Given how much hatred there is between Shiites and Sunnis, this could well qualify for a basic physics problem in Shiite science textbooks. Or maybe our Cartman dude from South Park will be delighted to hear a lecture on the cold science of hanging by Ms. Garrison.
It is actually quite easy to explain why Barzan was decapitated while hanging and there is no need to invoke some "divine act" theory as Basam Ridha, the spokesman for Iraqi Prime Minister Nuri al-Maliki's office did. My guess is that the hangman didn't take the Official Table of Drops seriously.
John F Burns from New York Times reports that Barzan was dropped about 8 feet (or 2.43 metres) while his hanging. (Btw, according to the drop table, in modern times, a person weighing 51 kgs is given a 8 feet long drop hanging. I find it hard to believe Barzan was only around 51 kg to be given this much drop ). That means, his velocity just before his neck snapped was about 7m/s ( = sqrt(2gh) ). The science of hanging tells us that the amount of force required to snap the neck is about 4,400 Newtons. So, its safe to assume that Barzan probably felt a force of about 5,000 N. Witnesses from the execution chamber claim that just as Barzan was falling, they heard a snap and saw the noose rope fly up "instantaneously". So , lets assume that he was decapitated very quickly and took place in about 1/10 sec. Therefore, the impulse on Barzan was about 5000/10 = 500 N-sec. This impulse is the change in momentum because of the snap. Lets assume that right after the snap, his body velocity decreased to about 1/10th of what it was before the snap, i.e., to about 0.7m/s. That means, if his mass was M, his change in momentum was about 6.3M Newton-sec. This is also equal to 500 Newton-sec. So a reasonably good and crude estimate for his body mass is about 80 kg ( even though lots of assumptions were made in the calculation ) !
In any case, I would argue that Barzan probably has the most painless execution amongst the three who were hanged recently in Iraq even though decapitation "looks" more cruel.
Isn't science cool ? Many times, it definitely is very cold. If you think this calculation is in bad taste, you probably need to face reality and think the same about lots of other stuff including the death penalty.