# 123: Centrifugal Force

Centrifugal Force |

Title text: You spin me right round baby, right round, in a manner depriving me of an inertial reference frame. Baby. |

## Explanation

Black Hat has strapped James Bond to a centrifuge and claims the centrifugal force will be lethal. Bond objects that there is no such thing, but just centripetal force. This is a common misconception among science teachers which is addressed in the explanation below:

Thorough explanation of centripetal and centrifugal forces |
---|

Newton's famous second law of motion states that the net force acting on a body is equal to its mass times its acceleration (if its mass is constant). The law is a vector law, however, so both force and acceleration are vector quantities. (Vectors have not only a size but a direction, and are usually represented as arrows.) Acceleration is defined as the rate of change of velocity with respect to time, where velocity is a vector. Therefore, whenever the length of the velocity vector (known as the speed) changes or the direction changes, there must be an acceleration, and therefore a net force.
Now, consider a body moving in a circle at a uniform speed. Although the length of the velocity vector is uniform, it is constantly changing direction. This means that there must be an acceleration and therefore a net force on the body. It turns out that the acceleration and force are both pointing The sun exerts an inward gravitational force on the Earth to keep it moving in its near-uniform near-circular motion. Another example of a centripetal force is as follows: if you were to hold one end of a string whose other end is attached to a ball, and then swung the ball around over your head, you would be supplying the inward force to keep the ball moving in its circle. Now, Newton's first law states that an object at rest will stay at rest and an object in uniform linear motion will stay in its motion unless acted on by a nonzero net force. Any frame of reference for which this is the case is termed an But what if you are rotating with respect to an inertial frame? We know from experience (having been in a car as it has rounded a turn, or any similar turning motion) that objects at rest do The term "fictitious" implies that it does not really exist, and therefore zealous science teachers can go out of their way to claim that they are not real. But, since James Bond is rotating with respect to Black Hat and any other stationary onlookers (who are all in an essentially inertial frame; see the parenthesized paragraph below), he will experience a real centrifugal force. As the centrifuge rotates faster, the centripetal force needed increases, therefore the centrifugal force he feels increases, and eventually the force will crush and kill him. (The observing frame is not technically inertial either, as it is on a planet which is rotating and revolving about a star which is moving non-inertially. The resulting pseudo-forces are very, very minor, however, and can only be detected by more sensitive instruments [e.g. a Foucault pendulum].) |

The thorough explanation above is summarized as follows:

- 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 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".

## Transcript

- [James Bond is strapped to a giant wheel suspended from the ceiling. Black hat is standing next to two levers.]
- Black hat: How do you like my centrifuge, mister Bond? When I throw this lever, you will feel centrifugal force crush every bone in your body.
- [Same scene, but a closer shot.]
- Bond: You mean centripetal force. There's no such thing as centrifugal force.
- Black hat: A laughable claim, mister Bond, perpetuated by overzealous teachers of science. Simply construct Newton's laws in a rotating system and you will see a centrifugal force term appear as plain as day.
- [Closer shot, only Bond's head is visible.]
- Bond: Come now, do you really expect me to do coordinate substitution in my head while strapped to a centrifuge?
- Black hat: No, mister Bond. I expect you to die.

**add a comment!**⋅

**add a topic (use sparingly)!**⋅

**refresh comments!**

# Discussion

Are you allowed to describe a force acting upon you when you are in an accelerating reference frame? I'm pretty sure you're not. The explanation says that from bond's point of view, he is at rest. Well, sort of. If you're in an accelerating car you can tell that you're not at rest because your inertia seems to be "pulling" you backwards. There's nothing actually pulling you, though. 108.162.219.202 05:24, 30 December 2013 (UTC)

- According to general relativity, that inertial "pull" is indistinguishable from being at rest with a force being applied. In the rotating frame, this apparent force is the centrifugal force. 199.27.128.62 05:58, 4 February 2014 (UTC)
- the explanation is correct, and you can describe forces acting on you in non-inertial frames. If you take Bond to be the origin of a rotating frame of reference then the position of Bond will be (0,0,0) at all times. So in that frame of reference, Bond is at rest (not "sort of at rest, really at rest). The equation of motion for Bond is

F + Fe + Fw + Fc = ma = 0

- (F is external force, Fe is the force due to angular acceleration of the frame (relative to some inertial frame), Fw is centrifugal force and Fc is coriolis force )
- Since the sum of the three "fictious" force are nonzero, and Bond is at rest in this frame, the force F must also be non-zero. This force F is the inward push of the centrifuge. In the moving car example, you can't tell if you are accelerating or if there is a massive graviational field pulling you backwards. From your perspective the experience is identical. If you take this idea and run with it you get general relavitity141.101.70.67 11:30, 6 August 2014 (UTC)

- I believe the OP is referencing the vestibular system. This is what allows humans to feel acceleration. The actual physics at hand is regarding reference frames, not the ability of the body to detect acceleration. In regards to the question of "Are you allowed to describe a force acting upon you when you are in an accelerating reference frame?", the answer is yes. You can pick whichever reference frame you wish, but we tend to pick the one that simplifies the calculations the most.Flewk (talk) 06:44, 25 December 2015 (UTC)

"Apparent force" is the best term to use to describe centrifugal force, and could be inserted in the text to clarify. 172.68.142.89 21:14, 14 June 2018 (UTC)

- "The surface of the Earth approximates an inertial frame."

This isn't correct at all. If you're standing on Earth, you're experiencing an acceleration of 9.8 m/s^2. 108.162.238.11 00:56, 12 April 2018 (UTC)

- Actually, that is incorrect. Right now i'm in my desk chair, not accelerating. The force of gravity is cancelled out by the force my chair exerts on me to maintain this status quo. You're correct that it's not an inertial frame, but that is because the
*force*of gravity, not some*acceleration*141.101.77.20 12 - 14, 6 July 2018 (UTC)

It's NOT appropriate that lazy science teachers "lie to children" in that and various other ways. The kids can understand far more than the teachers assume, so that their choices of limitation are self-fulfilling prophecy, producing ignorant victims of the public school system. — Kazvorpal (talk) 01:39, 21 September 2019 (UTC)