On Angular Momentum, General Relativity,etc... etc... etc...

[Pi Man]

I was posting some replies to a thread the other day when I got to thinking about centrifigul, centripital, inertial, and gravitational forces. My question is going to be hard to explain, but(hopefully) worth it.

consider the following situation. You are in a large torrus shaped, man made craft someplace in the universe where the gravity is negligable. The craft is rotating to simulate gravity.

cross-section:

     <------  Direction of rotation
    ___________
   /           \
  /             \
 /               \
|                 |
|                 |
|        O    o|-<| <-----you
|                 |
|                 |
 \               /
  \             /
   \___________/
    --------->

Certainly, you will experience inertial forces, which, according to GR, are equivelant to gravity. So, you feel like you're standing on the floor and being pulled down by gravity, and everything is hunky-dory(did I spell that right?) Then you jump.

    and land here
    ___________
   /        +  \
  /          \  \
 /            \  \
|              \  |
|               \ |
|        O       \| <-----boing
|                 |
|                 |
 \               /
  \             /
   \___________/
       ----->  Direction of rotation

To the outside observer, you would be traveling in a stratght line. But, to you, you would be jumping straight up in the air(toward the axis of rotation anyway) and land in the same spot you jumped, and everything is hunky-dory. And then you consider a completely different situation.

     <------  Direction of rotation
    ___________
   /           \
  /             \
 /               \
|                 |
|                 |
|        O        |
|                 |
|                 |
 \     o|-<      /
  \             /
   \___________/

Now you are stationary(relative to the frame of reference where the axis of rotation is stationary, but where the frame of reference is not rotating with the space craft) and floating, weightless in space. You would not feel any gravity from the rotation of the craft because the gravity (inertail force) comes from the changing of your state of motion.

Now, my question is: "what would the explanation for this be from the perspective of somebody else (person B) standing on the inside of the craft, feeling the inertial force?" Would that person B be valid in saying that you are somehow in orbit? Any other explanation I can think of would require that there be a way to show, via a physical experiment, weather you were experiencing inertial forces or a gravitational field, which violates the central principal of GR!. However, the "in orbit" explination wouldn't work either.

Please give me some meaningful feedback on this! It's keeping me up at night! It's the reason why I'm a computer geek/junkie! I'm suffering severe psycological dammage because of it! PLEASE!!!! YOU MUST HELP ME!!!

*Disclaimer: I know gravity and inertial "forces" are not actually forces, but, in lack of a better word, your stuck with the word forces.

[daver]

You're in such a rotating object, on the inside surface, on a bicycle. Even if you are blindfolded, you'll find that there are two orthogonal directions, spinward and poleward. If you cycle to the spinward direction, you get heavier. If you cycle against the spinward direction, you get lighter. If you cycle polewards, your weight stays the same. To an observer inside the centrifuge, the hovering person has just gone so fast in the anti-spinward direction that he is weightless.

[Grey]

Please give me some meaningful feedback on this! It's keeping me up at night! It's the reason why I'm a computer geek/junkie! I'm suffering severe psycological dammage because of it! PLEASE!!!! YOU MUST HELP ME!!!

Remember that general relativity says that a constant acceleration is equivalent to a constant gravitational field. But in a spinning centrifuge, the acceleration is not constant when viewed in the non-rotating frame (in the spinning frame, of course, it's not acceleration at all, but "gravity"). It's always directed toward the center, which means that its direction rotates as the torus does. That means that the transformations between the two frames aren't quite so simple, and accounts for the difference between spinward and poleward motion that daver points out.

[Pi Man]

Oh. Ok.

[newt]

Pi Man said:

But, to you, you would be jumping straight up in the air(toward the axis of rotation anyway) and land in the same spot you jumped, and everything is hunky-dory. And then you consider a completely different situation.

Pi Man, if you jump, you'll travel prograde; you won't land in the same spot.

An article you may find interesting:

http://www.spacefuture.com/pr/archiv..._gravity.shtml

Cheers. Newt.

[one edit due brain fart]

[Pi Man]

Thanks newt. Very cool, and answers most of my questulubs!

