Non-slipping domains of a pulled spool

Abstract

We have investigated the pulled spool by considering pulling angles up to . Our focus was on downward pulling forces with pulling angles in the range of to . In this range we have found a domain of pulling angles where the spool never starts to slip independent of the strength of the pulling force. The size of the domain depends on the static friction coefficient and on the moment of inertia of the spool. The non-slipping domain is mainly formed around the critical angle where the static friction force becomes zero. For low static friction the non-slipping domain decays into two different domains. We have determined the limiting angles of the non-slipping domains and explored the transitions from a single domain to two separated domains in parameter space.