Astronaut in Space With a Spinning Gyroscope

[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.