For example, when we turn in a bike, we have to bend slightly inward for the centripetal force. However, considering there’s no concept of “ground” underwater, do submarines still have to bend inwards? If yes, is it for the same reason as bikes?
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On the assumption that you mean “lean in” by “bend”, then a submarine doesn’t have to. They can just turn flat, like a car, by turning the rudders at the back.
Bikes have only one way to apply continuous force, their tire contact patch. You have to tilt this to get your normal force from the ground to push you around the turn. This is roughly analagous to why airplanes roll to turn (they’re using lift, not ground normal force, but they still have to tilt it). You can turn an airplane with just rudder but it’s ugly.
Submarines, on the other hand, aren’t going particularly fast and can generate *huge* control forces because water is dense. So they can just turn with their rudder and call it good. In principle, they have all the controls needed to do a rolled turn, like an airplane, but they don’t need to.
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