How does the astronaut in the following video do what he is doing ? https://youtu.be/7ZPVg3qD07g?t=145

This question is kind of a follow up to Why don't we ever see astronauts on space walks adjusting their orientation by rotating their arms?

I was under the impression that linear motion and rotational motion were analogous with displacement, velocity, acceleration, mass, momentum, force being analogous with angular displacement, angular velocity, angular acceleration, moment of inertia, angular momentum and torque respectively.

We all know that an astronaut in space cannot undergo any linear displacement without having some external force ( the most he can do is throw objects, or gases in one direction and move in opposite direction , but even then the Center of mass of the man + object system will stay right where it was ) . In short, the center of mass should wind up back where it started.

So, how come in case of rotational motion, the astronaut is able to undergo angular displacement without any external torque ? He is facing one way and at the end he has rotated and is facing another way, without there being any external torque during the process. What is the physics i am getting wrong here ? Whatever he does, should he not wind up back where he started ?

  • $\begingroup$ Angular speed or angular displacement doesn't require any torque until angular speed is constant. Only change in angular speed requires torque. $\endgroup$ Apr 23 at 7:10
  • $\begingroup$ @JohnRennie Thanks for that link. I would never have found that question. The question seems to be same as mine, and it goes to the root of the issue much more precisely and eloquently . I will look at the answers, hopefully they will have good answers $\endgroup$ Apr 23 at 7:18
  • $\begingroup$ @VikashKumar I know it does not. My question was WHY it is the case, that linear displacement requires external force, but angular displacement does not require external torque $\endgroup$ Apr 23 at 7:20
  • $\begingroup$ Again, linear displacement or linear velocity doesn't require any force until velocity is constant (both magnitude and direction). External forces requires only when change in velocity is needed. $\endgroup$ Apr 23 at 7:24
  • $\begingroup$ @VikashKumar " External forces requires only when change in velocity is needed " This is not true. External forces are also required when linear displacement (or change in linear/translational position) is needed . However, external torque is not required when " angular displacement " is needed. This difference in linear displacement and angular displacement was the heart of my question $\endgroup$ Apr 23 at 7:27

When the astronaut first begins spinning his arms around he applies force to them to begin their spin. So according to Newton's third law of motion the arms apply an equal and opposite force on his body spinning it in the opposite direction. As long as he keeps rotating his arms in one direction his body keeps rotating in the opposite direction. When he stops rotating his arms the force used to stop their spin causes an equal and opposite force to stop the spin of his body. If he stops spinning his arms when he is facing away from where he was when he started, that is where he will stop. However his center of mass will not have translated except for possibly from some air resistance from the motions.

  • $\begingroup$ I agree with you but how is it physically possible for someone to rotate their arms in the clockwise sense while the rest of the body to rotate in anticlockwise sense? $\endgroup$
    – Möbius
    Apr 23 at 8:37
  • $\begingroup$ @Möbius It is due to conservation of angular momentum . If your arms have angular momentum in one direction, the rest of body will have equal angular momentum in the other direction and hence rotate in the other direction $\endgroup$ Apr 23 at 10:21
  • $\begingroup$ yes I realised that but how is it physically possible because if my body rotates in one direction then my arms will also move in the same direction since my arms are attached to my body right ? $\endgroup$
    – Möbius
    Apr 23 at 12:07
  • $\begingroup$ No actually, the shoulders can rotate quite a bit. Watch him doing it again. $\endgroup$ Apr 23 at 13:08

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