Pouring tea in a plane - upside down

Let me start with the video. Here is a guy flying a plane in a barrel roll and pouring some tea at the same time. Talk about multitasking.

How can he pour upside down? Well, there are two ways to look at this. First, I can look at this in the frame of the plane. For this case, I can invoke the fake force - centrifugal force. Oh yes, I am going to do it. You probably remember all your physics instructors warning you to never ever do this. Well, they say that because they are afraid you will do something bad with it. Here, I will only use the centrifugal force for good.

What is the centrifugal force? Well, suppose I am in a rotating frame and I want to pretend that it is not rotating. To do this, I will need to come up with some fake forces to account for the behavior of objects in this frame. A fake force is one that is not based on fundamental interactions (most forces you see are electromagnetic forces and some are the gravitational force). Here are some previous posts about fake forces if you are still interested.

• Fake vs. real forces
• Why are fake forces very useful (sometimes)
• Centripetal force, centrifugal force - what is the difference?
• When is the centrifugal force the same as the centripetal force?
• Origins of the words "centrifugal" and "centripetal"

So, I am in the frame of reference of the aircraft. The aircraft is doing a barrel roll - meaning that it is moving both forward and in a circle perpendicular to the main direction of motion. The center of this circle is outside of the plane. First (to make sure we agree on the situation) here is a diagram of the plane doing the maneuver.

Note: I am not a pilot except for in Microsoft Flight simulator - in that I landed a 747 on a tiny runway. Ok - back to the aircraft. Let me draw the interior at say the instance where it is sideways.

Here the "F-net" force is the net apparent force in this frame. So the red ball would kind of fall if released. At the top, as long as the fake centrifugal force is greater than the gravitational force, the ball will "fall" up. The magnitude of the centrifugal force would be:

It is important to note that the "v" in this expression is the velocity as it moves around the circle - not the total or forward velocity.

Now on to the other way to look at this problem - from outside the aircraft. In both the frame inside the aircraft and outside, there must be an agreement about the motion of the ball (or "free falling tea"). Here is a quick video of a vpython simulation. A couple of notes:

• The red ring represents the aircraft (you are looking at it "head on")
• The blue ball is some object in the aircraft.
• For the first part of the barrel roll, the ball is being supported by something - maybe it is Harry Potter with his invisible cloak on.
• After that time, the ball is released. Notice that the path of the ball after that point is parabolic.

Ok, now you can watch the simulation (sorry for the poor quality - I will have to work on that)

So, from the outside, after the ball is released, it moves towards the "floor" of the plane which happens to be in the up-ish direction.

One final note (but is it ever really 'final'?) This is very similar to one of my all time favorite demos - the water on the serving tray suspended by a string.