To alternate turns at a one player video game, such as tetris, or asteriods. The phrase is a reference to the act of passing the controller, or "rock" between people.
"Pass the Rock" meaning pass the ball but using another word for the ball. There is a ball brand called the Rock and people commonly say this when they want you to pass the ball to them.
A sunburn or suntan focused on the left arm. It is caused by the left side of the body being the only half that gets exposed to sunlight while driving. Presumably, it would be located on the right side of the body in countries where they drive on the left side of the road.
British slang for a scientist or technical expert, esp . when the speaker is not certain of the expert’s specific field of study. Not necessarily derogatory, but typically used by persons without a technical background. In the US, the equivalent would be “egghead”, “squint”, or “geek.”
Origin of the word is unknown. Started sometime in World War 2. Given the typical evolution of British slang, could easily have started because what these experts did was confusing or “baffling” to the common person.