Rotating Space Station: Exploring Centrifugal Force

[radonballoon]

Ok, so I'm having trouble imagining why a "centrifugal force" would exist for a rotating space station. As I understand it if there was only vacuum inside the station then anyone inside it would not move toward the "floor" (outer wall), so I can only imagine that it would be the air inside the station pushing everyone outwards. If this is the case, would there be much force at all acting on anyone inside?

Also this is similar to a question I have for a rotating bucket of water. Is gravity required in the first place for the water to stay in the bucket if swung vertically?

 

[darkSun]

A centrifugal force would exist inside the space station, for the same reason that it exists inside a car taking a turn. The inertia of the people inside would resist the centripetal force provided by the floor of the space station as makes them rotate with the station.

If the air would experience the centrifugal force, why wouldn't the people?

Also, gravity is not required for the water to stay in the bucket--the experiment is usually done to show that the laws of gravity are presumably "violated".

The same thing would happen without gravity, even if it was swung slowly--the only force on the water would be centripetal (or centrifugal from its point of view), and it would just continue to stay in the bucket.

 

[radonballoon]

The people inside the car feel the force of the turn only because they are attached to the car in some way (in this case by gravity/seatbelts), the people in the space station would be floating before the station spun, they would not be attached in any way to the station. The air in the space station would be attached in a way to the walls due to the fact that they expand to fill the volume. If I'm wrong in any way feel free to tell me, but I'm not seeing any way for them to feel the force of rotation.

I don't mean that gravity is required to keep it in the bucket, I'm wondering if gravity is needed at the very beginning before rotating it in order for water to stay in it while rotating (to provide some sort of starting velocity if you will).

 

[radonballoon]

Ok thinking about it some more, I think I understand. Obviously if someone was floating nothing would happen, but if he then collided with one of the walls he would be accelerated in the direction they were moving, and then this happens again and again until he is moving with the same speed as the wall. And I guess the same would apply to the water in a bucket..no gravity necessarily needed.

 

[russ_watters]

Right, so you don't need to wear a seatbelt or be in gravity for a turning car to make you feel a centrifugal force.

You also don't need gravity. As this is a kind of "artificial" gravity, it isn't the same thing as and has no need for a connection to regular gravity.

Also...from your first post, a space station doesn't have a vacuum in it. The people would die...

 

[DeShark]

but if he then collided with one of the walls

What makes him collide with the walls at all? In an inertial reference frame, he would remain at a constant position and velocity (with respect to the space station). If we assume he starts off stationary with respect to the space station (in reality he is traveling in a straight line at the same velocity as a point on the space station), then after a while, he will (from his point of view) start accelerating towards the edge of the space station. This acceleration is caused by the so-called centrifugal force. Does that clear it up any?

 

[Archosaur]

It might be helpful to think about centrifugal force this way.

Anything with mass has inertia, which is the property of matter that resists acceleration. An obvious example is when you slam on the gas and your body feels like it's being pressed against the back of your seat. But, keep in mind that acceleration is the change in velocity over time, and velocity is not just speed, it also includes direction.

When you slam on the gas on a straight strip of freeway, your direction stays the same and your speed changes, so your velocity changes (you accelerate), so the inertia of your body resists that acceleration.

But your speed doesn't have to change at all in order for you to be accelerating. If something is moving at a constant speed, but is constantly changing direction (like the a person at the outer wall of a rotating space station), its velocity is changing. It is accelerating and its inertia resists that acceleration.

Inertia resists acceleration. When you increase your speed, there is a net forward force on your body. Your body feels a force in opposition of that force, like the contact force against a driver's seat.

It's no different when you are revolving. When you move in a circle, there is a net force on your body toward the center of that circle (centripetal force), and your body feels a force in opposition, out away from the circle (centrifugal force).

Centrifugal force is just a product of inertia. Inertia resists all types of acceleration, even when speed is constant.

 

[Dale]

There does not need to be any contact for there to be a centrifugal force. The centrifugal force is an artifact of the non-inertial coordinate system. It is a fictitious force and affects all objects analyzed in the rotating frame.

