Physics Question (for book)

[TromboneAl]

My main character is on a rotating spaceship. He is hanging on to the inner ring, as in this diagram:

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The space between the inner and outer rings is empty.

He let's go when at the six o'clock position. Here's what I figure:

1. He'll be flung off along a tangent to his travel (green), but because the ship is still rotating, it will seem to him as if he falls along the blue arrow, directly away from the center of rotation. He will land at the point which was "below" him.

2. His speed does not increase as he gets further away from the center. If he were to climb down a ladder his perceived "weight" would increase, but as he falls he doesn't touch anything.

But something's not adding up for me. If he stood on the outer ring he'd "weigh" more, but as I have it above, he wouldn't hit with any additional force, because he isn't accelerating.

Where have I gone wrong?

Thanks,

Al

 

[jjquantz]

Actually, he won't land "directly below his starting point" due to the Coriolis effect, but I'm too tired tonight to figure out the details of his apparent trajectory. If the details are really important it would be necessary to know the dimensions and rotational velocity of the spaceship in order to figure out the landing location.

You are right about the impact speed compared to the "apparent weight." The apparent weight is magnitude of the force that the ladder (or floor) needs to push on him in order to keep him moving in a circle. This will increase as his distance from the center of rotation increases. Once he's in motion, however, he will continue at that speed until something causes him to stop (thank you Sir Isaac Newton).

 

[RobbieB]

It's the classic slingshot.

It's space so there are no significant gravity forces.

He will feel the centripetal force keeping him attached to the center ring. At release he will feel nothing and will continue on the velocity vector at release and finally impact on the outer ring some time later

 

[Texas Proud]

Just my thinking... am not an engineer etc....


From what I read, he is letting go when he is pointing at the 6 position.... if so, I think he will fly along your blue line... IOW, I do not think that he will go off along the green line....

WHY? because the force keeping him in place is his holding on going at the 12 position.... there is no force going toward the 8 position.... think about when you were on a merry go round... when you let go you went straight out, not at an angle....


I think he will continue along the blue but the point that was there will have moved and he will not hit the point he was aiming (if he was aiming).... I also do not think the Coriolis effect would affect the travel he is going since he is in space.... now, if there were an observe standing on the outer ring he would appear to be falling along a curve, but that is observational and not his real motion....


Now let's see if someone who is smart enough can tell me if I am wrong or right!!!

 

[RobbieB]

If he lets go at 6:00 he will continue at 90 degrees (straight) and hit (his hips) about 8:30~8:45. Due to the offset. If he was small and the inner wall was a spindle it would be 9:00. Ninety degrees.

 

[harley]

I think the last answer on this page from Cornell University might fit your question. It sounds like if the guy just lets go he'll spiral around the center, slowly moving outward until he intercepts the outer wall. It's far beyond me to figure out where he would land, but I think you could make it work however you want.

 

[GalaxyBoy]

Here's one sci-if visualization of the problem:

http://youtu.be/HVSlKqOXf2k

 

[TromboneAl]

I think the last answer on this page from Cornell University might fit your question. It sounds like if the guy just lets go he'll spiral around the center, slowly moving outward until he intercepts the outer wall. It's far beyond me to figure out where he would land, but I think you could make it work however you want.

Yes, that last answer is my understanding of it, although I'm figuring that any force from the air is irrelevant.

Here are some real-world death-defying volunteers to help me:

It's a bit more complicated, because there's a wall (the yellow line):

My current thinking is that as he falls, that wall will catch up to him, hit him, and accelerate him. He will slide down along the wall, and end up hitting the outer ring pretty hard.

 

[RobbieB]

Simple slingshot.

Jon Yoder

Assuming there is no gravity when he releases he will continue moving along the tangent at the release point until he hits the wall. Since the wall is moving too at the same velocity he will hit the wall at the same angular distance he was when he released his grip.

 

[Texas Proud]

Yes, that last answer is my understanding of it, although I'm figuring that any force from the air is irrelevant.

Here are some real-world death-defying volunteers to help me:

It's a bit more complicated, because there's a wall (the yellow line):

My current thinking is that as he falls, that wall will catch up to him, hit him, and accelerate him. He will slide down along the wall, and end up hitting the outer ring pretty hard.

Watching that video, it is amazing how many stupid people are out there

 

[stepford]

At the moment of release he is moving horizontally at a velocity of v=omega*r, where r is the radius of the inner ring he'd been holding onto and omega is the rotation rate of the whole system. He will continue to move at this velocity until hitting the outer wall of radius R.

Assuming that r is much smaller than R he has a distance of roughly R to travel before hitting the outer wall. This will happen in time T= R/v = R / (omega*r) by which time the system will have rotated through an angle of theta = omega*T = R/r.

In other words, he will hit the outer wall directly to the left of his release point, but depending on the relative size of the inner and outer rings the station may move through pretty much any angle by the time impact occurs.

That's as much physics as I've done in 3 months and 6 days (but who's counting).

 

[jjquantz]

At the moment of release he is moving horizontally at a velocity of v=omega*r, where r is the radius of the inner ring he'd been holding onto and omega is the rotation rate of the whole system. He will continue to move at this velocity until hitting the outer wall of radius R.

Assuming that r is much smaller than R he has a distance of roughly R to travel before hitting the outer wall. This will happen in time T= R/v = R / (omega*r) by which time the system will have rotated through an angle of theta = omega*T = R/r.

In other words, he will hit the outer wall directly to the left of his release point, but depending on the relative size of the inner and outer rings the station may move through pretty much any angle by the time impact occurs.

That's as much physics as I've done in 3 months and 6 days (but who's counting).

+1 to this solution - if I weren't so lazy this is the approach I would have taken, says the ex-physics teacher.

 

[TromboneAl]

In other words, he will hit the outer wall directly to the left of his release point, but depending on the relative size of the inner and outer rings the station may move through pretty much any angle by the time impact occurs.

That's as much physics as I've done in 3 months and 6 days (but who's counting).

Many thanks.

Based on this thread, here's a rough draft. Reasonable?

I lay on the side of the passageway looking “down” into the cafeteria. I smiled, impressed at how well I’d gotten the hang of microgravity. Pride goeth before a fall. With a tiny push off, I launched myself into the chamber.

Stupid, stupid! The instant I let go, I realized my error, and flailed in an attempt to spin around and grab the lip of the entrance.

Didn’t work.

I drifted toward the far wall. All good, except that as I floated, the side wall of the cafeteria caught up. One of the vending machines nudged into me. I was still moving slowly, and the collision wasn’t bad.

But that machine was accelerating me, pushing me in the direction of the ship’s spin, like a malevolent force laughing at my stupidity.

I grabbed its edge. Too smooth. Too rounded. I tumbled farther toward the outer wall of the cafeteria, accelerating as I fell.

I pushed off toward the center of the room, grabbing for one of the ubiquitous perches. I wrapped my thumb and middle finger around it, but couldn’t hold on. I needed the dinobirds’ claws. Or their wings.

Floating free, I looked down between my feet at the approaching far wall.

Impact in three, two, one … bang! Both feet hit a drink machine, and my knees smashed up into my chest. Oof! Rolling off, I ended up wedged between two machines, each the size of a refrigerator. Now I weighed maybe 200 to 300 pounds, as if wearing an unreasonably heavy backpack.
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[HFWR]

I can't even spell fizzicks!