Music

Rudiments

Source: Wikipedia

Roll

Rolls are notated as tremolos, with slashes through the note stem. Each slash indicates dividing the note in two.

And for longer notes

or

More info available in the notation guide. Also, there is a difference in how the rolls are played depending on the tie between the notes:

head other  
is played as
is played as

in terms of the roll length (not the number of notes comprising the roll itself).

Videos: buzz roll (link).

One useful method, but perhaps a bit draconian, to learn playing rolls is the one employed by Art Blakey:

Blakey also received some instruction from Chick Webb, who once sat Blakey down with a snare drum and a metronome, set the metronome to a very slow tempo, and told Art to roll for a hundred beats. “And if you stop, I’ll break your skull,” Webb said. “He was a disciplinarian,” Blakey said.

Art Blakey hall-of-fame page on PAS.