Ithaslongbeenrecognizedthattherotationofsingleparticlesplaysaveryimportantroleinsimulationsofgranularflowusingthediscreteelementmethod(DEM).ManyresearchershavealsopointedoutthattheeffectofrollingresistanceatthecontactpointsshouldbetakenintoaccountinDEMsimulations.However,evenforthesimplestcaseinvolvingtwo-dimensionalcircularparticles,thereisnoagreementonthebestwaytodefinerollingandsliding,anddifferentdefinitionsandcalculationsofrollingandslidinghavebeenproposed.Ithasevenbeensuggestedthatauniquerollingandslidingdefinitionisnotpossible.Inthispaperweassessresultsfrompreviousstudiesonrollingandslidingindiscreteelementmodelsandfindthatsomeresearchershaveoverlookedtheeffectofparticlesofdifferentsizes.Afterconsideringtheparticleradiusinthederivationofrollingvelocity,allresultsreachthesameoutcome:auniquesolution.Wealsopresentaclearandsimplederivationandvalidateourresultusingcasesofrolling.Suchadecompositionofrelativemotionisobjective,orindependentofthereferenceframeinwhichtherelativemotionismeasured.
