What I found most interesting is how my cycling habits changed over my two weeks with the eBike, mostly for the better. In most states, cyclists need to come to a complete stop at stop signs... and as anyone who has ever ridden a bike or shared a road with a cyclist knows, most cyclists generally do an Idaho Stop if they believe it's safe. I do it, too. Knowing that I could quickly get back up to speed with the aid of the electric motor, I found myself more willing to sacrifice my forward momentum and come to a complete stop when there was a car approaching an intersection.
The Ohio Revised Code 4511.01  distinguishes motorized bicycles and mopeds from motorcycles or scooters by describing them as "...any vehicle having either two tandem wheels or one wheel in the front and two wheels in the rear, that is capable of being pedaled and is equipped with a helper motor of not more than fifty cubic centimeters piston displacement that produces no more than one brake horsepower and is capable of propelling the vehicle at a speed of no greater than twenty miles per hour on a level surface." One brake horsepower converts to 0.75 kW, or (rounded) 750W. Thus, a bicycle with an electric helper motor operating under 750W, and not propelling the bicycle over 20 mph, does not qualify to be registered under Ohio state law. Local jurisdictions may have other regulations.
A local unit of government having jurisdiction over a road or bikeway (including the Department of Natural Resources in the case of state bike trails) is authorized to restrict e-bike use if: the use is not consistent with the safety or general welfare of others; or the restriction is necessary to meet the terms of any legal agreements concerning the land on which a bikeway has been established.