PARADOXES WITH SPINNING WATER
Archimedes discovered his famous law: the buoyancy force exerted by water upon a submerged body equals the weight of the water displaced by the body1
In a rotating world, such as Earth, Archmedes' buoyancy law acquires a twist (no pun intended), with some surprising manifestations. One such surprise is the paradox of the floating cork described next. Another is the iceberg paradox (p. 25).
The experiment. An amusement park with a spinning swimming pool would be a dream of any child, even one
1 The following thought experiment explains why this law is true. I want to explain why a bowling ball lying on the bottom of the pool feels the buoyancy force equal to the weight of water that this ball displaces. As a thought experiment, imagine replacing the ball with the same shaped water ball. This water ball will hang still, since the water is assumed to be still in the pool. We conclude that the gravity exactly cancels the buoyancy for the water ball. So for the water ball at least, the buoyancy equals the weight of water. But the buoyancy force depends only on the shape, and thus is the same for the bowling ball. This proves Archimedes' law. In short, Archimedes' law boils down to two things: (1) still water stays still if undisturbed, and (2) the buoyancy force upon a body depends only on the body's shape, but not the material it's made of.