a tidy little animated graphic to illustrate the effect.

'Luthon64



I'm a bit confused to what the issue you have,
 since the camera actors and pencil is in the spinning ship,
 we should see the pencil drop down to the floor in a straight line.

I think you mentioned the floating pencil which sounds wrong.
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Mefiante
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« Reply #16 on: November 24, 2014, 12:03:00 PM »

… we should see the pencil drop down to the floor in a straight line.
Not so because the pencil will follow a genuine straight line trajectory once it is released (in accordance with Newton’s first law), as seen from an inertial frame of reference.  But because it is seen from the non-inertial frame of reference of the rotating spaceship and astronauts, it will therefore appear to them to follow a curved path from its point of release to the “floor” of the spaceship.  Draw an external set of axes and plot snapshots of the points where the pencil and astronauts will be at successive points in time.  Now plot the pencil’s positions as seen from the astronauts’ position.  They’ll see a curved trajectory, the curvature of which depends on the angular speed of the spaceship and its radius.

It’s a worthwhile exercise because it shows how intuition can fail.

I think you mentioned the floating pencil which sounds wrong.
No, I didn’t.  Have a careful look at who wrote what.

'Luthon64
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BoogieMonster
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« Reply #17 on: November 24, 2014, 13:13:32 PM »

It’s a worthwhile exercise because it shows how intuition can fail.

Intuitively I actually expect the object to fall on a curved path, the intuitive reasoning I used (probably incorrect) was that of swinging something in a circle on a rope then releasing it, which results in instant outward movement (it won't float), but along a curved path.... in this case your hand is playing the part of the rope up until you release. This allowed me to clearly visualise what's happening while assuming "my" frame of reference is standing still, but still knowing it's rotating. (EDIT: On second thought this sounds completely incorrect)

I do have a caveat though: The reasoning here seems to assume, as many physics problems do, a vacuum. I would expect the air in the vessel, having been there for an appreciable amount of time, to be moving more-or-less at the same speed as the vessel thanks to what I recall about fluid dynamics. It would, intuitively, seem to me that the air in the vessel combined with the aerodynamics of the object will counteract some of this "swing" of the object as it falls. IOW: I'm not sure by how much, but I'd expect the effect to be counter-acted to some degree given a breathable atmosphere.
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Mefiante
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« Reply #18 on: November 24, 2014, 13:53:50 PM »

Assuming that the object’s density is significantly greater than that of air, the effect on the object’s motion of the atmosphere being dragged along by the spaceship is negligible, just as it is here on Earth where the atmosphere is also being dragged along both the Earth’s rotation and its revolution around the Sun.

It seems to me that the key point here keeps getting missed.  As viewed from an external inertial frame of reference (pay special attention to the second paragraph of that entry), the pencil describes a circular motion (or, more generally, a helical one if the ship also has a component of motion along its axis of spin) until the moment it is released.

Upon its release, the pencil follows a straight line path as viewed from that external frame of reference.  This is what Newton’s first law of motion guarantees because there are no longer any unbalanced forces acting on it.  The pencil’s speed can be calculated from the ship’s rate of rotation in conjunction with the perpendicular distance of the pencil from the ship’s axis of rotation, while its direction will be tangent to the circle (or helix) it was following at the time of its release.  That straight path will inevitably carry the pencil to the outside periphery of the spaceship (i.e., to its “floor”).

Now here’s the kicker:  As seen from our external frame of reference, while the pencil is travelling along its rectilinear path, the rest of the ship and the astronauts are still following their previous circular (or helical) trajectory.  Ergo, from their perspective, the pencil will appear to follow a curved path towards the floor.

If the point still isn’t clear to anyone interested, I strongly urge them to go through the exercise I suggested earlier.

'Luthon64
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BoogieMonster
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« Reply #19 on: November 24, 2014, 14:11:14 PM »

I understand.  Grin
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Brian
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« Reply #20 on: November 24, 2014, 14:34:04 PM »

Quote
the pencil follows a straight line path as viewed from that external frame of reference.  This is what Newton’s first law of motion guarantees because there are no longer any unbalanced forces acting on it.  The pencil’s speed can be calculated from the ship’s rate of rotation in conjunction with the perpendicular distance of the pencil from the ship’s axis of rotation, while its direction will be tangent to the circle (or helix) it was following at the time of its release.  That straight path will inevitably carry the pencil to the outside periphery of the spaceship (i.e., to its “floor”).

Fok...dis lekker as jy so dirty praat!
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brianvds
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« Reply #21 on: November 24, 2014, 14:45:12 PM »

I think I more or less have a handle on it now.

Next up: Plot the path of the object relative to a person running up the cylinder while time traveling. :-)
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cr1t
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cr1t
« Reply #22 on: November 24, 2014, 14:47:31 PM »

Assuming that the object’s density is significantly greater than that of air, the effect on the object’s motion of the atmosphere being dragged along by the spaceship is negligible, just as it is here on Earth where the atmosphere is also being dragged along both the Earth’s rotation and its revolution around the Sun.

It seems to me that the key point here keeps getting missed.  As viewed from an external inertial frame of reference (pay special attention to the second paragraph of that entry), the pencil describes a circular motion (or, more generally, a helical one if the ship also has a component of motion along its axis of spin) until the moment it is released.

Upon its release, the pencil follows a straight line path as viewed from that external frame of reference.  This is what Newton’s first law of motion guarantees because there are no longer any unbalanced forces acting on it.  The pencil’s speed can be calculated from the ship’s rate of rotation in conjunction with the perpendicular distance of the pencil from the ship’s axis of rotation, while its direction will be tangent to the circle (or helix) it was following at the time of its release.  That straight path will inevitably carry the pencil to the outside periphery of the spaceship (i.e., to its “floor”).

