Purpose <p>In the present work, the transient rotordynamic response of a tapered composite shaft-disk system while passing through the critical speed is studied.</p> Design/methodology/approach <p>The transverse shear deformation effects and gyroscopic effects are included in the formulation using the Timoshenko beam theory. The expressions for potential and kinetic energies of the system are derived, and the equations of motion are obtained using Hamilton's principle. Solutions to these equations are computed using the finite element method with combined Lagrange-Hermite interpolation functions along with the direct time integration method.</p> Findings <p>A comprehensive parametric study is conducted to examine the effects of system parameters on the behavior of a tapered composite shaft-disk system operating under constant angular acceleration. Additionally, the study examines the effects of material property coupling and fiber orientation on the response of the system. It is demonstrated that compared to uniform composite shafts, a tapered composite shaft exhibits higher critical speeds and lower vibration amplitudes while passing through the first critical speed. It is also shown that the composite shaft-disk system has significantly lower vibration amplitudes across all operating speeds, leading to smoother system operation.</p> Originality/value <p>The study highlights the benefits of using tapered composite shafts over uniform ones, emphasizing improvements in critical speed and reduction in vibration amplitudes, which are crucial for the reliable and efficient operation of rotating composite structures.</p>