Conservation of angular momentum GIF

Conservation of angular momentum GIF.

https://s3-us-west-1.amazonaws.com/h...r_momentum.gif
https://s3-us-west-1.amazonaws.com/h...r_momentum.gif

How is it working? Physicists, please correct me if I have the wording wrong here:

The man and the wheel essentially act as a closed system. An externally-applied torque (the standing man spinning the wheel by hand) produces vertical angular momentum in the wheel. When the wheel is turned horizontal, the man must spin counter to the wheel's rotation, to conserve angular momentum.

One interesting usage is in spacecraft telescopes. Such spacecraft need to be pointed in a very specific direction. If a spacecraft must be rotated by very small amounts, they can do so with an electric motor attached to a flywheel, called a reaction wheel. When the rotation of the spacecraft changes, the reaction wheel is used to counter-rotate the spacecraft proportionally.

Reaction wheel from Kepler spacecraft:

https://s3-us-west-1.amazonaws.com/h...tion_wheel.jpg

"An externally-applied torque (the standing man spinning the wheel by hand) produces vertical angular momentum in the wheel."

The angular momentum is the scalar moment of inertia of the wheel times the vector angular velocity of the wheel and is thus a vector aligned with the vector direction of the wheel's spin along the axle axis. So when he spins it the angular momentum is horizontal, not vertical.

The seated man is using the bicycle wheel as a reaction wheel to torque himself around exactly as the telescopes (and other satellites) use their reaction wheels to orient themselves.

Reaction wheels produce a smoother motion than control jets and have the advantage that they never run out of fuel as long as the solar paddles can keep charging the batteries.