In the previous chapter, we considered rotor-bearing systems for a single-mass rotor with different levels of complexity in restoring and dissipating forces of supports. We analyzed the rotor system for the transverse (bending) translatory and rotary motions by considering the respective inertias. However, we ignored an important dynamic behavior of the rotor system, the gyroscopic effect, which especially predominates in high-speed heavy rotors. In the present chapter, we shall still be dealing with a single-mass (in the form of thin disc or long cylinder) rotor system with a slender massless shaft and will come back to the assumption of rigid bearings in transverse directions unless otherwise stated. However, now we shall include the effect of gyroscopic effects and will explore the motion of the rotor for the synchronous as well as the asynchronous whirl. For the present case, we shall analyze the rotor system using two different approaches: first the quasi-static analysis (which gives better physical insight into the effect of gyroscopic effects; however, it can be applied ideally to simple systems only), and second the dynamic analysis (which can be easily extended to multi-DOF systems). An important aspect, which we will observe from the present chapter, is that because of the gyroscopic effect, the whirl natural frequency is dependent on the rotor spin speed. Another interesting phenomenon that can be observed is that the rotor can have forward and backward whirling motions and the splitting of whirl frequencies takes place. Moreover, for the present case the distinction between the rotor spin speed, the whirl natural frequency, and the critical speed will be made clearer through a Campbell diagram (Campbell, 1924).