There could be many reasons that he cut his hair, but the main reason is that he phased into a werewolf for the first time, therefore he is now part of the Quiluete pack. You may notice, all the werewolves are made to cut their hair to a certain length and also get a tattoo on their arm.
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he cuts it in new moon as soon as he joins the wolf pack.=xxx=
Jacob cuts his hair in New Moon after becoming a werewolf. The shapeshifters all keep their hair short bacause as a wolf, it makes them shaggy, which many find is uncomfortable. Jave eventually grows his hair out again in Eclipse, and when asked by Bella why he is doing so, he blames his crush on her and tells her that she thought she liked him better w/longer hair.
no
Jaacob tells charlie hes a werewolf in breaking dawn.
she chose him in new moon, but in eclipse the status between Jacob and Bella changes. he realizes that he REALLY loves her and near the end, Bella realizes she loves Jacob so it was a hard decision.