Many engineering mechanisms contain rotating objects with unique designs that exhibit gyroscopic effects. These objects generate inertial forces and torques due to their rotating masses. The complex motions of these rotating objects, known as gyroscopic effects, result in the action of inertial torques. One such inertial torque was described by mathematician L. Euler, while other torques were predicted intuitively without analytical models. This chapter explains the physics behind the generation of inertial torques by the masses of a specific group of spinning objects with cylindrical geometry. The rotating masses of these objects produce centrifugal and Coriolis forces and torques, in addition to the known inertial torque. A new analytical method has been developed to formulate mathematical models for these inertial torques. This method allows for the derivation of expressions for the inertial torques generated by rotating objects with unique designs. The mathematical models for the inertial torques depend on the geometry of the rotating objects. Previous modelling of the thin ring was found to be inaccurate, so accepted assumptions were removed to obtain correct solutions for inertial torques. An example of this is presented by the annulus and torus (Appendix A), which provide accurate models for inertial torques, considering their small cross-sections as thin rings. The various designs of rotating objects present a challenge for researchers to derive mathematical models for their inertial torques, which give rise to gyroscopic effects.