The centripetal acceleration is the special form the acceleration has when an object is experiencing uniform circular motion. It is:

ac

=

v2 r

and is directed toward the center of the circle.

Newton's second law can then be written as:

ΣF

=

ma

=

m v2 r

I prefer NOT to use the phrase "centripetal force" because it makes you think there is a magical force that appears when an object is experiencing uniform circular motion. There is no such thing, and, in my opinion, you should never put a centripetal force on a free-body diagram.

When an object is experiencing uniform circular motion there is definitely a net force directed toward the center of the circle, but this force comes from one or more of the standard forces we've discussed already. Depending on the situation, it could be the force of gravity, the normal force, tension, friction, some combination of these, or even a combination of components of these.