(Woops! Brain fart! ops: ) :wink:

[AstroSmurf]

Rotating FOR's are weird - as long as you don't move up and down too much, everything is hunky-dory (to borrow a word), but if you do, everything starts to go wonky.

So, if we ever get rotating space stations, I suspect newcomers would need some time to adjust.

[Grey]

So, if we ever get rotating space stations, I suspect newcomers would need some time to adjust.

Indeed. The best way to minimize these effects is to increase the radius which reduces the angular velocity if you keep the apparent gravity constant.

[Pi Man]

By then, almost everybody will have taken a vacation to a tourist attraction on the moon, so gravity adjustment might not be such a big deal.

[kilopi]

Pi Man, if you jump, you'll travel prograde; you won't land in the same spot.

Isn't that exactly what Pi Man's illustrations show?

[Pi Man]

Um... Well... Sort of. I thought that if you jumped up in the air (toward the axis of rotation) you would land on the same spot on the floor, but by then, the floor will have moved(spun) to another spot. So, I thought that if you jumped, you would land on the same spot as far as your frame of reference was concerned.

[AstroSmurf]

Um... Well... Sort of. I thought that if you jumped up in the air (toward the axis of rotation) you would land on the same spot on the floor, but by then, the floor will have moved(spun) to another spot. So, I thought that if you jumped, you would land on the same spot as far as your frame of reference was concerned.

To borrow Larry Niven's terminology, you will actually land spinward of the point you jumped from. That's my interpretation anyhow.

[kilopi]

you will actually land spinward of the point you jumped from. That's my interpretation anyhow.

Or, as newt said, prograde.

But, that's what Pi Man's illustrations show.

[Pi Man]

My illustrations show that you would land on the same spot on the floor, from your perspective, but the floor will have moved. So, you will land on the same spot on the floor but in a different place in space from the perspective of a non-rotating frame of reference.

[AstroSmurf]

My illustrations show that you would land on the same spot on the floor, from your perspective, but the floor will have moved. So, you will land on the same spot on the floor but in a different place in space from the perspective of a non-rotating frame of reference.

No, my point was that you'd land in a different spot, both in the rotating and the non-rotating frames of reference. Not sure, haven't done the math. At any rate, in the rotating frame you won't go straight up-and-down but move in the direction of rotation at the same time as well.

[kilopi]

No, my point was that you'd land in a different spot, both in the rotating and the non-rotating frames of reference. Not sure, haven't done the math. At any rate, in the rotating frame you won't go straight up-and-down but move in the direction of rotation at the same time as well.

Well, sure, nothing is exact. But to first approximation, Pi Man's illustrations show what would happen. A person would have to jump pretty high before the difference would be noticeable, if the rotating frame were large enough to be realistic.

Conceivably, it could be small enough that one's head would be at the center of rotation--but that would play hob with your equilibrium.

[AstroSmurf]

Well, sure, nothing is exact. But to first approximation, Pi Man's illustrations show what would happen. A person would have to jump pretty high before the difference would be noticeable, if the rotating frame were large enough to be realistic.

Conceivably, it could be small enough that one's head would be at the center of rotation--but that would play hob with your equilibrium.

It would do that anyway; you'd be weightless for the entirety of the jump, so there wouldn't be any special change in the center. But then, the same goes for jumping under gravity; it's just the motion your body describes that's different.

[kilopi]

It would do that anyway; you'd be weightless for the entirety of the jump, so there wouldn't be any special change in the center. But then, the same goes for jumping under gravity; it's just the motion your body describes that's different.

Yep. When you jump, you're in "freefall". But I meant your equilibrium as you spun around the center--your feet would be experiencing normal gravity, your head would not, in a small radius rotation. But that's not really what we're talking about in Pi Man's example

Why do you think the motion your body would describe would be so different?

[AstroSmurf]

To avoid further pointless discussions about what it would look like, I ran a quick simulation using Povray

This is a simple bouncing ball, perfect elasticity and so forth; I haven't made any special assumptions about simulated gravity, but it's a 12-meter-radius cylinder and the ball moves about 2 m upwards each bounce, which takes it 60 degrees around the center of rotation.

The reason for the weird trajectory, put simply, is this:
- The floor has constant angular velocity around the center of rotation. However, the direction of the actual direction it's moving changes.
- The ball follows a straight-line path, but since the distance from the center of rotation varies, its angular velocity will change.

