Notwithstanding any other provisions of law, local authorities of any city which is on a natural island with an area in excess of 20,000 acres and which is within a county having a population in excess of 4,000,000, may, if they determine such rules and regulations to be necessary in view of the special problem existing thereon with respect to the size and nature of the streets of the city and with respect to the characteristics and nature of the city itself, adopt rules and regulations by ordinance or resolution on the following matters:
(a)
Regulating the size of vehicles used on streets under their jurisdiction.
(b)
Regulating the number of vehicles permitted on streets under their jurisdiction.
(c)
Prohibiting the operation, on streets under their jurisdiction, of designated classes of vehicles.
(d)
Establishing noise limits, which are different from those prescribed by this code, for vehicles operated on streets under their jurisdiction and prohibiting the operation of vehicles which exceed such limits.
(e)
Establishing a maximum speed limit lower than that which the local authority otherwise permitted by this code to establish.
This section shall not apply to vehicles of utilities which are under the jurisdiction of the Public Utilities Commission while engaged in maintenance and construction type service work.