I think that Captain Renault didn't arrest Rick because he trusts Rick and what Rick is doing. He thinks Rick is a smart person and that his judgement is good. I also think he didn't arrest Rick because he is loyal. The film shows many different competing and conflicting motivations in the characters.
The different types of energy include thermal energy, radiant energy, chemical energy, nuclear energy, electrical energy, motion energy, sound energy, elastic energy and gravitational energy.
