The problem of bending vibration of a rotating beam is a nonlinear one when the vibration takes place in a plane not perpendicular to the plane of rotation. The nonlinear term arises from the Coriolis acceleration. From the nonlinear equation established, it is found that the existence of periodic solutions depends on the initial conditions, and the most important parameter which affects the periodic solutions is the nondimensional amplitude Ā. The percentage error in the frequency of vibration due to neglect of the Coriolis acceleration is a function of the parameter Ā only. For most of the present-day applications the error is negligible.