Horizontal Circles

A net force toward the centre keeps an object on its circle:

$$F_{\text{net}} = \frac{m v^2}{r}$$

It is not a new force: a tension, a friction or a normal force does the job.

A puck on a string: $\relax T = mv^2/r$.

Seen from above: the string tension is the force toward the centre.

A car on a flat curve: $\relax f_s = mv^2/r$, up to the friction limit.