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I'm not a car guy, and I don't know about the differentials, but don't continuously variable transmissions allow for this? I'm guessing they're not in common use on race cars, but in principle, shouldn't they allow for a 3.01 ratio?

Yes, a CVT uses a steel belt around two cones, and can have any ratio between them.

Most race cars use mechanical transmissions with automatic controls as that's the most robust design. Some stunt vehicles use automatics or CVT as landing with the wheels at different speeds than the vehicle causes a massive shock through the drivetrain. In a manual that shock goes right to the engine, in automatics there is usually some amount of absorption of rotational shocks due to the less rigid coupling.

Diffs are almost always a ring and pinion gear.

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