# Astronaut rotates in space without external torque

1. Jan 31, 2012

### perky

Imagine an astronaut in free space. He (or she) has zero angular or linear momentum with respect to a fixed intertial frame of an outside observer.

The astronaut is intially standing up (sic) with his arms by his sides and his legs together, with zero degree offset between the top half of his torso and his bottom half. He twists 90 degrees, his bottom half torso moves clockwise and the top half anticlockwise. While he's in the 90 degree offset position he raises his arms, and then twists back. Because the top half now has larger moment of interta it won't turn back as much as the bottom half. When he's back in the zero degree offset position he lowers his arms and he's back to his intitial starting position, except he has now rotated a little as measured by the observer.

Imagine we could construct a machine to do that, very quickly and with very small changes each time. In reality the net angular momentum of course is zero, the 'other half' always has equal and opposite angular momentum to the first half. However because the machine always resets itself back to its original position the external observer could measure an average angular momentum that appears to come from nowhere without having applied an external torque.

This implies to me that we need to know exactly what is going on deep inside a system, even on the atomic or even sub-atomic level, before we can be sure our macrosopic measurements have any meaning at all.

Last edited: Jan 31, 2012
2. Jan 31, 2012

### D H

Staff Emeritus
This is how cat's manage to land on their feet.

You don't need to know what's happening deep down to model this. The falling cat problem is a well-studied problem. Some reading:

TR Kane and MP Scher, A dynamical explanation of the falling cat phenomenon, Int'l J. Solids and Structures (1969)
http://pentagono.uniandes.edu.co/~j...inicursoJK-Uniandes/robotic examples/kane.pdf

R Montgomery, Gauge theory of the falling cat, Fields Inst. Commun., 1 (1993), 193-218.
http:://web.mit.edu/shawest/Public/Papers/cat_gauge_theory.PDF [Broken]

R Littlejohn and M Reinsch, Gauge fields in the separation of rotations and internal motions in the n-body problem, Rev. Mod. Phys. 69 (1997), 213â€“276
ftp://www.phy.pku.edu.cn/pub/Books/...20of%20internal%20motions%20in%20the%20N-.pdf

Last edited by a moderator: May 5, 2017
3. Feb 1, 2012

### perky

Thanks, interesting post (although mathematically a bit beyond me!)

Take the falling cat scenario. Imagine if a box of negligable mass were to surround the cat in a way that it orientates itself to the cat, e.g. lots of elastic strings connecting the cat to the walls of the box which try to minimize their stored energies by changing the position of the box, and we were unable to see inside the box. We can measure the mass of the box/cat system (which would be just the mass of the cat if the box has negligable mass). When the box is dropped it would appear to rotate but with no external torque applied. We actually do need to model the contents of the box to explain it, a simplistic model of the box being a fixed mass won't do. The same could be said of any object in space, unless we can model what's inside the object our measurements or assumptions of angular momentum conservation may not be accurate.