Circular motion requires an inward acceleration. Newton's second law therefore requires the net radial component of the real forces to point inward with magnitude

$$\sum F_r=m\frac{v^2}{r}$$

for uniform circular motion, where the radial positive direction is chosen toward the center.

This relation does not introduce a new physical interaction called a centripetal force. Tension, friction, gravity, normal force, or a combination of forces can supply the required inward net force. “Centripetal” describes the role of the net radial force, not its physical origin.

Example: a car on a flat curve

A car travels around a level circular curve of radius $r$. Vertically, the normal force balances its weight. Horizontally, static friction between the tires and road can provide the inward force required for the circular acceleration:

$$f_s=m\frac{v^2}{r}.$$

The important point here is not a separate “centripetal force”: the horizontal contact force is the real interaction producing the radial acceleration. Whether the available friction is large enough to prevent sliding is a separate contact-friction question.

Example: a mass on a string in a vertical circle

The required inward net force remains $mv^2/r$, but the real forces contributing to it change around the path.

At the bottom of the circle, inward is upward, so

$$T-mg=m\frac{v^2}{r}.$$

At the top, inward is downward and both tension and gravity point toward the center:

$$T+mg=m\frac{v^2}{r}.$$

The tension can therefore vary around the path even when the speed is the same.

A reliable procedure

1. Draw only the real forces acting on the object.
2. Choose the inward radial direction.
3. Resolve the real forces along that direction.
4. Apply $$\sum F_r=m\frac{v^2}{r}.$$

A centrifugal force should not be added when solving the problem in an inertial frame. Centrifugal force is an inertial-force concept used when describing motion from a rotating reference frame.