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 ?