The Law In San Diego, California?

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(b) All of the following apply to a motorized bicycle described in subdivision (b) of Section 406:

(1) No person shall operate a motorized bicycle unless the person is wearing a properly fitted and fastened bicycle helmet that meets the standards described in Section 21212.

(2) A person operating a motorized bicycle is subject to Sections 21200 and 21200.5.

(3) A person operating a motorized bicycle is not subject to the provisions of this code relating to financial responsibility, driver's licenses, registration, and license plate requirements, and a motorized bicycle is not a motor vehicle.

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That is fine if you are riding an 1000w electric bike. Gas bikes fall under subdivision (a) of Section 406.
 
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