The analysis of rotating instabilities has been primarily driven by modal (eigenvalue) analysis for many decades. However, recent advancements in non-modal (energy amplification) stability analysis have opened up a new technique of stability of fluid flow. This approach enables a quantitative description of the short-term behavior of disturbances, providing a clear perspective on the subject. We illustrate the application of non-modal stability analysis techniques, employing tools such as the energy norm and singular value decomposition (SVD). This work provides a concise introduction to linear stability theory, with an emphasis on non-modal effects. Our investigation, utilizing the numerical range of the Orr–Sommerfeld and Squire operators via the energy norm, reveals that rotation induces both energy growth and instability at low Reynolds numbers. This phenomenon was rigorously traced using our computational code, which employs non-modal approaches. By analyzing the maximum energy amplification curve, we demonstrate the influence of Reynolds number (Re) and rotation number (Ro) on the transient energy of disturbances. Additionally, we conducted a parametric study to determine the critical values of wave numbers by examining the maximum energy amplification curve.