Unified Cranking-Model Description of Bohr and VMI Approache

A unified analysis based on the cranking model is presented, demonstrating that both the Bohr and Variable Moment of Inertia (VMI) models arise as limiting cases of this framework. This result resolves the apparent contradiction between the two models by showing that they correspond to different physical limits of the same formalism. In addition, this analysis explicitly reveals the contribution of Coriolis effects to the rotational energy and moment of inertia.