Astronaut in Space With a Spinning Gyroscope

[georgir]

Conservation of angular momentum, exactly. You can only spin some part of you while spinning another part the other way. The cat can flop around all it wants but all it will achieve is look silly.
Just like you spinning your arms, unless you got a loose joint at your shoulder and can do a complete 360 revolution (actually it will require a completely cut off and detached skin and flesh, yuck), you'll end up in exactly the same position and orientation you started.
[actually, the blood flowing through us meatbags makes my statement wrong, and maybe that can be abused for turning in space, i don't know. but the math for a simple solid (flexible, but nowhere detached) object is easy and categorical, no net turning is possible]

 

[A.T.]

This is in fact completely wrong, the cat would not be able to turn in a vacuum,

Because it would be dead in vacuum, right?

But seriously, you are in fact completely wrong. Air is not needed for this maneuver. It's all about conservation of angular momentum. That's why they investigated this as part of the space program, and trained astronauts wearing space suits for the space walks.

See this paper:
http://pentagono.uniandes.edu.co/~j...inicursoJK-Uniandes/robotic examples/kane.pdf

More pictures from the study:
http://www.theatlantic.com/video/index/244829/can-an-astronaut-move-like-a-falling-cat/

Related lecture at MIT (at 20:30):
http://techtv.mit.edu/collections/l...cle-smarts-stability-translation-and-rotation

unless it rotated its internal organs or something.

Because only internal organs have rotational inertia, or what?

 

[rcgldr]

Conservation of angular momentum, exactly. You can only spin some part of you while spinning another part the other way.

but that is good enough to end up facing some other orientation after you stop spinning one part of your body. As mentioned, imagine spinning your arms in near vertical circles so when viewed from the side, your arms rotate clockwise, and your body rotates counter clockwise, when you stop whirling your arms, you end up facing in a different direction. You can bend at the waist and swivel your legs to rotate about your body's main vertical axis. So absent any external forces, you can change your orientation, but you can not move your center of mass in any linear direction.

 

[georgir]

you're all not getting it. your arm can not do a complete 360 degree turn unless it is detached or it twists and winds up more and more at your shoulder. you do a rotation, but you undo it as you untwist your shoulder.

a simpler case is an astronaut holding a heavy object. he can stretch his arms further away or pull them closer, changing the distance of that object from the center of gravity and thus axis of rotation. a layman can think that rotating the object with stretched arms and unrotating it with arms pulled close nets an overall rotation but in reality, the rest of your body is also pulled and pushed farther and closer to the axis of rotation, so it balances out - every time you unrotate the object, you unrotate the rest of your body and return to exactly the original orientation, no matter how stretched your arms are. the only way to beat that is to let go of the object and grab it in a new place, so it has done a full rotation that does not need to be undone.

 

[Dale]

you're all not getting it. your arm can not do a complete 360 degree turn unless it is detached or it twists and winds up more and more at your shoulder. you do a rotation, but you undo it as you untwist your shoulder.

No, you are not getting it. This is well established in the space program and there is even training and studies on executing these maneuvers in emergency situations:
http://mvl.mit.edu/MVLpubs/MVL_09.03_StirlingNewmanWillcox.pdf

First, there are many 360º rotations that you can do. For example, stick your arms straight out along the axis from left shoulder to right shoulder, then rotate them along a conical surface inclined say 20º from the shoulder axis. You can do that motion. Second, in many cases you do not even need to do a complete 360º rotation because you can change your moment of inertia. If you do 180º rotation of some joint with a high moment of inertia posture and then change to a low moment of inertia posture and do a -180º rotation rotation of that same joint then you will change your angular position.

 

[A.T.]

your arm can not do a complete 360 degree turn unless it is detached or it twists and winds up more and more at your shoulder. you do a rotation, but you undo it as you untwist your shoulder.

If that's how your shoulder joints work then you should have them checked. Most people can certainly swing their arms 360° in the sagittal plane continuously, without introducing torsion that needs untwisting. If you do this while floating in space, the rest of the body will counter rotate in the sagittal plane. For other rotation axes see the video of the astronaut here at 25:00:
http://techtv.mit.edu/collections/l...cle-smarts-stability-translation-and-rotation

Here is a video of a cat flipping around in only ~0.3sec. It should be obvious that this cannot be achieved with aerodynamic forces, unless you have vary large surface area limbs (like a bird wing).

https://www.youtube.com/watch?v=RHhXbOhK_hs

 

[aeroseek]

The flipping cat example is considered solved: before the internet Physicists would argue for hours over the concept - but it is clear to me the rule is: you can twist anyway you want but you can't move your centre of mass.

About the man in the box or let's put the cat in a box, and the box on a trolley with frictionless wheels (magnetic bearings?)

Then what?

