Pic from Nascar racingThe centripetal force is the net force acting towards the centre of the circle. Since it is the net force , then it must be contributed by some forces like tension, normal reaction, friction, weight etc. Most of the time it is a combination of these forces . A roller coaster has weight and normal reaction. A car has normal reaction and weight. A planetary body has gravitational force. The problems in circular motion are successfully solved only if the forces are identified correctly and aknowledging that the resultant force is towards the centre of the circle. The acceleration a is v2/r and is related to period using v=rw. In gravitation , there is a simplified scenario due to the existence of only gravitational force around a massive body , the gravitational field strength is the centripetal acceleration. Therefore equating g = GM/(r2) = (v2)/r or (w2) r enable you to calculate period and velocity of the satellite circulating the massive body M.
