It can be shown that whistler waves with low parallel phase velocity can be subject to strong cyclotron damping, even when the wave frequency is well below the cyclotron frequency. This resonance arises as a result of the Doppler effect which is proportional to the plasma density and increases the frequency experienced by electrons moving in the opposite direction to the wave. In this paper the dispersion relation of whistler waves in a cylindrically bounded plasma is obtained and then solved. This geometry is desirable for its relevance to experiment and also for comparison with theoretical results by other authors. In addition to cyclotron damping, Landau damping as well as electron-ion, electron-electron, and electron-neutral collisions are all included thus enabling the relative importance of these damping mechanisms to be evaluated. The dispersion relation that is obtained is used to explore the transition from Landau dominated damping to cyclotron dominated damping.