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JoshuaZ comments on Harry Potter and the Methods of Rationality discussion thread, part 5 - Less Wrong
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It seems that they might act in a hybrid Aristotelian/Newtonian manner. Certainly in canon they talk about broomsticks having maximum speed not maximum acceleration. And people have trouble pulling from being near to hitting the ground, something which sort of makes sense in an Aristotelian framework because objects want to go to the ground.
Outside canon, the movement of the broomsticks in the movies does seem to be a definite mix but this is likely more due to standard movie physics than anything else.
I remembered the top speed from the whole Firebolt/Nimbus sequence of events, but I don't regard that as even weak evidence for Aristotelian mechanics.
Wind resistance/drag means that there's a 'terminal velocity' even in free fall; change of acceleration simply changes a broomstick+wizard's terminal velocity upwards, doesn't remove it at all.
(Another example: my car operates according to Newtonian mechanics in the real world - but still has a top speed, which is why I'm not setting land-speed records on Nevadan salt flats in my spare time.)
But the terminal velocity should then be a function of the cross-section of the person on the broomstick. Instead the brooms themselves have maximal velocities.
I don't think Quidditch players vary all that much in cross-section. As well demand that auto manufacturers list their speeds as a function of how clean the car exterior is, how inflated the tires, what weight is being borne, the altitude, etc.
EDIT: OK, after looking at the descriptions on the Harry Potter Wikia, I've changed my mind. The Seeker article specifically characterizes seekers as small and lightweight and the fastest players on the team. Which, fortunately for my self-esteem, is consistent with my position that canon uses Newtonian mechanics.
Broomsticks have very tiny cross-section, so cross-section due to the person will be the majority of the air resistance. The difference in size between say Harry Potter and some of the big Slytherin Beaters should matter a lot.
Newtonian brooms are supported by canon then even more, aren't they?
Most Beaters are large and burly, and all the Seekers (with their premium on top speed) are the opposite. Exactly as expected with Newtonian brooms (or horses).
But if air resistance didn't matter because brooms move at a fixed velocity/acceleration in an Aristotelian manner, one would expect Seekers to have normally distributed body sizes as Quidditch team captains select for things like piercing eyesight, lightning reflexes, or just simian arms.
(Harry & Draco are both relatively small and thin; Viktor Krum is tall, but also 'thin'.)
Yes, that supports Newtonian broomsticks quite strongly.
It makes sense by postulating that a broomstick always goes where it's pointed (no Newtonian momentum), but there is a maximum angular speed for turning the broomstick. The rider applies force to turn the broomstick, which means there's resistance, so it's not difficult to assume that the resistance creates an effective maximum angular speed.
This doesn't sum up to Newton, of course, because this maximum angular speed isn't dependent on current linear speed.