Can an astronaut rotate herself?

[physicstudent_B]

Homework Statement

An astronaut has been left outside the space station, her back towards the station. The astronaut is not rotating (angular momentum ~ L = 0) and cannot reach anything. Is it possible for the astronaut to rotate herself into facing the space station?

Homework Equations

Conservation of angular momentum

The Attempt at a Solution

I think that the astronaut cannot rotate herself only by moving. So the answer would be no. She could maybe throw something from her backpack (if she has something) to change her angular moment.

 

[gneill]

Do some research on the "Falling Cat Problem"

 

[physicstudent_B]

OK, of course the astronaut is not a rigid body ... so she can rotate herself. Thank you!

 

[haruspex]

Nearly 50 years ago I failed to convince a visiting Russian physicist that this was possible. I was handicapped by being a mere maths undergrad in a slightly off-axis swivel chair and the worse for vodka. The two historians and the lawyer also present were no help.

 

[physicstudent_B]

And there was no Youtube 50 years ago.
(look at 5:45)

 

[mpresic]

Even if the astronaut were a rigid body, he or she could still rotate albeit inefficiently. For example, let the astronaut raised his hands over his (her) head, and consider this the initial orientation. Now if (s)he moved his arm forward, his legs would go backward. When the astronaut moved his arms over his head again, the astronaut would return to the initial orientation. Now if the astronaut moved his arms out to one side, the legs would go to the other side. When the astronaut returned his arms directly over his head, (s)he would again return to the initial orientation.

Now assume the astronaut moved his arms forward so his feet went backward. Now the astronaut moves both arms to one side, and his legs go the the other side. Now the astronaut moves his arms directly over his head again, (in one step; not the two steps (s)he took to get to the side). The astronaut would have his/her arms directly over his head, but (s)he would have rotated. This is because, as is well (should be) known to students of college freshman mechanics, finite rigid body rotations are non-commutative.

As a grad student, I briefly talked to some (other) grad students and they do not buy this argument, but at the same time they could not refute it.

 

[haruspex]

let the astronaut raised his hands over his (her) head,

Bit of a struggle for a rigid body.

 

[mpresic]

to Hauspec, Granted. The astronaut would have to be a collection of coupled (assumed rigid) bodies rigid arms and legs. Maybe the analysis of the falling cat is the best idea.