But if you’re talking about a non-rotating frame of reference, why would you state that “you’ve got a constant acceleration, towards the center of the space station”? This statement definitely tells me that the person is trying to convey the perspective of the dude on the space station. If you were talking about the non-rotating reference, wouldn’t you say “the floor must exert a constant acceleration…”?
Saying that you’ve got a constant acceleration towards the center is like saying that here on Earth we have a constant acceleration up.
CurtC, floors do not exert acceleration; they exert FORCE. Objects, such as the dude on the space station, simply accelerate – and from our frame of reference, they accelerate toward the center of rotation. They do so because they are acted on by a force that is exerted by the floor.
No, erislover, we do NOT have an acceleration up. We have an acceleration DOWN – more accurately, we have an acceleration toward the center of the Earth, caused by gravity. If we did not have such an acceleration, we would be flying away from the Earth.
The reason that people on the surface of the Earth experience similar phenomena as people inside a rotating cylinder in space is because of gravity. Gravity acts not only on our bodies, but on the fluids in our bodies, and on the objects around us; it also anchors us to the outside of a rotating object, but it’s imperative to understand that the rotational mechanics of the Earth are virtually insignificant compared to its gravity. OTOH, the gravity of a space station is insignificant compared to its rotational mechanics.
I’m sorry, but I am missing why there isn’t a pseudo-accelleration upwards to counter gravity. There is a force acting on a mass. In the case of an orbiting mass I can see why there would only need to be one component of force/accelleration as the object is truly continuously falling, but an object like a ball on the ground isn’t continuously falling, it isn’t in orbit, and it feels a force upwards, directly countering the force of gravity. Maybe I just need a better explanation, Nametag.
The reason I say that is because to maintain uniform circular motion in the face of a gravitational accelleration of 9.8 m/s/s, our tangential velocity would need to be much larger than it is (as I understand it).
No, I’m still about, antechinus. I forgot about this thread, and wandered of to GQ to find more interesting things to discuss. So, ok you guys win. My brain hurts now, and i’m going to go put ice on it But i still submit there is a real force acting to push you outward from the center from a certain frame of reference. At least a couple posters agreed with me on that point. I admit some confusion on my part as to direction of acceleration, which seems counterintuitive at times. Too bad we can’t draw vector diagrams at each other here. That might help clear things up.
Actually, a person standing on the surface of the Earth is accelerating upwards… But it’s probably best if you pretend I didn’t say that ;). Isn’t GR fun?
But yes, from a certain frame of reference, there is a force pulling you away from the center. I might nitpick calling it a “real” force (forces like that are usually referred to as “fictitious forces”), but it’s certainly a valid and measureable force, if that’s what you meant.
But perhaps a linear example would be simpler. Suppose you’re in a rocket ship in deep space, and the ship is firing its engines. You’re standing on the “floor” of the ship, on the end towards the engines. The ship, and everything in it, is accelerating in the direction of the nose of the ship. But to you, inside the ship, it feels like there’s a force pointing towards the tail of the ship. So, acceleration (with reference to inertial frame) is noseward, apparent force (in the inside-the-ship frame) is tailward. It’s the same sort of situation in the rotating space station.
Earth’s rotational speed at the equator is 464.2 m/s. The formula for undergoing uniform circular motion given accelleration or velocity is given here: http://mcasco.com/p1cmot.html
|a| = |v|[sup]2[/sup]/r
The mean radius of the earth is 6.371 x 10[sup]6[/sup]m. We know the only accelleration in question (by Nametag’s hypothesis) is gravity’s, causing approximately 9.8 m/s/s. This means, to travel uniformly in a circle, we would need to have a tangential velocity of 7.901 x 10[sup]3[/sup]m/s.
We don’t have such a velocity, we already know that our velocity is 464.2 m/s. So, err… I know if I’m wrong I must sound like an idiot, but I don’t understand the issue so please, school me.
You seem to have misapplied the formula you gave at the beginning. the formula is correct and solves for “centripetal” acceleration, given angular velocity, v and radius, r. (Don’t shout at me for using "centripetal, it’s convenient in this case). The result, according to my trusty scientific calculator, is a slight outward acceleration of approximately 3.38 x 10^2 m/s/s. This is tiny in comparison to the acceleration due to gravity, so we can comfortably ignore it in most cases.
I think you and I have different definitions of “tiny”. An accelleration of 338 m/s/s seems damn big compared to 9.8 m/s/s. Dunno about you tho, it is all relative!
I do not think that formula is for angular velocity, whose units are radians/s. The units would not work out if this was the case.
