This will vary from state to state, but in MA anyone who holds a class D (i.e. standard consumer vehicle) license is also allowed to ride any moped that's 49cc or below. I think there's now a yearly registration fee[1] that the owner must pay. So, for example, if I have a moped in good standing with the state, anyone with a valid drivers license is allowed to borrow it and legally ride it[2].

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[1] I want to say I paid something like ~30 USD, but this was ~10 years ago. Unlike a standard vehicle, however, there is no inspection check pre-requisite for safety nor emissions. I think the fee is purely for tags. Helmets are definitely a requirement though.

[2] AFAIK there are no additional insurance requirements though. There weren't any ~10 year ago when I one, but I can't remember if that's because my comprehensive car insurance did double-duty in the event were I to, say, hit a pedestrian in a crosswalk and they were to sustain damage.

These are motorised 'foot propelled' scooters, not small scale motorbikes. I don't know if these (and electric skateboards) are properly covered by UK law.