Centrifugal force

Centrifugal force is where gut feeling and formal reasoning appear to clash. In this article I intend to address on one side the way that gut feeling goes awry, and on the other side I want to explain why the formal reasoning proceeds in the way it does.

There is actually a James Bond film in which the villain (or one of his assistents, I don't remember) attempts to kill Mr Bond by cranking up the speed of a pilot training centrifuge. From his stricken position Bond manages to sabotage the controls, and the pilot training centrifuge idles to a halt.

Clearly, it's possible to kill someone who is in the seat of a pilot training centrifuge. If the centrifuge is pulling a lot of G's then the heart cannot keep up blood supply to the brain.

From cause to effect: gravitation

In the case of the Earth's gravity the formal reasoning has three steps. I'll give these steps for me standing up.

1. The Earth exerts a gravitational force upon all objects; the Earth exerts a gravitational force upon me.
2. As a consequence, my feet exert a force upon the floor.
3. As a consequence, the floor exerts a force upon my feet.

When I am standing up the parts of me that are in actual contact with the ground are the soles of my feet. My feet are compressed by the rest of my body pushing down against my feet and the ground pushing up.

Another way of looking at this is to think of the situation when you are standing on a weighing scale. What the weighing scale measures is how hard it is compressed. Your feet are pressing down on the weighing scale, and the ground pushes up against it.

What the pressure receptors in your feet and all through your body sense is the state of compression. The mind automatically translates that experience of compression to sensing a gravitational force. Your gut feeling knows gravity when it senses it.

From cause to effect: centripetal acceleration

In the case of standing up inside the pod of a pilot training centrifuge, pulling G's, the formal reasoning has two steps.

1. The floor exerts a force upon my feet, causing centripetal acceleration.
2. As a consequence of my inertia, my feet exert a force upon the floor. (This force that my feet exert upon the floor is a force in centrifugal direction.)

In this case the formal reasoning has only two steps, and compared to the case of gravity the causal chain is the other way round. Between the case of gravitation and centripetal acceleration there is a reversal of what is identified as cause and what is identified as effect.

In the case of gravitation and in the case of being subject to centripetal acceleration the physical sensation is identical, and you can't stop your mind from automatically translating the experience of compression to sensing a gravitational force. Consciously or subconsciously, when you are in a state of centripetal acceleration your mind automatically supposes a centrifugal force. Specifically: a gravitational force in centrifugal direction that is being exerted upon you.

If you would put a vector representing that "gravitational force" in a diagram, you would attach it to your center of mass. This supposed "gravitational force" in centrifugal direction is in equal measure exerted on every part of you, an exhaustive representation would position an infinity of vectors at each infinitisimal part of you. In general, if that "gravitational force" in centrifugal direction acts upon some object, all of the force can be thought of as acting upon a single point: the object's center of mass. If that object is resting on a floor, the contact patch exerts a force in centrifugal direction upon the floor of the centrifuge pod.

Inertia

There is inertia in the sense of Newton's first law and inertia in the sense of Newton's second law. Authors using the expression 'centrifugal force' sometimes have the first sense in mind, and sometimes the second, and often they shift from one sense to the other without announcing it, which I think they should.

If you are in a pilot training centrifuge, and you drop an object it will proceed to the floor and then hit the floor. Proceeding to the floor is described by Newton's first law: an object on which no force is exerted will move in a straight line. The pod of the pilot training centrifuge moves along a curvilinear path, and thus it intercepts the released object.

If you are in the pod of a pilot training centrifuge, and you are standing on a weighing scale, then inertia in the sense of Newton's second law is at play: a force is required to accelerate you, and the amount of force is proportional to your mass, hence the centrifugal force that you automatically suppose is proportional to your mass.

Formal reasoning

In formal physics reasoning, it's not allowed to refer to inertia as a force. In physics the concept of 'force' is defined as 'a reciprocal interaction between two objects'. Example: electrostatic interaction. Two electrically charged particles, one positive one negative, are in interaction with each other, giving rise to a mutual attractive force. It is very useful to keep the concept of force limited to reciprocal interactions only. Defining force in this way makes it slot in with Newton's third law. (Arguably, Newton's third law provides the very definition of what a force is.)

Inertia involves a single object; it does not have the characteristic of mutualness that typifies a force. It's best to assign inertia to a category of its own.

Putting reversal of cause and effect to use

There are circumstances where it can be useful to opt for thinking with reversed cause and effect. For instance, when you are thinking about the tension in helicopter blades during fast rotation. Then you visualize yourself as co-moving with the helicopter blades, and then you can imagine yourself experiencing a centrifugal force.

It's important, though, to keep thinking in terms of reversed cause and effect in its proper context. For example the case of the pilot training centrifuge. Let's say you are in the control room, and you're watching the machine go around. That is the inertial point of view, and it would be a big mistake to introduce the same reversed cause and effect into the motion with respect to the inertial point of view.

If you are drawing up a diagram that represents a snapshot in time of a system that is rotating, then you have to decide in advance whether you want it to represent an inertial point of view or a co-rotating point of view. Depending on your point of view you are assuming a different rundown from cause to effect.

I often notice a mixup. Some phenomenon is first discussed as seen from a co-rotating point of view, then the author announces a description as seen from an inertial point of view, but he keeps using the centrifugal force that applies only in the context of the co-rotating point of view.

The statement: "centrifugal force only exists in a rotating frame of reference" is another way of saying: "You can reverse cause and effect only in the context of a rotating frame of reference."

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Last time this page was modified: January 23 2010