Now here’s the kicker:  As seen from our external frame of reference, while the pencil is travelling along its rectilinear path, the rest of the ship and the astronauts are still following their previous circular (or helical) trajectory.  Ergo, from their perspective, the pencil will appear to follow a curved path towards the floor.

If the point still isn’t clear to anyone interested, I strongly urge them to go through the exercise I suggested earlier.

'Luthon64


I'm still not convinced. Because the pencil does not loose its forward momentum.

If you are in a plane and you drop a pencil, the pencil will appear to go straight down.
If you are outside said plane you would see the curved trajectory, and that would be the same for our spinning space station
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Rigil Kent
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« Reply #23 on: November 24, 2014, 15:46:15 PM »

If you are in a plane and you drop a pencil, the pencil will appear to go straight down.
The plane flies in a straight line at a constant speed, say eastwards. While the pencil is released, it continues moving eastward at the same rate as the plane. So if you are inside the plane, you notice only its earth-ward motion, and not its eastward motion. This explains why the pencil appears to be falling straight down to an observer inside the plane. But if the same exercise was repeated while the plane briskly accelerated, it would look as if the pencil described a curved path while falling.

Since the space station is rotating it is accelerating continuously in the sense that it changes direction the whole time. When the pencil is released, it loses the centripetal force gluing it to a circular path around the hub of the space station. So it can no longer accelerate along with the rotating space station anymore and it flies off in a straight line, and eventually crashes into the floor somewhere different to where it was released. From the inside of the space station, it's path looks curved, just like from inside of the accelerating plane.

Rigil
« Last Edit: November 24, 2014, 15:58:25 PM by Rigil Kent » Logged
Mefiante
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« Reply #24 on: November 24, 2014, 15:50:59 PM »

I'm still not convinced.
Then you really should do the exercise I suggested.  Holler if you need help with that.

'Luthon64
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brianvds
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« Reply #25 on: November 25, 2014, 04:30:19 AM »

I'm still not convinced.
Then you really should do the exercise I suggested.  Holler if you need help with that.

'Luthon64

When I first got my head around this years ago, I also spent much time drawing diagrams (or at least imagining them), in between pulling out my hair and so on. :-)

I have always found mechanics and relative motion the most difficult aspect of physics, and indeed any science. Seems you need a particular kind of mind for it, that I apparently don't have. Which is not to say you can't understand it if you don't have that kind of mind, but you will have far more difficulty understanding it.
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Rigil Kent
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« Reply #26 on: November 25, 2014, 06:48:40 AM »

Being trained mostly in biology, of course I have my own list of pet peeves in movies
What was your take on The Human Centipede?

Rigil
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cr1t
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cr1t
« Reply #27 on: November 25, 2014, 08:59:17 AM »

I'm still not convinced.
Then you really should do the exercise I suggested.  Holler if you need help with that.

'Luthon64


Ok so from the web.

http://askthephysicist.com/ask_phys_q&a.html

Quote
When the ball is simply dropped from say h=1 m, the Coriolis force is relatively small because the velocity is small for most of the time of the fall. So, the deflection should be modest. I will try to estimate the amount of deflection. The centrifugal force is mg and is always radially out, choosing +y radially out, ay=-g+ayCor; I will argue that the ball does not acquire enough speed for the Coriolis force to have a significant radial component, so ayCor≈0, and  y≈h-½gt2, vy≈-gt. So, the time to fall is approximately t≈√(2h/g)=0.45 s and vy≈4.4 m/s. The Coriolis acceleration, if the velocity is purely radial, points in the backward direction (to the left in my figure above) and would have a maximum magnitude of about 2v√(g/R)≈3.9 m/s2. If the ball drops almost vertically the Coriolis acceleration would be approximately ax≈2m





So the pencil would not have gained enough Coriolis effect to be deflected much.

In conclusion i don't think you can berate the film makers to much.

A little more on it
http://en.wikipedia.org/wiki/Artificial_gravity#Rotation

Quote
To reduce Coriolis forces to livable levels, a rate of spin of 2 rpm or less would be needed. To produce 1g, the radius of rotation would have to be 224 m (735 ft) or greater, which would make for a very large spaceship
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Mefiante
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« Reply #28 on: November 25, 2014, 09:33:25 AM »

I have always found mechanics and relative motion the most difficult aspect of physics, and indeed any science. Seems you need a particular kind of mind for it, that I apparently don't have.
You may well be right.  I’ve always found it useful to pick an appropriate frame of reference that allows the various motions to be described as simply as possible.  Of course, it takes some practice to recognise such, and one could still argue that there’s the “right kind” of intuition involved in selecting such a frame to begin with.



Ok so from the web.
My goodness, that physicist certainly knows how to complicate things inordinately!   That’s not to say those answers are wrong, merely far more confusing and convoluted than they need to be.  There is a far simpler and clearer approach.  Once again, I urge you to do the exercise yourself, rather than relying on vague hand-waving such as “the Coriolis force is relatively small” and “the deflection should be modest”, followed by an approximation of dubious worth.  Nothing beats a precise formulation because the Coriolis effect isn’t limited to letting go of a pencil close to the outer edge of a rotating spaceship.  Its reach is considerably wider than that.

ETA:  The ISS is a bit smaller than that 440+ metre diameter suggested by Wikipedia.

'Luthon64
« Last Edit: November 25, 2014, 09:46:22 AM by Mefiante, Reason: Size counts... » Logged
brianvds
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« Reply #29 on: November 25, 2014, 14:47:16 PM »

Being trained mostly in biology, of course I have my own list of pet peeves in movies
What was your take on The Human Centipede?

Rigil


Thankfully, I haven't seen it. :-)
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