The video here shows a clear demonstration of conservation of angular momentum. Given the experiment is performed within an isolated system, this is my thoughts:
The spinning bike wheel continues (if no friction) to have the same rotational kinetic energy during the whole experiment. When the guy in the video starts to rotate, the additional rotational kinetic energy must come from the guy, there is no other option, if the total energy must be conserved. The guy uses not only energy to turn the wheel, but also to make himself rotate. Where does the rotational kinetic energy of the guy rotating goes, when he stops the rotation? It dos not convert into new kinetic energy. It dos not convert into potential energy. So it can only be converted into heat, if the total energy must be conserved.
That would mean, that the guy is supposed to use less energy to flip the wheel back again, than he used to flip the wheel the first time in order to conserve energy. Because if he used energy to stop his own rotation, we can’t say that all kinetic rotation energy of the guy on the turntable is turned into heat.
However, the guy spending more energy to flip the wheel the first time, and less energy to flip the wheel the second time seems odd the me. He must still use energy, not only to flip the wheel back again, but also to create the counterforce, that stops the turntable from rotation. All in all it would make sense, if he had to use the same amount of energy every time he flips the wheel no matter what direction, and as a result of that, heat is not produced as an explanation of where the kinetic rotating energy of the guy on the turntable goes, when he stops rotating. The explanation now is that he uses energy to stop his own rotation.
If the spinning bike wheel where rotating in the opposite direction in the beginning of the experiment, he would also have to invest energy in making himself rotate. So why would that be different, when flipping the wheel back again? Energy is used to make the turntable rotate in the opposite direction, which causing the turntable to stop.
If this is true, which I believe for now, and he is actually using energy to make rotational kinetic energy disappear, that must lead to loss of energy in the isolated system.
For example if the potential energy of a spring is converted into the acceleration of a mass, energy is conserved. But if the potential energy of a spring is converted into making a mass decelerate (even that this is hard to imagine), energy is not conserved, because both the potential energy of the spring, and the kinetic energy of the mass who has been decelerated is lost from the system forever.
So, if my conclusion is right, performing this experiment again and again in a heat isolated room, would cause the temperature in the room to fall, because the total energy in the room would decrease.
By performing two experiments side by side any torsions on the earth would cancel out each other, so we do not need to include this in the total energy calculation of the isolated system.