There are different designs for trommels, you definitely need to provide a sketch of your particular arrangement. For instance, there are trommels that just sit on tires or rollers, whilst others have a shaft running through the middle, with an electric motor in one end and several bearings along the shaft. They can be smaller than an oil drum and turned by hand, or as long as a couple of full sized containers. They also serve a multitude of applications, from mining to construction, or just trash segregation, which will affect the power required to drive the trommel.
You mentioned calculating a kinetic friction coefficient, but that is not something that is normally calculated, usually you either take a conservative number from a comprehensive tribology table, or you test your particular arrangement.