Answer:
Because he knows that if he tries to go after Frodo and Sam, the other two hobbits will be tortured and killed, and he refuses to countenance that: 'Our choice then,' said Gimli, 'is either to take the remaining boat and follow Frodo, or else to follow the Orcs on foot.
Answer:
Aragorn chose not to follow because he had heard from Boromir himself how it had affected him, and probably felt the Ring was better with no outside influence.