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Why is the statement, that centrifugal force as a pseudo force does not obey Newton's third law (action = reaction) ?

Lets say I'm within a rotation g cage in space, then I feel weight right the same way I would be on Earth. The centrifugal force tends to pull me "down" , but the floor responds with a "reaction" , keeping me at rest with regard to the cage.

Isn't the situation very similar to the situation at earth, where I'm attracted by gravitation instead of a pseudo force? Nobody would identify gravitation as a pseudo force, however, from the equivalence principle bot are the same and cannot be distinguished.

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    $\begingroup$ In your second paragraph, I think the force pair to the normal force is the force your body exerts back on the centrifuge, and not the centrifugal force. Force pairs are found between two different objects. The centrifugal force and normal force on your body and just two forces acting on 1 object. However, I think you found a good way of doing experimental physics. For instance, how would one measure inertial forces (I prefer to use the word 'inertial force' as opposed to pseudo force)? Probably in the way you are thinking about here $\endgroup$ – DWade64 May 14 '18 at 12:58
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    $\begingroup$ Then the force which pulls me "down" on the centrifuge (and which gives me a feeling of weight) is not the centrifugal force? What else then? $\endgroup$ – michael May 14 '18 at 13:06
  • $\begingroup$ What's tricky here is that the normal force is inherently a reaction force. It's only present when something causes it to be present. But I agree. In the rotating reference frame, there is definitely a centrifugal force pushing down and a normal force pushing up. These forces happen to be equal and opposite. They wouldn't be considered 3rd law force pairs. But then again, they way you are thinking about it (experimentally and practically), I don't think there is a problem with that. It's probably useful to think that way. Actually I probably would. It's easier to consider pseudo forces $\endgroup$ – DWade64 May 14 '18 at 13:20
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    $\begingroup$ when there is no normal/tension/contact forces present. For instance, consider an accelerating bus. A block is in the middle of the aisle. As the bus accelerates, the block slides back. Until the block hits the back of the bus, there is nothing stopping the pseudoforce. It's only when it hits the wall does the normal force give an equal/opposite force to the pseudoforce $\endgroup$ – DWade64 May 14 '18 at 13:21
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    $\begingroup$ "Why do pseudo forces not obey Newton's third law?" Because it doesn't exist. You can make up any random force that doesn't follow the laws of nature. $\endgroup$ – Steeven May 14 '18 at 13:36
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The centrifugal force tends to pull me "down" , but the floor responds with a "reaction" , keeping me at rest with regard to the cage.

A number of ways to test if two forces are not an action-reaction pair:

  • Do the two forces act on two different bodies? Here, the body in both cases is question is you: The upward force on you by the floor versus downward force on you be the fictitious centrifugal force. These are not an action / reaction pair.

  • Are the forces always equal but opposite? Suppose you try to jump. The normal force will increase, but the centrifugal force remains the same. These are not an action / reaction pair.

  • Does the action / reaction pair result from the same interaction? In this case, one of the forces is the normal force while the other is the fictitious centrifugal force. Once again, these are not an action / reaction pair.

There is a reaction to the floor pushing you up via the normal force, and that is you pushing the floor down via the normal force. You can see this in action (not recommended) by washing a load of jeans and T-shirts. After the water drains but before the spin cycle starts, rearrange the contents so the jeans are on one side and the T-shorts on the other. The unbalanced nature of the reaction can make the washing machine bounce around, perhaps even walk.

What about the reaction to the centrifugal force? There is none. The fictitious centrifugal force is the odd force out. It cannot be paired with some other force. More importantly, what centrifugal force? An inertial observer sees only one force acting on you, the normal force exerted by the floor. There is no centrifugal force. It's a fiction, designed so that we can conveniently use Newton's first two laws of motion in a domain where, strictly speaking, those laws does not apply.

Isn't the situation very similar to the situation at earth, where I'm attracted by gravitation instead of a pseudo force? Nobody would identify gravitation as a pseudo force, however, from the equivalence principle bot are the same and cannot be distinguished.

In general relativity, gravitation is indeed a pseudo force. In Newtonian mechanics, it is a real force. The Newtonian reaction to gravity pulling you down is you pulling the Earth up gravitationally.

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