Why do some drums (e.g. timpani, rototom) have a distinct pitch, while others do not? What is the physical difference that results in a distinct pitch or lack thereof?
It's a much simpler job to tune a drum which has one head. Timps are such. One head will produce one pitch (plus the complex overtones) when it's stretched regularly. When it's uneven, it'll try to produce several different pitches, resulting in a bit of a mess. Rototoms are similar, with just the one head. I don't think they'd do the job with two.
The majority of drums with two skins/heads are not impossible to tune so that they produce a pitch, but for that to be successful, both heads need to be in tune, which is often not what happens on a standard drumkit, for instance. It's bad enough getting the beater head regulated, without then repeating the operation on the other.