Fig 13Going round a curvealways toward the centrea = v² / r
Anything moving in a circle is accelerating, even at constant speed, because its direction keeps changing. That needs a net force pointing at the centre: F = m·v²/r. It isn't a new kind of force. Something has to supply it: tyre friction for a car, tension for a ball on a string, gravity for the Moon. For a car on a flat curve, friction can provide at most μ·m·g, so the top speed is v = √(μ·g·r). Double the speed and you need four times the grip.