# 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

In this comic, 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.

Issac Newton was the first to announce that any body will be in a stable state of motion iff (if and only if) no force is applied. No motion at all is a stable state, as is constant translation. Imagine yourself on a bicycle: if you are going fast and do not brake, only the friction of the air, tires and internals of the bike will slow you down if you are not going uphill.

Now ride your bike on a circular track, at considerable speed. You will feel the "centrifugal" force, which is actually a centripetal force that you are applying to leave your straight course. That is what moving along an orbit really is: constantly changing the direction of movement, which needs a constant force.

Black Hat argues that within a spinning inertial system, "centrifugal" force is real. Here is why: to transform equations to a subsystem, everything inherent to the system as a whole must be subtracted, including the centripetal forces, which leaves a centrifugal force on the other side of the equation. Wikipedia hints that while the centripetal force is universal, the centrifugal force is bound to the specific inertial system.

## 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.

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# 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)