If we solve for what the net accelleration must be to keep us on the ground, it is
|v|[sup]2[/sup]/r = 464.2[sup]2[/sup]/6.371x10[sup]6[/sup] = 33.82x10[sup]-3[/sup]m/s. Which varies from your result by a tiny factor of 10[sup]-4[/sup]. (Of course, you could have just forgot the little minus sign, but that isn’t as funny.)
This number is not some “slight outward accelleration”, it is the net centripetal accelleration necessary to maintain circular motion given our velocity. If gravity’s accelleration into the sphere is 9.8m/s/s, and the net accelleration necessary for circular motion is the answer I gave (and you gave, but seem to have misunderstood), then there you have it: upward accelleration of that difference. Or, there I have it. Or something.
Damnit, someone validate me! The more I talk, the more right I convince myself I am. If I am tumbling headlong to stupidity I’d like it to stop before someone gets hurt.
Erislover, do you truly not understand the difference between acceleration and force? Gravity is a FORCE. Gravity is NOT ACCELERATION. The acceleration DUE TO Earth’s gravity is 9.8 m/s[sup]2[/sup], and we see that acceleration when AND ONLY WHEN there are NO OTHER FORCES acting on the object in question, and ONLY in a non-inertial frame of reference that is stationary with respect to a point on Earth’s surface. If there are other forces acting on the object, then gravity is only a component of the force vector, and CONTRIBUTES (not “is”) only a component of the acceleration vector. There IS, however, another force acting on most objects, the force exerted by the Earth itself, equal and opposite to the force that we exert on it. When viewed in a non-inertial frame of reference stationary with respect to a point on the Earth’s surface, this force is exactly equal and opposite to the force of gravity, and objects on the Earth’s surface are not accelerating with respect to that frame of reference. When viewed in an INERTIAL frame of reference that is stationary with respect to the Earth’s center of rotation, this force is slightly less than, but still opposite to, the force of gravity, and there is a net CENTRIPETAL acceleration – that is, DOWN.
NOTHING on Earth’s surface EVER accelerates UPWARD without an additional force being applied to it. You can refer to the acceleration COMPONENT contributed by the upward force “an upward acceleration” if you want to, but if there’s no motion upward, then calling it that is wrong.
Suppose I’m standing on the deck of a rotating space station holding a tennis ball. Further suppose I throw the ball against the direction of rotation at precisely the speed of the rotation. Would the ball seem to be weightless (at least until it comes in contact with a bulkhead)?
**First half:**What an extraordinarily dishonest quote, erislover. If you’re going to chop out the part of my post that answers the question you’re needlessly asking, it’s polite and ethical to use an ellipsis (…) to indicate the missing portion. In this case, that’s
You do see, don’t you, that a person standing on the Earth’s surface is stationary in such a frame of reference? That a stationary person, by definition, is not accelerating? That there is therefore no net force? That all forces are balanced, which is to say equal and opposite? That that idiotic “we’d all fly off” comment is the result of taking a statement regarding a non-inertial frame of reference, and applying it to an inertial one? That if the force the Earth exerts weren’t equal and opposite to the one we’re exerting on the Earth, we’d either be moving the Earth or sinking into it?
Second half: Your original statement was that there was an acceleration upward, which is manifestly false: the only acceleration is downward. There is, however, less acceleration downward than would be imparted by gravity. You appear to think this is the same thing – it isn’t. I will concede, though, that you are less ignorant of physics than you are of English.
As for the GR (General Relativity) comment, GR treats gravity as a fictitious force, in exactly the same manner as the centrifugal force. So to Einstein, the reason we can walk around on the surface of the Earth is that the Earth is accelerating upwards against our feet, not because it’s pulling down on us. It’s the guy in free fall who isn’t accelerating. Just don’t ask how it’s possible that a person who’s constantly accelerating can nonetheless stay in the same place.
And Ranger, if you thow a ball against the rotation, it will indeed be in free fall, but it won’t look like that to you, since you’re not in free fall. To you, it’ll look much like a thrown ball would on Earth: It’ll keep going until it hits a wall or the floor. If it moves a significant amount vertically, though, it won’t look like a ball thrown on Earth: You can do weird things like throwing a ball in a loop, if you throw it nearly straight up. In the rotating frame, this is explained by the Coriolis force, another “fictitious” force like the centrifugal force.
But i still submit there is a real force acting to push you outward from the center from a certain frame of reference. At least a couple posters agreed with me on that point. I admit some confusion on my part as to direction of acceleration, which seems counterintuitive at times. Too bad we can’t draw vector diagrams at each other here. That might help clear things up.
The more I talk, the more right I convince myself I am. If I am tumbling headlong to stupidity I’d like it to stop before someone gets hurt.