In my humble opinion, this is the best demonstration the world has of conservation of angular momentum. Unfortunately it does not demonstrate what it claims to.
If we take measurements of the esteemed professor's turntable demonstration, one rotation at the extended arms position and another of the contracted arms position and compare the actual results to his predicted results, we find a discrepancy.
I measured the extended rotation between 24:35 and 24:39. Timing it from the point where the weight crosses his shoulder. I took three measurements using a stopwatch. The results are as follows: 3.58 3.59 3.58
I also measured the contracted rotation between 24:52 and 24:54 using the point where the weights line up. Taking more measurements because of the variation in results. 1.66 1.69 1.79 1.69 1.78 1.71 1.73
This gives us the following result: Extended position: 3.6+-0.2 seconds per rotation. Contracted position: 1.7+-0.2 seconds per rotation. According to his own calculations the expected result from his contracted position based on the measurements for the extended position should be 1.2+-0.1
This is a discrepancy of 0.5+-0.3
About thirty percent slower than predicted by professor Lewin.
That is the best, but any of the demonstrations you measure produce similar results. The larger the change in magnitude of radius, the exponentially larger the discrepancy.