Centripetal Acceleration/Artificial Gravity

[danielceland]

Hi my name is Daniel and i am very much interested in the many different concepts of physical science.

I have been studying entry level physics at my local university for about 6 months now, however i am looking for a definitive answer to a question i have about centripetal acceleration.

I propose the following,

Imagine a space station (shaped like a big wagon wheel) which spins on a fixed rotational axis about its center, with a particular constant angular velocity. Imagine that this circular motion generated a constant centripetal acceleration towards its center, whereby the occupants inside (positioned on the inner edge of this wheel-like structure) would feel a force equivalent to 9.8m/s^2 (i.e. gravity on earth) pushing them into the inner edge (their 'perceived' floor) of this space station. This force would be exactly the same, at ANY point along the inner circumference.

Spanning the diameter and joining each side, are two corridors (imagine a 2D perfect circle with a cross inside) which intersect at the center of rotation.

My understanding of centripetal acceleration is this -

At the center of rotation you would feel NO acceleration (i.e. turning on the spot), whereas at the outer edge you would feel the maximum acceleration possibly generated by the system.
As you approach the center, i would then imagine that the acceleration you, or I, would feel would get less and less and less until you reach the absolute center. Then it would be zero.

Imagine I am standing stationary inside this station and looking up, through one of these corridors so that i can look through the center and see the other side. Imagine that YOU are standing stationary on the opposite side and can see ME in the same manner.

Phew! Now that I've set the scene i can ask my question!

If I was to throw a tennis ball to you with enough force, could YOU catch that ball without it hitting the walls of the corridor?

I think that it could do two things.

1. As soon as it leaves my hand it is then prone to other forces acting upon it. Therefore it may attempt to curve in some direction and start to bounce off the walls of the corridor.

2. As soon as it leaves my hand it will start to negatively accelerate (i.e. slow down) as it follows the path of the corridor towards the center. If i throw it with JUST ENOUGH force so that it VERY SLOWLY crosses the center of rotation, it will then start to accelerate again so you can catch it.

Which is correct?

 

[danielceland]

I asked my physics professor and he gave me two possible answers. He said that the balls motion is relative to the observer. A second perspective can be taken as if you are looking at the system from the top down.

Later he corrected these with a third answer. He then stated that i would have to throw it at a particular angle so that it would curve into the center.

I am still confused.

Is there a single correct answer or something completely different?

Any thoughts?

 

[danielceland]

By the way this IS NOT a homework question. Please feel free to respond.

 

[Jasongreat]

To start with I am no physicist, just a layman, so I might lead you down the wrong path. It just seems you are wanting to complete a thought you have and since it seems like no one else wants to answer I will atleast help you get a dialogue started.
Where is your force towards the center going to come from? If I understand your scenario, you are expecting, the spinning to force you there, is that correct? If you tied a string to yourself, the centripetal force would be the tension on the string, and if you didnt have the string the pressure your body would exert on the outer wall would be the centripetal force, wouldn't it?

 

[danielceland]

Yes that is correct.

The force is generated from the centripetal acceleration which is generated by the space station rotating at a particular angular velocity.

Think of it like a merry-go-round at a playground.

 

[Jasongreat]

When you throw the ball, since it is not physically attached to anything, would it have any force on it besides your arm strength? What I'm trying to get at is it wouldn't have centipetal force acting on it from the time it left your hand until I grabbed it on the other side. And since you would be moving at a certain speed when you threw the ball, the ball would be also moving at that speed as well, right? The station would be spinning in opposite directions on either side, wouldn't it? Even if we say that it is turning clockwise, on the bottom half it would be right to left, the top half would be left to right, right?

 

[danielceland]

The force that you would experience as 'gravity' on the inside of the circumference is the equal and opposite force (Newton's 3rd Law) of the centripetal acceleration.

As soon as I release the ball with enough force, through the center, i would perceive it to go straight through the corridor to yourself; awaiting it on the other side.

I also thought about the ball starting to curve in the same direction of the rotation and towards the center. But then i thought that it's already rotating when i release it. That's why i would see it go in a straight line relative to my observation point.

Holy crap!

Maybe this should be in the relativity threads instead.

 

[dgOnPhys]

Hi Daniel,

there is no relativistic effect here this is the right thread.

There are two points of view here one can use to solve the problem:
1)an inertial frame
2)a non-inertial rotating frame

In the inertial frame the problem is very simple as soon as you let go of the ball no forces are acting on the ball so it will continue in a straight line, given by the vector composition of (apparent) initial velocity (when you let go of the ball) and the tangential velocity of the station.

In the rotating frame (see http://en.wikipedia.org/wiki/Rotati...tion_between_accelerations_in_the_two_frames") you will see two apparent forces: centrifugal and Coriolis; the first pushes the ball away from the center, the second pushes it sideways, perpendicular to its instant velocity (if you look at the station and the direction of spinning is counterclockwise, the ball will deviate to the right)

Going back to the initial question of getting the ball across it is easier to look at this in the inertial frame:
- if you throw the ball very fast (compared to the tangential velocity of the station) it will basically proceed straight along the corridor initial direction and get to the opposite side of the corridor while the station corridor rotates of a small angle
- if you gradually reduce the initial speed of the ball at some point it will hit the sidewall of the corridor
- not sure what will happen if you throw very slowly... I think in that case you can invoke the equivalence principle and expect the ball to fall back into your hand (like you threw it up straight in the air in a gravitational field)

Hope this helps :)

 

[danielceland]

Yes it does, thank you.

A rotating reference frame...hmmm.
That seems to make me think in quite a different way.

 

[Brin]

I'm a senior Physics student at a university,
I just want to make it clear: Spinning space station, with axis towards the middle would not produce the gravitational force towards the middle you are trying to describe.
I.e. this situation would not be "like gravity" because of the centripetal acceleration. Instead, you'd find yourself plastered to the edge of the wheel due to the centrifugal forces.

Though, in theory you could just stand up and walk on the walls at that point. But you wouldn't be walking down any corridors :)

As you noted, it'd be like a merry-go-round, but note what happens when you're on the merry-go-round: You fly off unless you can hold on!

 

[dgOnPhys]

Hi Brin

you raise a good point, I had just assumed Daniel was using centripetal in place of centrifugal (a common confusion of terms) because he was looking at the rotating station from an inertial frame but re-reading his initial post it is not really clear what he meant by "inner edge". I was thinking of the highly idealized circle with a cross, in that case the inner edge would be the correct one but if one thinks of being inside this space station than the "inner edge" would be on the wrong side.

Up to him to clarify this one

 

[K^2]

The way they tend to explain centripetal/centrifugal forces (two completely different, but related effects) in school physics is absolutely terrible. But then again, it's not entirely trivial to explain in general, so some confusion is to be expected.

And yeah, if you throw a ball on a rotating station "straight up", it will appear to move along a curve, so it won't hit a person standing on the opposite side of the station.

 

[dgOnPhys]

...
And yeah, if you throw a ball on a rotating station "straight up", it will appear to move along a curve, so it won't hit a person standing on the opposite side of the station.

Hi K^2,

the ball will hit the other person if its speed is high enough...

 

[K^2]

Go to inertial frame. In any finite time-of-flight, the station will rotate some finite angle. So you'll never hit the spot you aim at. Yes, you can make the error negligible compared to the size of the target, but I do not believe that is what the OP asked.

 

[dgOnPhys]

Well K^2

if your target is a point you are right but we were playing tennis here ;)

Whichever the interpretation of the initial problem I think we agree