Centripetal force is like when you spin a bucket around on a string, the bucket pulls outward, just like satellites. The satellite is the bucket and the atmosphere is the string. Centripetal force is the force that is stopping the object form flying outward. 
On the Scrambled Egg Ride you begin to spin, slowly at first, then faster and faster.  It feels like you are being pushed outward by some force.  The force that you feel is inertia, which is trying to move you in a straight line.  Your body is trying to go in a straight line but is being held in position by the car you are riding in.