When did it become mandatory to wear hard shell football helmets?

1920s and 1930s,

Explanation:

it's worth reiterating that helmets were not mandatory. That wouldn't happen until 1943. During the 1920s and 1930s, variations of the leather helmet appeared, but in 1939, the game changed –or at least became safer– when John T. Riddel introduced the first plastic helmet

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football or basketball players.