Centripetal, as the name suggests, means towards center. Centripetal force refers to a force that causes a body to move in circular motion. In comparison, centrifugal force tries to push a body away from the circular motion. Hence, the centripetal force acts towards the center, although the centrifugal force acts away from the center.
According to Newton's second law of motion, the force acting on a body can be written as the product of its mass and acceleration. Hence, the centripetal force provides an acceleration (towards the center) to a body and this acceleration is known as the centripetal acceleration.
Centripetal acceleration can be written in terms of the radius of the circle, r and the angular velocity, w as:
`a = w^2r`
Hence, the centripetal force can be written as
`F = ma = mw^2r`
Hope this helps.