Changing the collision detection from continuous dynamic to discrete worked. Alternatively not rotating the object also made the problem go away. Explanation by @Dracorat as to the *why* of the problem:
"Continuous dynamic attempts to alter a RigidBody's position if it's intersecting with another. Since the usual alter direction would be invalid, it is struggling with it. It's also a very expensive algorithm. You'd use it only if you believe an object is moving so fast that it might pass completely through something in between frames."
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