# Would a ball bounced in a centrifuge return to the floor?

In other words, does the centrifugal force inside a centrifuge only work to simulate gravity when an object is "attached" to the reference frame inside the centrifuge?

1G at sea level is normally about 9.8 m/s^2, correct?

However Centrifugal Force is different than Gravity.

If you were to jump straight up in a centrifuge, would you move laterally when you landed? Would you land at all, or continue flying straight up until you hit the other side of the centrifuge?

(Spoiler:)

Another example, the broken window inside the giant centrifuge at the end of Interstellar:

(a thrown baseball should be affected by the same forces as a bouncy ball bounced against the floor, correct? Either continuing flight path with 9.8 m/s^2 downward acceleration, or not)

If a window, suspended above the floor of a centrifuge, were broken, would the pieces fall to the floor of the centrifuge, as with gravity, or continue on a relative velocity to the centrifuge?

Your intuition is correct. So-called centrifugal force is a product of mass and acceleration in a rotating frame. If you're in a centrifuge, and you let go of the rotating frame, you're no longer accelerated radially, but merely keep the momentum imparted onto you by it and your own force as you let go of it.

If this centrifuge was setup in zero gravity, like e.g. space wheels, if you jumped, then your trajectory would be a product of both the direction of your jump (your vertical component), as well as direction of the frame's rotation at the point you let go of it (your horizontal component). But, unless something acts on you while in air so the product of both these velocities you're now a subject to change its magnitude (either accelerate or decelerate you, like, say, air within the space wheel co-rotating with it), you're now in constant motion, i.e. no longer accelerating, so no simulated gravity by constant acceleration.

Let's illustrate this a bit; If we say that you jumped at the same speed that the wheel rotates and towards its center of rotation, you'd jump at a 45° angle to your normal and the same angle towards the center of rotation. Since the rotating frame moved while you were in the middle of the air, you might land at the same spot you jumped from, which would seem a bit spooky, but that's the fun of rotating frames. This perceived effect on your motion once you let go of the rotating frame even has a name: Coriolis effect:

This image is from Wikipedia and might not be the best to illustrate the point since it shows an object falling in a rotating frame away from the center of rotation, so here's a couple of animations from a film taken during cosmonaut training in Star City centrifuge system in the 60's (to my knowledge still the largest centrifuge that actually hosted people during experiments, even though Americans built some larger ones that were never really used):

Better example, but tells only half of the story of jumping from the rotating frame towards the center of rotation, since it doesn't also include return path back to the rotating frame. And this centrifuge was built on the Earth with additional vertical component of Earth's gravity, so it wouldn't be the best example anyway. I think I'll rather let you imagine how this would look like in zero gravity, but try to first guess in which direction the centrifuge on the last two animations rotates (hint: not the one you'd think).

• This makes me curious: Would the air inside a massive centrifuge (the kind you see housing millions of people in sci-fi movies) simply become a wind tunnel compared to the ground/people? Objects on the ground would have plenty of friction to keep them moving but the air seems like it would just turn into a tumbling mass of extreme turbulence moving a significant fraction of the speed that the centrifuge is rotating. – thanby Aug 10 '15 at 5:16
• @thanby It's making me dizzy! Friction would slow down all turbulence, shear with respect to the outer wall, and local rotation (vorticity) fairly quickly, and the air would stabilize into a single, rotating atmosphere without any wind in the rotating frame of the cylinder. The Coriolis force is happening in the images because something that was at rest in the rotating frame is being suddenly thrown. – uhoh Jan 8 '17 at 6:38
• @thanby Yup, the oft-pictured huge rotating cylinder has major air movement problems and is not a viable habitat. – Loren Pechtel Mar 24 '17 at 2:47

The short answer is that when you throw a ball in a centrifuge in space, it travels in a straight line until it hits something. It experiences no pseudo gravity and effectively is not experiencing any acceleration.

The problem is simplified somewhat by evacuating the air so it's a vacuum. Lets say the surface of the centrifuge is moving at 50km/h, you're standing on the surface, and you can throw a ball at 50km/h.

First you drop the ball - simply releasing it from your hand. The ball will fly forward in a straight line at 50km/h, you are also moving at 50km/h, but will be pushed up by the surface of the centrifuge. This will create the visual illusion the ball is falling even though it's actually you being pushed up.

Next you throw it backwards at 50km/h so it has zero net velocity. What happens? The ball stays right where it is when you threw it, hanging in space with no force acting on it. If you stay standing where you are on the surface of the centrifuge, next revolution you will smack into the ball at 50km/h. From your perspective, it will look like the ball flies away from you at 50km/h, flies around the centrifuge, then smacks you in the head - even though it was actually just hanging in space. This is where a centrifuge deviates most absurdly from actual gravity, in a rotating cylinder, the illusion of gravity is caused by the object moving in a straight line until it intercepts the floor (which is curving up), an object with zero net velocity will simply hang there as the floor of the cylinder spins under it.

