I’ve come across this website of a self-appointed researcher who claims that the law of preservation of angular momentum is wrong. He penned a large number of (poorly written) papers (and published them on his website, together with the rejection letters from the journals to which he submitted them) presenting his views. In a nutshell, they all boil down to the following arguments (at least that’s how I understand them; I’m paraphrasing here):

In the classic ball-on-a-string experiment that is used in high schools to illustrate angular momentum (ball rotates on a string, then the length of the string and thereby the radius of rotation is reduced, which accelerates the angular velocity of the ball), accepted physics say that angular velocity is inversely proportional to the square of the radius. So if you start with a given radius and a rotation of (his example) two revolutions per second, and then reduce the radius to a tenth of the initial radius, then the ball should now rotate at two hundred revolutions per second, or 12,000 revolutions per minute, which is more than what one observes in these experiments. Additionally, he appears to be making a conservation of energy argument: When the ball is now going at 200 rather than 2 revolutions per second, with a radius (and hence perimeter) of its circular orbit now a tenth of what it was before, then the non-angular velocity (in metres per second) has increased by a factor of ten. That means kinetic energy (E = 0.5mv²) also increases, violating the law of conservation of energy.

Surely this guy is wrong somewhere, but I can’t spot where exactly, and I’d love to know why - not for online debating purposes but out of a layman’s curiosity.