In Washington State, a private road is just that: a road on private property, as opposed to a road on a public right-of way. Sometimes these roads have speed-limit signs. Does ignoring one of these signs carry any penalty besides being asked to leave the property and never return?
RCW 46.61.419 gives government police the right to enforce speeding violations as defined in RCW 46.61.400 in certain communities (condominiums and gated communities), per RCM 64.34, 64.32, or 64.38, if:
(1) A majority of the homeowner's association's, association of apartment owners', or condominium association's board of directors votes to authorize the issuance of speeding infractions on its private roads, and declares a speed limit not lower than twenty miles per hour;
(2) A written agreement regarding the speeding enforcement is signed by the homeowner's association, association of apartment owners, or condominium association president and the chief law enforcement official of the city or county within whose jurisdiction the private road is located;
(3) The homeowner's association, association of apartment owners, or condominium association has provided written notice to all of the homeowners, apartment owners, or unit owners describing the new authority to issue speeding infractions; and
(4) Signs have been posted declaring the speed limit at all vehicle entrances to the community.
Thus there can be a speeding ticket. However, if you speed on my uncle's farm, that's just trespassing because that isn't one of the specified community types. The law only allows speeding enforcement by government law enforcement officers (not private security), and limits how low the maximum speed can be set. This raises an interesting question regarding speed enforcement on the Boeing bridge off S 104th in Seattle, which is private property and not part of a "community", yet quite urban and frequently used.