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On a banked corner, the reaction to the car's weight (blue arrows) is doing part of the work of holding the car in the corner. Add the varying amounts of friction (red arrows) provided from each tire at the limits of traction, and the total lateral forces (green arrow) pushing the car into the turn will increase with the banking angle. In order for the centrifugal force pushing the car out of the turn to now be equal to the forces pushing the car into the turn, you'd have to go around the bank faster (for the nit-picking physics nerds out there, this obviously isn't a proper free body diagram).
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