[BlueAnodizeAl]

I was posting some replies to a thread the other day when I got to thinking about centrifigul, centripital, inertial, and gravitational forces. My question is going to be hard to explain, but(hopefully) worth it.

consider the following situation. You are in a large torrus shaped, man made craft someplace in the universe where the gravity is negligable. The craft is rotating to simulate gravity.

cross-section:
Code:

<------ Direction of rotation
___________
/ \
/ \
/ \
| |
| |
| O o|-<| <-----you
| |
| |
\ /
\ /
\___________/
--------->



Certainly, you will experience inertial forces, which, according to GR, are equivelant to gravity. So, you feel like you're standing on the floor and being pulled down by gravity, and everything is hunky-dory(did I spell that right?) Then you jump.

Code:

and land here
___________
/ + \
/ \ \
/ \ \
| \ |
| \ |
| O \| <-----boing
| |
| |
\ /
\ /
\___________/
-----> Direction of rotation


To the outside observer, you would be traveling in a stratght line. But, to you, you would be jumping straight up in the air(toward the axis of rotation anyway) and land in the same spot you jumped, and everything is hunky-dory. And then you consider a completely different situation.
Code:

<------ Direction of rotation
___________
/ \
/ \
/ \
| |
| |
| O |
| |
| |
\ o|-< /
\ /
\___________/


Now you are stationary(relative to the frame of reference where the axis of rotation is stationary, but where the frame of reference is not rotating with the space craft) and floating, weightless in space. You would not feel any gravity from the rotation of the craft because the gravity (inertail force) comes from the changing of your state of motion.

Now, my question is: "what would the explanation for this be from the perspective of somebody else (person B) standing on the inside of the craft, feeling the inertial force?" Would that person B be valid in saying that you are somehow in orbit? Any other explanation I can think of would require that there be a way to show, via a physical experiment, weather you were experiencing inertial forces or a gravitational field, which violates the central principal of GR!. However, the "in orbit" explination wouldn't work either.

Please give me some meaningful feedback on this! It's keeping me up at night! It's the reason why I'm a computer geek/junkie! I'm suffering severe psycological dammage because of it! PLEASE!!!! YOU MUST HELP ME!!!

*Disclaimer: I know gravity and inertial "forces" are not actually forces, but, in lack of a better word, your stuck with the word forces.

It's all two dimensional vector physics, I don't have time right now to answer this as it is complex, but if I remember tonight I'll put together some numbers to explain this tonight. If you use Physics I reletive vectors you should get a nice neat little mathematical model of this.

*Edited for grammer and spelling.

[newt]

Hope this doesn't prolong the "pointless discussion" (are there any?) :wink: but I do not agree with kilopi's contention that one will land in the same spot (regardless of perspective) or that one is in freefall. As I understand it, it's a matter of tangential velocity at different radii from the axis of rotation. You jump up; the velocity you had when standing is in excess of that you would have had had you started at the radius of the height you reach at the top of your jump, and you travel further than the spot on the floor you jumped from, in the timeframe of your jump (different tangential velocities, same angular velocity).
In the same context, if you drop something from over your head, it will land in a retrograde direction. Cheers. Newt

P.S. Future sage wisdom: If you're going to hurl, face "West". You'll keep your shoes clean.

[Kizarvexis]

Wouldn't all this depend on the speed of rotation? I mean we are on a rotating spheriod right now, but when I jump up, I land in the same place. Does being on the inside rather than the outside make a difference? Would being in a 10 meter rotating cylinder be different than being on Babylon 5 (O'Neil type station) where the diameter is around 1 mile?

Kizarvexis
And if some person with good graphic skills could make an animation of this, that would really be cool for those of us having a hard time visualizing this.

[kilopi]

Why would you not agree that when you jump up (so that you're not touching floor, wall, ground, etc.), you're in freefall? Are you making some claim about air friction or something?

