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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.

https://www.youtube.com/watch?v=Mcy4fVLHumI&t=1423s

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.

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closed as off-topic by Sean E. Lake, Mike, Jon Custer, Alfred Centauri, niels nielsen Jan 23 '18 at 8:08

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The expectation for the results of this experiment depends (surprisingly sensitively) on the distribution of mass in the victim's presentor's body, and on the precision with which they align their own center of mass over the axle (Even being a centimeter off alignment adds something like $0.7 \,\mathrm{kg\,m/s}$ to the total moment of inertia of the system assuming a $70\,\mathrm{kg}$ person (because of the parallel axis theorem, right)). And it matters if you can hold your center of mass in the same place as they run the experiment; and that is hard.

The results you've calculated are pretty good for a live-action classroom demonstration.

If you want to the system to a precise test you're going to need much better knowledge of the moments of inertia involved. In principle you could build a machine for doing this in a classroom environment, but you'll still have to deal with the friction of the bearing (which exerts a torque on the system meaning that we don't expect perfect conservation of angular momentum).

Instead I would ask the designers of spin-stablized satellites that unfold after reaching orbit (a very common design) how well their machines agree with the conservation of angular momentum.

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You should experiment with a centrifugal governor. Using it in reverse of its normal mode of operation, by pulling the central spindle up and down. This would give you a much more controlled experiment as the moment of inertia is then precisely known. The remaining source of uncertainty is the angular speed of course. I did this experiment at university many years ago, and here is what we did.

  • First, we had to make sure that we could move the spindle up and down without slowing it down. We used a small disk with a dimple into which the spindle went and made sure it was all well oiled. Then moving the disk up and down moved the spindle without introducing any extra friction.
  • Then one had to measure the angular speed accurately. We used a stroboscopic device.

Eventually, we confirmed conservation of momentum to within a couple of percents.

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This is a classroom demonstration, not a rigorous experiment. Hence there's a discrepancy. To echo dmckee's answer, the distribution of mass here is a person's body, and human bodies are not rigid bodies. You cannot get precise results for non-rigid bodies without some very complex calculations.

As another illustration for why non-rigid bodies are not good for simple experiments - if you run into a wall at 5 m/s, energy conservation predicts that you would bounce off the wall at 5 m/s. However you are far more likely to collapse in a heap in front of the wall. Does that mean energy conservation doesn't hold either? No, because if you threw a ball at the wall at 5 m/s instead you will indeed see it bounce back at 5 m/s.

If you want to disprove conservation of angular momentum you'll have to do more careful experiments. You'll have to do it multiple times. You can't just do it once, take a video of it and then measure "time" by watching that video multiple times - you need to actually repeat the experiment. It can be done. First year physics undergraduates do similar experiments as part of their curricula.

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