 

[radonballoon]

I know that it's a pseudo force that arises when you use a non-inertial reference frame. However, say there is nothing but vacuum and a hollow donut if you will, and an object floating in the vacuum inside the donut. The object is not touching the donut, and then it begins to spin. In an inertial reference frame (the particle's for now), there is no force on the particle and therefore it cannot move. It cannot move until it hits a wall, at which time it will begin moving, and then it will keep colliding with walls until it moves with the wall. Once this happens the reference frame of the particle becomes non-inertial and there is then the "Coriolis force" arising from this reference frame. This is all I meant. Contact IS necessary to begin motion.

 

[Archosaur]

I know that it's a pseudo force that arises when you use a non-inertial reference frame. However, say there is nothing but vacuum and a hollow donut if you will, and an object floating in the vacuum inside the donut. The object is not touching the donut, and then it begins to spin. In an inertial reference frame (the particle's for now), there is no force on the particle and therefore it cannot move.

This is correct, but it doesn't describe a "rotating space station"

 

[Dale]

I know that it's a pseudo force that arises when you use a non-inertial reference frame. However, say there is nothing but vacuum and a hollow donut if you will, and an object floating in the vacuum inside the donut. The object is not touching the donut, and then it begins to spin. In an inertial reference frame (the particle's for now), there is no force on the particle and therefore it cannot move. It cannot move until it hits a wall, at which time it will begin moving, and then it will keep colliding with walls until it moves with the wall. Once this happens the reference frame of the particle becomes non-inertial and there is then the "Coriolis force" arising from this reference frame. This is all I meant. Contact IS necessary to begin motion.

No, it is not. Let's say you have two coordinate systems: A is an inertial coordinate system, and B is rotating at an angular velocity of ω≠0 about the z axis of A with all the axes co-located at t=0. If a particle (z≠0) is at rest in A then it must be in motion in B. No force needs to "start" this motion, it is simply a consequence of the transformation between the two coordinate systems. Such a particle will have a velocity in B which is perpendicular to the z axis and proportional to the distance from the z axis. This will result in a Coriolis force which is -2 times the centrifugal force and so the particle will orbit the z axis in B.

 

[DaveC426913]

I have to agree with Radonballoon. He has established initial conditions wherein the occupants are not rotating with the space station; they are floating and stationary wrt an external reference point, such as Earth, and in vacuum.

If they make no contact with the walls, they will not experience artifical gravity. Furthermore, there is no force that will cause them to come into contact with the walls.


The issue here is that RadonBalloon has set up a rather contrived set of initial conditions. To start the occupants at rest (wrt to an external ref point), while inside the station, requires either:
1] spinning the space station up to speed after the occupants are in it, or
2] providing a large window for the occupants to zip into the space station while it's rotating. (of course, if the window were at the axis of rotation, it wouldn't have to be large)

He's right, but it's awfully hard to set up such circumstances. In all practical scenarios, occupants will enter the space station by first making contact with it externally and spinning up to speed, before moving into the SS proper. It's practically unavoidable.

 

[Dale]

I have no problem with the initial conditions. The point of his question is not whether or not the initial conditions are likely but rather to determine what happens given the initial conditions.

The centrifugal force is the force that causes "artificial gravity". It exists for all objects regardless of their motion in the rotating reference frame and is proportional to the distance from the axis of rotation.

What is often forgotten is the Coriolis force. It exists only for objects that are moving in the rotating reference frame (not rotating in the inertial frame), and it can work to counteract the centrifugal force. So an object that is at rest in the inertial frame will be acted on by a Coriolis force that is twice the magnitude of the centrifugal force and points towards the axis of rotation. The combination of the centrifugal force and the Coriolis force is what makes the behavior correct, so that an object at rest in the inertial frame will "orbit" the axis in the rotating frame.

No form of contact is required for either the centrifugal or the Coriolis force, but you have to consider both.

 

[DaveC426913]

I have no problem with the initial conditions. The point of his question is not whether or not the initial conditions are likely but rather to determine what happens given the initial conditions.

The centrifugal force is the force that causes "artificial gravity". It exists for all objects regardless of their motion in the rotating reference frame and is proportional to the distance from the axis of rotation.

What is often forgotten is the Coriolis force. It exists only for objects that are moving in the rotating reference frame (not rotating in the inertial frame), and it can work to counteract the centrifugal force. So an object that is at rest in the inertial frame will be acted on by a Coriolis force that is twice the magnitude of the centrifugal force and points towards the axis of rotation. The combination of the centrifugal force and the Coriolis force is what makes the behavior correct, so that an object at rest in the inertial frame will "orbit" the axis in the rotating frame.

