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From classical physics we know that the acceleration of the center of mass of an object is zero if there is no external forces.

Can someone tell me what's wrong with this counter example:

Counter example: imagine a cat in a box in space with frictionless surfaces so that there is no external forces on it. Now consider the cat at a moment in time where its eyes are open, then the center of mass of the cat (or the box and the cat) is at some point in space at that moment. A moment later the cat blinks, thus its center of mass has moved. But there was no external forces!

(We can always imagine that the cat does some motion which will make the center of mass move)

Imagine the cat raising its leg instead of blinking since that caused trouble to you. Then surely the center of mass moves!

Can someone tell me what's wrong with my counter example?

Edit: since the box is frictionless and thus can't move, and we always can move the center of mass of the cat if the cat could make any movement. Then I think the only solution is that the cat can't make any movement even just a little blink, it will freeze somehow if there was no friction in the box that she can use to move.

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  • $\begingroup$ Would it be reasonable to solve the paradox to say that the cat can't move in any way that it's center of mass will change? Meaning the cat will stay still and won't be able to breathe even so that the center of mass will not accelerate? $\endgroup$
    – 00100
    Commented Jul 14, 2021 at 20:48
  • $\begingroup$ "the cat blinks, thus its center of mass has moved" This is not correct. How come you are assuming this to be true? In which direction would you expect the centre of mass to move? $\endgroup$
    – Steeven
    Commented Jul 14, 2021 at 21:10
  • $\begingroup$ We can imagine an imaginary cat with its eyelash in a position and with certain mass and certain movement such that the center of mass changes. It's obvious that we can make it do some movement that will change the center of mass. What is not obvious is that if she can do such movements. $\endgroup$
    – 00100
    Commented Jul 14, 2021 at 21:12
  • $\begingroup$ I know it's impossible by the laws of physics. I'm just asking if such cat can break those laws. What will stop a cat from blinking in space in such a way that the laws break? $\endgroup$
    – 00100
    Commented Jul 14, 2021 at 21:15
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    $\begingroup$ Maybe the downvotes are just an expression of the combination of frustration about you ignorance of basic physics combined with how you ask your question and reply to comments? $\endgroup$
    – Oбжорoв
    Commented Jul 15, 2021 at 6:46

2 Answers 2

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When the cat closes its eyelids, not just the eyelids but its whole body moves in a way that the center of mass does not move.

Imagine a person in space holding some mass in the fist of his stretched hand.
If this person now folds this hand, not only the hand will move towards the body, but the body will also move towards the fist.

This will happen because the arm muscles will pull the fist, and the fist in turn will pull the arm (and the body) with the same force. The result is a net movement of both the fist and the rest of the body such that the center of mass of the person doesn't move.

Same is true for the cat. The eyelashes will be pulled down, and they in turn, will pull the body up.

Still easier example to imagine is a person pulling a piece of mass using a rope. In every case, the center of mass will not move.

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  • $\begingroup$ That's sounds reasonable although have no idea how to verify it's true. $\endgroup$
    – 00100
    Commented Jul 14, 2021 at 21:47
  • $\begingroup$ On a smooth surface tie a rope to a heavy object (perhaps half your weight). Then hold the the other end of the rope and give a hard quick pull to the rope. If the surface is really smooth, you'll see that not only the object moves towards you, but you will also move towards the object. (...while I think of a better experiment). $\endgroup$
    – manisar
    Commented Jul 14, 2021 at 21:50
  • $\begingroup$ Ok, the above experiment is much better doable on two boats in water - one with the object and the other with the person pulling the object. $\endgroup$
    – manisar
    Commented Jul 14, 2021 at 21:52
  • $\begingroup$ topendsports.com/biomechanics/center-of-gravity.htm so such movements by athletes that change center of mass are impossible in the absence of external forces $\endgroup$
    – 00100
    Commented Jul 15, 2021 at 14:18
  • $\begingroup$ Yes, but though moving the COM of a body or system is not possible in the absence of external forces, orienting the body (parts of system) in different ways around the COM is definitely possible. See how astronauts can move parts of their body, but not the body as a whole - reddit.com/r/space/comments/77y7cc/astronaut_stuck_in_midair. Here, there is some movement of COM, because of the presence of air, and exhalation by the astronaut without which it would not be possible to move at all. Summary - you move one part, another part will move to compensate and keep the COM fixed! $\endgroup$
    – manisar
    Commented Jul 15, 2021 at 16:20
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The center of mass of the cat does not move. I know this by conservation of momentum.

You can attack that argument as "circular"; however, at this point, the burden is on you to show that the C-o-M moves.

It may be difficult to do that with a mere blink. You may want to start out with a one dimensional cat of length $L$ and mass $M$, with two masses $m$ (the eyelids) connected by a spring $k$, the contraction/expansion of which represents blinking.

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  • $\begingroup$ My argument is as follows: imagine a cat that blinks in empty space where there is no external forces on it. I claim the center of mass will change, since we can imagine a cat with enough heavey eyelash so that when the cat blinks the center of mass will change. Also, the cat will always be able to do that movement, since it's a result of a chemical reaction that is independent of the situation the cat is in. $\endgroup$
    – 00100
    Commented Jul 14, 2021 at 20:58
  • $\begingroup$ @00100 Right, I get that. Now model it as suggested. Make the spring "ideal" (massless, no damping), and leave the 2 $m$'s oscillating. Track the COM. Make the eye-lid masses different, if need be. Do whatever you need to to make the COM move. Good luck. $\endgroup$
    – JEB
    Commented Jul 15, 2021 at 14:27

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