[AstroSmurf]

I do not agree with kilopi's contention that one will land in the same spot (regardless of perspective) or that one is in freefall. As I understand it, it's a matter of tangential velocity at different radii from the axis of rotation. You jump up; the velocity you had when standing is in excess of that you would have had had you started at the radius of the height you reach at the top of your jump, and you travel further than the spot on the floor you jumped from, in the timeframe of your jump (different tangential velocities, same angular velocity).
In the same context, if you drop something from over your head, it will land in a retrograde direction. Cheers. Newt

Slight correction: freefall is the same as moving in a straight line (no perceivable difference to the moving guy), but otherwise you're right. Note that my simulation isn't directly analogous to a jumping guy; the ball jumps slightly "backwards" too, in order to keep bouncing in the same spot. If it had moved straight upwards, it would have landed "in front of" the spot it started from. However, to check what really happens to a jumping guy, you need to check lots of stuff like jump impulse, angular "spin" of the jumper and so forth. Povray is not a physics engine - I simply projected a ball moving in a straight line into a rotating frame.

Kizarvexis: This isn't dependant on the speed of rotation at all; slower rotation or smaller radius simply means slower "jump time", lower simulated gravity and so forth.
(edited to correct for stupid orientation mistake)

[AstroSmurf]

I ran two more scenarios. Both have been adjusted to match what you'd actually see, in that initial "horizontal" speed is what's required to maintain "orbit" around the center of rotation. Yellow balls are in a non-rotating frame of reference; red ones in a rotating frame.

[kilopi]

Are the yellow balls showing a strong acceleration to the right, or a deceleration to the left?

[AstroSmurf]

Neither - they move in straight lines with constant speed (look closely). The apparent deceleration/acceleration of the red balls is due to the rotation of the frame of reference. The images don't show this perfectly since they are 3d images and perspective distorts the view somewhat.

If viewed from a non-rotating frame of reference, the spacestation is rotating clockwise in the pictures. The yellow balls show how the ball would move from this viewpoint - simple, straight lines.

If viewed from a rotating frame of reference, the station doesn't move at all, but the balls describe trajectories very different from what you'd see on the earth or with a constantly accelerating frame.

Note that the equivalence of gravity and acceleration holds only if both magnitude and direction is constant. For a rotating FOR, the direction keeps changing, so things behave differently.

[kilopi]

Neither - they move in straight lines with constant speed (look closely).

They appear to be a lot more closely spaced at the end--is that air friction, or a 3d effect? In either case, it would seem to be exaggerated. What is the vertical scale?

[AstroSmurf]

They appear to be a lot more closely spaced at the end--is that air friction, or a 3d effect? In either case, it would seem to be exaggerated. What is the vertical scale?

It's a 3d effect. Radius of cylinder is 10 m, so the ball is quite a bit further away at the end.
Falling ball sample: Starting 1.5 m above "floor", which is eye level of observer.Ball starts falling 4 m away, finishes 10 m away (guesstimate).
Povray source code, partial:

#declare Radius = 10; // Station inner radius
#declare Height = 1.5; // Height at start of fall
#declare Ratio = (Radius-Height)/Radius;
#declare Angle = degrees(acos(Ratio)); // Rotation speed of station
#declare Speed = acos(Ratio)*(Radius-Height); // "orbital" speed at start of fall

#declare Count = 0;
#while (Count <= 1.1)
	sphere { <0,-Radius+1.5,0> 0.05 pigment { Yellow } // Non-rotating FOR
		translate <0,0,Count*Speed>
	}
	sphere { <0,-Radius+1.5,0> 0.05 pigment { Red } // Rotating FOR
		translate <0,0,Count*Speed>
		rotate Angle*Count*x // Back-rotation to simulate rotating FOR
	}
	#declare Count = Count + 0.1; // Determines how many "ticks" to show
#end

Note that both the speed and angular movement are constant. The angular movement was calculated to show the entire fall trajectory in the image - anything goes, really, but I had to pick a value. Note that the trajectory starts out vertically, but coriolis effects become more pronounced the longer the ball falls.

[Grey]

Wouldn't all this depend on the speed of rotation? I mean we are on a rotating spheriod right now, but when I jump up, I land in the same place.

It depends on the radius of the object spinning. In fact, when you jump up here on earth, you'll land in a slightly different location, but it's a small enough difference that you wouldn't ever notice it. If you make your space station really big (rotating slowly to keep the effective "gravity" at 1g), these effects would be minimized.