When we release a suspended object, we recover the potential energy due to gravity as the object travels back through the height raised. When we release an extended spring, we recover the potential energy as the object travels back through the distance stretched. But when we release a rotating object, how is the centrifugal potential energy recovered? I know that if we integrate the centrifugal force over the radius, we can numerically recover the potential, but I still feel as if I am missing something. Thank you for your time!