xkcd.WTF!?

Explanation ➲

Black Hat has strapped James Bond to a centrifuge and claims that the centrifugal force will be lethal. Bond objects that there is no such thing, but just centripetal force. The notion of centrifugal force is a common one, as we experience it whenever we turn. Teachers will initially teach Newtonian mechanics in an inertial frame, and in inertial frames, the centrifugal force is zero. Instead, a body that moves in a circle does so because of a centripetal force (acting towards the center of the rotation). This is a reasonable (and correct) view, but it is a subtle point that many students find hard to grasp, as it seems to contradict their personal experience of centrifugal forces. For the sake of exposition, teachers may claim that "There is no such thing as centrifugal force." This, however, is also a misconception, which is addressed in the explanation below:

Observers' point of view (Black Hat, us, etc.)

James Bond is moving in a circle, and is therefore accelerating. The force keeping him there is an inward force of contact against the centrifuge, a centripetal force. Via Newton's third law, since the centrifuge is pushing Bond inward, Bond is pushing the centrifuge outward. The centrifuge's material is strong enough not to break under this force, however.

James Bond's point of view

In James Bond's frame of reference, Bond is at rest. He is kept there by two forces: the above-mentioned inward force of contact against the centrifuge, and an outward centrifugal force. He feels both forces.

As mentioned in the explanation, as the centrifuge rotates faster, the forces needed to keep him in motion get larger, so the force he feels gets larger. This will eventually kill him. The conclusion will be the same regardless of which frame of reference is chosen.

Teachers of mechanics are well aware of this; however, in introductory expositions, these ideas are often not taught. In theoretical mechanics, one describes the positions and velocities of the particles in a model relative to a frame of reference. This means that a time is chosen to be time 0, and positions are chosen to be (0,0,0), (1,0,0), (0,1,0), and (0,0,1). With these chosen, the position and time of any particle in the system can be described. It is an axiom of Newtonian Mechanics that there exist "Inertial Frames." In an inertial frame, a particle will remain at rest or at a constant speed unless acted on by an external force, and Newton's second law takes a simple form: F = ma. The surface of the Earth approximates an inertial frame. In a non-inertial frame, such as one rotating with a giant centrifuge, or moving with an accelerating vehicle, a particle will accelerate, relative to the frame. Newton's second law, when formed in such a frame, is much more complicated, as it has terms for the linear acceleration of the frame, the angular acceleration of the frame, the centrifugal force, and the Coriolis force. These extra terms are sometimes called "fictitious forces," as they result from the choice of the frame of reference. The mathematics required to describe problems in a non-inertial frame is more sophisticated, and all problems may be solved using an inertial frame. Thus is reasonable that teachers at school level "lie to children" and teach the mechanics in inertial frames.

James Bond was almost killed by a centrifuge in Moonraker. The final statement by Black Hat is that said by Auric Goldfinger in Goldfinger in response to James Bond's question "Do you expect me to talk?"

The title text is inspired by Dead or Alive's famous song from 1985, "You Spin Me Round."

Randall feels very strongly that the centrifugal force is a real thing. He links to this comic in the first footnote of his what if? article One-Second Day and the 6th footnote of Earth-Moon Fire Pole, stating that it is a real thing, and that he will go so far as to strap arguers to a centrifuge that he or someone he knows apparently owns. He also cites it in 852: Local g

As can also be seen in the footnote on page 132 in his What If? book, he will even fight you about it. From the book:
"Furthermore, if you're on the equator, you're being flung outward by a centrifugal force¹."
^"1Yes, centrifugal. I will fight you."
(The article itself is about what happens if you lose all your DNA, so it has not much to do with this "real" force... The sentence is just stating that the actual weight loss from losing all your DNA is similar to the weight loss you would experience by moving from the poles to the equator due to this force.)

Black Hat is featured as a Bond villain once again in 2747: Presents for Biologists.