Centripetal force

"Centripetal" describes a direction, not a mechanism — it simply means "toward the centre". Centripetal force is not a new fundamental force standing alongside gravity and tension; it is the name given to whatever net force happens to point toward the centre of a circular path, and identifying it is always a matter of asking what physical force is actually doing the pulling. Swing a ball on a string and the tension supplies it. Drive a car around a curve and friction between tyres and road supplies it. Keep a satellite in orbit and gravity supplies it. There is no additional force to draw on the diagram beyond whichever of these is actually present.

The outward-pushing "centrifugal force" that everyday language reaches for is the accounting error in the opposite direction: it is what a rotating, non-inertial observer feels compelled to invent to explain why they seem pressed outward, but from the stationary, inertial viewpoint that any correct force diagram uses, no such outward force exists. What a passenger in a turning car actually feels is their own inertia — their body's tendency to keep travelling in a straight line while the car turns underneath them — which is the absence of enough centripetal force on their body, not the presence of an outward one.

The required magnitude is F = mv²/r, and the exponent on v matters just as it did for kinetic energy: doubling speed around a fixed radius quadruples the force needed to hold the circular path, not doubles it, which is why cars lose grip on curves so much more suddenly at higher speed than the speed increase alone would suggest.