Centrifugal force pushes something outward, what force is there similar but pushing inward?
Sometimes (and in fact usually) there is. Answering this question will require explaining first what centrifugal force is which requires explaining both centripetal force and pseudoforces. First, let’s talk about pseudoforces. When a reference frame accelerates, objects in that frame (which tend not to accelerate in an inertial frame per Newton’s first law) experience an acceleration that is equal to and opposite in direction to the acceleration of the frame. For example, when you brake your car, you pitch forward. When you hit the gas, you are pushed back. And when you turn right or left, the kids playing sardines in the back seat get thrown the other way. This last example with the kids is an example of centrifugal force. When an object moves in a circle, it has to always be accelerating inward. For an object in orbit, this acceleration is caused by gravity pulling in. For a roller coaster in a loop, this is caused by the track pulling in. This is called a CENTRIPETAL force. So… if