 

[A.T.]

you're all not getting it. your arm can not do a complete 360 degree turn unless it is detached or it twists and winds up more and more at your shoulder. you do a rotation, but you undo it as you untwist your shoulder.

I think your confusion comes from the wrong idea that angular momentum requires rotation. That is not the case. Even a linearly moving object has angular momentum w.r.t. to any point, that is not on the objects path. If an object moves on a circular path, then it has angular momentum, even if it doesn't change it's own orientation.

If you swing your arms around, you don't twist them, and your thumb always points where your head is. But each part of the arm moves in circles around the left-right-axis, so the arms have angular momentum. And the rest of the body has equal but opposite angular momentum.

 

[jbriggs444]

The flipping cat example is considered solved: before the internet Physicists would argue for hours over the concept - but it is clear to me the rule is: you can twist anyway you want but you can't move your centre of mass.

About the man in the box or let's put the cat in a box, and the box on a trolley with frictionless wheels (magnetic bearings?)

Then what?

One assumes that the trolley+cat+box starts out motionless and that not only are the wheels frictionless but that all other external net forces (wind resistance, etc) are also zero. One also assumes that the cat can't "jump" the box so that it moves from its starting position relative to the trolley. One assumes that the cat cannot get out of the box.

Let m be the mass of the cat. Let M be the mass of the trolley+box. Let w be the size of the box in the direction of the tracks.

Given the assumptions about frictionlessness, there are no external forces on the system. No net acceleration of the center of mass. Given the assumption about starting at rest, the center of mass of the cat+box+trolley system has a fixed position. It will not move.

Given the assumption about the box not moving relative to the trolley and the cat not being able to get out of the box, the center of mass of the box+cat+trolley system is constrained to a finite region of size $\frac{w m}{M}$ relative to the trolley.

Accordingly, the trolley cannot move more than $\frac{w m}{M}$ from its starting point in this scenario. It can move that far if the cat moves from one end of the box to the other.

 

[jbriggs444]

If the trolley is positioned on tracks that curve back and forth, a side to side "skating" method of propulsion might be possible.

edit: Not just back and forth curves. And "skating" is not the only mode that can work.

 

[A.T.]

One also assumes that the cat can't "jump" the box so that it moves from its starting position relative to the trolley.

And if you glue the box to the trolley, then you also have to rule out that the cat can jump the entire trolley, or even lift one axis to rotate it. Otherwise it might do something like this:

https://www.youtube.com/watch?v=m_6NGjXujxQ

 

[rcgldr]

If the trolley is positioned on tracks that curve back and forth, a side to side "skating" method of propulsion might be possible.

That would involve an external force. By moving the center of mass within the box, a side to side force is exerted onto the curved track, which would respond with both side and forward forces (assuming angled part of track), allowing the box to be propelled.

edit: Not just back and forth curves. And "skating" is not the only mode that can work.

And if you glue the box to the trolley, then you also have to rule out that the cat can jump the entire trolley, or even lift one axis to rotate it. Otherwise it might do something like this: video of tic tacs

Lifting one axis is only needed because the wheels can't pivot far enough. With split or free line or drift skates (different names for the same thing, like a skateboard cut into two and using inline skate wheels), or a snake board / street board (like a skateboard hinged in the middel or with both ends that can pivot), there is no need to lift the wheel(s). In the case of a skateboard once sufficient speed is achieved, the tic tac like method of propulsion can be peformed without lifting the wheels off the pavement. For the initial start, the rider leans to one side, exerting a side force onto the wheels, which exert a side force onto the pavement, and the pavement exerts an opposing side force onto the wheels, accelerating the rider and skateboard in the direction of lean. Note that the pavement is exerting an external force on the rider and skateboard, which allows them to accelerate. Then the skateboard is turned into the direction of velocity acquired by that acceleration, in the case of the video, lifting of the front wheels is done so the skate board can rotate more quickly and freely. (and technically the skateboard is turned a bit past the direction of velocity so that the next lean produces a component of acceleration in the desired (forward) direction). The process is then repeated, leaning to one side or the other (relative to the skateboards new orientation). At sufficient speed instead of leaning to generate side forces at the wheels, the rider can just twist side to side generating a torque onto the skateboard while weaving and steering the skateboard out of phase so that side forces on the wheels continue to propel the skateboard forward.

 

[Dale]

About the man in the box or let's put the cat in a box, and the box on a trolley with frictionless wheels (magnetic bearings?)

Look at the forces and torques that can can be supported. The trolley can support torques along all 3 axes and forces along the vertical and left-right axes, but not along the forward-backward axis.

 

[A.T.]

Lifting one axis is only needed because the wheels can't pivot far enough.

It's not clear what kind of wheel steering aeroseek's trolley allows, so I assumed none. I also assumed that "friction-less wheels" means that they still have lateral resistance, just no rolling resistance.