No form of contact is required for either the centrifugal or the Coriolis force, but you have to consider both.

I'm not sure what you're saying here. Are you saying that, if
- the occupants are in their space suits
- floating in the middle of the space station
- with no initial motion wrt to the hub of the SS or to an external ref point
- and the SS is rotating
- and in vacuum
that they would experience a net force outward?

Surely you are not claiming this.

 

[Dale]

Are you saying that, if
- the occupants are in their space suits
- floating in the middle of the space station
- with no initial motion wrt to the hub of the SS or to an external ref point
- and the SS is rotating
- and in vacuum
that they would experience a net force outward?

I assume the "no initial motion" is specified in the inertial frame. If so, then no, they would not experience a net force outward in the rotating reference frame. They would actually experience a net force inward in the rotating reference frame. That net force is the sum of the centrifugal and Coriolis forces, and would cause them to orbit the axis in the rotating frame.

 

[DaveC426913]

I assume the "no initial motion" is specified in the inertial frame. If so, then no, they would not experience a net force outward in the rotating reference frame. They would actually experience a net force inward in the rotating reference frame. That net force is the sum of the centrifugal and Coriolis forces, and would cause them to orbit the axis in the rotating frame.

OK. I see what you're getting at. You're viewing the rotating reference frame as a perfectly valid frame and then examining what forces would cause the occupant to not fall outward.

If the occupant were at rest wrt the rotating frame then he would indeed fall outward. (External viewers would note that the occupant is merely under normal inertial motion parallel with the SS floor under him but headed toward a wall that's sloping up towards him.)


Still, this is pretty abstract. The rotating reference frame gives rise to fictional forces that are very difficult to describe. In fact, the object experiences no forces at all. Even when it encounters the outer wall for whatever reason, it does not experience centrifugal force; it merely experiences the inertia of its tangential acceleration.

I'm pretty sure that you're going to rebutt by saying the the rotating ref frame and its associated forces is indeed, perfectly valid, but I'm not sure it's helping the OP understand the issue.

 

[Dale]

OK. I see what you're getting at. You're viewing the rotating reference frame as a perfectly valid frame and then examining what forces would cause the occupant to not fall outward.

If the occupant were at rest wrt the rotating frame then he would indeed fall outward. (External viewers would note that the occupant is merely under normal inertial motion parallel with the SS floor under him but headed toward a wall that's sloping up towards him.)


Still, this is pretty abstract. The rotating reference frame gives rise to fictional forces that are very difficult to describe. In fact, the object experiences no forces at all. Even when it encounters the outer wall for whatever reason, it does not experience centrifugal force; it merely experiences the inertia of its tangential acceleration.

I'm pretty sure that you're going to rebutt by saying the the rotating ref frame and its associated forces is indeed, perfectly valid, but I'm not sure it's helping the OP understand the issue.

Actually I am not going to rebutt, that is essentially correct. The rotating reference frame is valid, but it is non-inertial. The fictitious forces (centrifugal and Coriolis) are required in order to "fix" Newton's 1st and 2nd laws in the rotating reference frame.

The only part I would object to is the idea that the fictitious forces (centrifugal and Coriolis) are very difficult to describe. They really are pretty straightforward once you are exposed to them, but most introductory courses just skip them entirely so they are confusing the first time. The most common mistake is to forget about the Coriolis force, so once you know not to do that the rest is not too difficult.

 

[Archosaur]

The issue here is that RadonBalloon has set up a rather contrived set of initial conditions. To start the occupants at rest (wrt to an external ref point), while inside the station, requires either:
1] spinning the space station up to speed after the occupants are in it, or
2] providing a large window for the occupants to zip into the space station while it's rotating. (of course, if the window were at the axis of rotation, it wouldn't have to be large)

What about:

3] The occupant is stuck to the "floor" by centrifugal force, but then he starts running in the opposite direction of the space stations spin until he isn't undergoing angular acceleration, so he doesn't "stick" anymore.

 

[Dale]

What about:

3] The occupant is stuck to the "floor" by centrifugal force, but then he starts running in the opposite direction of the space stations spin until he isn't undergoing angular acceleration, so he doesn't "stick" anymore.

Same as above. As he runs that direction the Coriolis force acts in a direction opposite the centrifugal force.