Hi,
Whether it is, or is not, the Law, why wouldn't you wear one? Don't you like yourself? VA state law is indefinite regarding Helmet use, but that doesn't mean it's a good idea to ride without one.
So far as the definition of a Moped, the attached link shows how the state defines one -
http://leg1.state.va.us/cgi-bin/legp504.exe?000+cod+46.2-100 In it, it states that
"Moped" means every vehicle that travels on not more than three wheels in contact with the ground that has (i) a seat that is no less than 24 inches in height, measured from the middle of the seat perpendicular to the ground and (ii) a gasoline, electric, or hybrid motor that displaces less than 50 cubic centimeters. For purposes of Chapter 8 (ยง 46.2-800 et seq.) of this title, a moped shall be a vehicle while operated on a highway.
As it is a
vehicle when operated on State Highways, the state may take the view that a Helmet is required, or it may not. It's ambiguous meaning that a cop could possibly cite you and you'd have to defend your action in court, or they may not. But, again, I have to go back to it's definitely the smart thing to do...
Happy Motoring!... Jim