So if you throw the ball at 50km/h in the direction of motion, then it will travel in a straight line at 100km/h and smack into the surface of the centrifuge due to the curvature of the cylinder. The trajectory is actually no different to throwing the ball at 100km/h in a non-rotating cylinder, in both cases the ball will travel in a straight line, getting closer and closer to the floor, until it hits it. The apparent trajectory is not a parabola, as it would be with gravity, but instead a segment of a circle, which can however be a good approximation for a parabola for small angles.

When you add air, you get air resistance which will act to generally slow the ball, and air will be swept along with the surface of the centrifuge, effectively making a wind that will carry things with it. Air pressure will tend to push less buoyant objects to the surface of the centrifuge, and lighter than air objects to the center.

Exactly whether you can throw an object across the centrifuge to the other side (or "around the world"), depends on being able to overcome the velocity of the surface of the centrifuge. If the surface was moving at 100km/h, then a ball thrown at 50km/h will always fly ahead in a straight line and smack into the floor. The larger and faster the centrifuge, the more closely it will emulate gravity.

• In the vacuum scenario, would not simply holding the ball be imparting your own momentum to it, so that when released it would continue on that same vector (parallel to your own at the exact moment of release) and appear to curve down and hit the floor, not complete a revolution in the same place? – thanby Aug 10 '15 at 5:13
• @thanby that's exactly right. In the first scenario, the ball is thrown against the direction of motion so that it ends up with 0 velocity. If the ball is merely dropped, it will indeed fly forward at 50km/h and hit the surface of the centrifuge as it curves up. The point of the 0 velocity experiment, is to demonstrate that there is indeed no acceleration acting on the ball - it will simply stay where it is, while the centrifuge revolves around it. – Blake Walsh Aug 10 '15 at 9:58
• @bdsl Whether the centrifuge is a spinning disk or cylinder, in a vacuum it will only impart force to things in direct, physical contact. When not in a vacuum, it can impart force indirectly via air or fluid which is set in motion by the surface. This is about real forces experienced by the object - not apparent forces caused by a rotating frame of reference. – Blake Walsh Aug 10 '15 at 10:32
• But centrifugal and coriolis forces are fictional forces. They aren't created by any object acting on another object, they are created by using a rotating reference frame. The frame isn't a physical object, its just a system of coordinates that we use to describe the position of things. – bdsl Aug 10 '15 at 10:36
• @uhoh ... and that's why we assume a vacuum and spherical cows. – Blake Walsh Jan 8 '17 at 17:07

The centrifugal force is a product of your frame of reference. Not a product of what you are or are not attached to. So it would not disappear simply because you no longer are in contact with the ground.

However, if you are in a reference frame with centrifugal forces you are also in a reference frame with coriolis forces. This pseudo force is proportional with your velocity relative to the frame of reference.

The consequences of this is that when you leave the floor where and if you return depends on your velocity. - However you don't actually have to leave the floor for this force to be noticable. If you start travelling against the spin of the cylinder the coriolis force would start to counteract the centrifugal force. When you travel at the same speed as the cylinders rotation. This means that you would be moving at the same veocity as the center of the cylinder from the perspective of an inertial reference frame. At this point the coriolis force and the centrifugal force presisely counteracts, and you would be left floating along the surface of the cylinder.

• Whoever downvoted the answer probably just didn't understand it, because as far as I can see it's not wrong and I think an analysis in terms of a rotating frame of reference is useful. But you should be more explicit that centrifugal and Coriolis forces are fictitious or pseudo forces. – Blake Walsh Aug 10 '15 at 17:32
• @BlakeWalsh I haven't voted yet, can you help clarify? I think a "reference frame" is a mathematical tool, not a place you can be. If you are physically rotating continuously about a point that is not your personal center of mass, there is a force making it happen. It could be the floor, it could be the gravity of a central mass (you'd be in orbit) but you can just happen to be in a continuously rotating frame (fixed rotational velocity $\omega$) which is rotating about a point far from your personal center of mass. – uhoh Jan 8 '17 at 6:40
• @uhoh I think the phrasing is indeed a little off and "in" should be "using" but I think it's more a problem with the expression than the concept. Can a human or projectile be "subject" to centrifugal or coriolis force? Strictly speaking probably not, but otoh it'd be experientially "real enough" for people living in a rotating cylinder that maybe there isn't much point stressing the fictitiousness. – Blake Walsh Jan 8 '17 at 13:23

To simplify the explanation, let's imaging you are standing on the inside surface of a large rotating drum in space. If you jump straight "up" (toward the center of rotation), you will have a velocity vector which will be the sum of your original motion along the circumference plus the "inward" motion you gave yourself by jumping. Excluding the effects of friction with an internal atmosphere, you will continue to travel in a straight line along this new vector (at uniform velocity). This path will be a chord line intersecting the drum at two points, one of which is the point of your "lift-off", the other will be your inevitable "landing" back on the drum surface.