Take quantum vortices, which are basically whirlpools of angular momentum in materials like superconductors and superfluids, giving them strange properties.
It seems to be able to right itself by flipping in the air without pushing off anything first, which would contradict the law of conservation of angular momentum.
Now because black holes are defined by only three parameters: mass, charge and angular momentum, any other information about objects that fall into the black hole appears to be erased from the universe.
In order to conserve angular momentum, her angular velocity, the speed of her turn, has to increase, allowing the same amount of stored momentum to carry her through multiple turns.
We could do this by throwing objects with a small mass and a lot of charge or angular momentum, so that the charge or spin increases faster than the mass.
What if they used internal gyroscopes near their center of mass, harnessing angular momentum to orient the spacecraft, then applying bursts of thrust to accelerate!